{"id":33461,"date":"2022-04-04T13:02:03","date_gmt":"2022-04-04T07:32:03","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=33461"},"modified":"2022-04-07T11:11:58","modified_gmt":"2022-04-07T05:41:58","slug":"big-ideas-math-geometry-answers-chapter-1","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-geometry-answers-chapter-1\/","title":{"rendered":"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry"},"content":{"rendered":"<p>Looking across the web for a friendly site that caters to all your needs regarding the Big Ideas Math Geometry Concepts? Don&#8217;t worry we are with you in this and we will provide you the Complete <a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-geometry-answers\/\">Big Ideas Math Geometry Answers<\/a> Chapter 1 Basics of Geometry. All the Solutions covered in the BIM Geometry Ch 1 Basics of Geometry Answer Key are as per the latest Common Core State Standards guidelines. Practice using the BigIdeas Math Chapter 1 Solutions via quick links available and clear the exams with flying colors.<\/p>\n<h2>Big Ideas Math Book Geometry Answer Key Chapter 1 Basics of Geometry<\/h2>\n<p>Access the Big Ideas Math Geometry Ch 1 Answers for all the topics and prepare accordingly. Find complete assistance on Geometry Chapter 1 including questions from Lessons 1.1-1.6, Performance Tests, Review Tests, Cumulative Practice, Assessment Tests, etc. All you have to do is simply tap on the quick links available and clear your ambiguities in no time. To make it easy for you we have compiled the BIM Geometry Chapter 1 Basics of Geometry Textbook Solutions aligned as per the BIM Textbooks.<\/p>\n<ul>\n<li><a href=\"#Basics_of_Geometry_Maintaining_Mathematical_Proficiency\">Basics of Geometry Maintaining Mathematical Proficiency &#8211; Page 1<\/a><\/li>\n<li><a href=\"#Basics_of_Geometry_Mathematical_Practices\">Basics of Geometry Mathematical Practices &#8211; Page 2<\/a><\/li>\n<li><a href=\"#1.1_Points,_Lines,_and_Planes\">1.1 Points, Lines, and Planes &#8211; Page(3-10)<\/a><\/li>\n<li><a href=\"#Lesson_1.1_Points,_Lines,_and_Planes\">Lesson 1.1 Points, Lines, and Planes &#8211; Page(4-7)<\/a><\/li>\n<li><a href=\"#Exercise_1.1_Points,_Lines,_and_Planes\">Exercise 1.1 Points, Lines, and Planes &#8211; Page(8-10)<\/a><\/li>\n<li><a href=\"#1.2_Measuring_and_Constructing_Segments\">1.2 Measuring and Constructing Segments &#8211; Page(11-18)<\/a><\/li>\n<li><a href=\"#Lesson_1.2_Measuring_and_Constructing_Segments\">Lesson 1.2 Measuring and Constructing Segments &#8211; Page(12-15)<\/a><\/li>\n<li><a href=\"#Exercise_1.2_Measuring_and_Constructing_Segments\">Exercise 1.2 Measuring and Constructing Segments &#8211; Page(16-18)<\/a><\/li>\n<li><a href=\"#1.3_Using_Midpoint_and_Distance_Formulas\">1.3 Using Midpoint and Distance Formulas &#8211; Page(19-26)<\/a><\/li>\n<li><a href=\"#Lesson_1.3_Using_Midpoint_and_Distance_Formulas\">Lesson 1.3 Using Midpoint and Distance Formulas &#8211; Page(20-23)<\/a><\/li>\n<li><a href=\"#Exercise_1.3_Using_Midpoint_and_Distance_Formulas\">Exercise 1.3 Using Midpoint and Distance Formulas -Page(24-26)<\/a><\/li>\n<li><a href=\"#Study_Skills:_Keeping_Your_Mind_Focused\">Study Skills: Keeping Your Mind Focused &#8211; Page 27<\/a><\/li>\n<li><a href=\"#1.1_-_1.3_Quiz\">1.1 &#8211; 1.3 Quiz &#8211; Page 28<\/a><\/li>\n<li><a href=\"#1.4_Perimeter_and_Area_in_the_Coordinate_Plane\">1.4 Perimeter and Area in the Coordinate Plane &#8211; Page(28-36)<\/a><\/li>\n<li><a href=\"#Lesson_1.4_Perimeter_and_Area_in_the_Coordinate_Plane\">Lesson 1.4 Perimeter and Area in the Coordinate Plane &#8211; Page(30-33)<\/a><\/li>\n<li><a href=\"#Exercise_1.4_Perimeter_and_Area_in_the_Coordinate_Plane\">Exercise 1.4 Perimeter and Area in the Coordinate Plane &#8211; Pae(34-36)<\/a><\/li>\n<li><a href=\"#1.5_Measuring_and_Constructing_Angles\">1.5 Measuring and Constructing Angles &#8211; Page(37-46)<\/a><\/li>\n<li><a href=\"#Lesson_1.5_Measuring_and_Constructing_Angles\">Lesson 1.5 Measuring and Constructing Angles &#8211; Page(38-43)<\/a><\/li>\n<li><a href=\"#Exercise_1.5_Measuring_and_Constructing_Angles\">Exercise 1.5 Measuring and Constructing Angles &#8211; Page(43-46)<\/a><\/li>\n<li><a href=\"#1.6_Describing_Pairs_of_Angles\">1.6 Describing Pairs of Angles &#8211; Page(47-54)<\/a><\/li>\n<li><a href=\"#Lesson_1.6_Describing_Pairs_of_Angles\">Lesson 1.6 Describing Pairs of Angles &#8211; Page(48-51)<\/a><\/li>\n<li><a href=\"#Exercise_1.6_Describing_Pairs_of_Angles\">Exercise 1.6 Describing Pairs of Angles &#8211; Page(52-54)<\/a><\/li>\n<li><a href=\"#1.4_-_1.6_Performance_Task:_Comfortable_Horse_Stalls\">1.4 &#8211; 1.6 Performance Task: Comfortable Horse Stalls &#8211; Page 55<\/a><\/li>\n<li><a href=\"#Basics_of_Geometry_Chapter_Review\">Basics of Geometry Chapter Review &#8211; Page(56-58)<\/a><\/li>\n<li><a href=\"#Basics_of_Geometry_Chapter_Test\">Basics of Geometry Chapter Test &#8211; Page 59<\/a><\/li>\n<li><a href=\"#Basics_of_Geometry_Cumulative_Assessment\">Basics of Geometry Cumulative Assessment &#8211; Page(60-61)<\/a><\/li>\n<\/ul>\n<h3><a id=\"Basics_of_Geometry_Maintaining_Mathematical_Proficiency\"><\/a>Basics of Geometry Maintaining Mathematical Proficiency<\/h3>\n<p>Simplify the expression.<\/p>\n<p>Question 1.<br \/>\n|8 &#8211; 12|<br \/>\nAnswer:<br \/>\nThe given absolute value expression is:<br \/>\n| 8 &#8211; 12|<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| -x | = x for x &gt; 0<br \/>\nSo,<br \/>\n| 8 &#8211; 12 |= | -4| = 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the given absolute value expression is: 4<\/p>\n<p>Question 2.<br \/>\n|- 6 &#8211; 5|<br \/>\nAnswer:<br \/>\nThe given absolute value expression is:<br \/>\n| -6 &#8211; 5|<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| -x | = x for x &gt; 0<br \/>\nSo,<br \/>\n| -6 &#8211; 5| = | -11 | = 11<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the given absolute value expression is: 11<\/p>\n<p>Question 3.<br \/>\n|4 + (-9)|<br \/>\nAnswer:<br \/>\nThe given absolute value expression is:<br \/>\n| 4 + (-9) |<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| -x | = x for x &gt; 0<br \/>\nSo,<br \/>\n| 4 + (-9) | = | 4 &#8211; 9 |<br \/>\n= | -5 | = 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the given absolute value expression is: 5<\/p>\n<p>Question 4.<br \/>\n|13 + (-4)|<br \/>\nAnswer:<br \/>\nThe given absolute value expression is:<br \/>\n| 13 + (-4) |<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| -x | = x for x &gt; 0<br \/>\nSo,<br \/>\n| 13 + (-4) | = | 13 &#8211; 4 |<br \/>\n= | 9 | = 9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the given absolute value expression is: 9<\/p>\n<p>Question 5.<br \/>\n|6 &#8211; (- 2)|<br \/>\nAnswer:<br \/>\nThe given absolute value expression is:<br \/>\n| 6 &#8211; (-2) |<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| -x | = x for x &gt; 0<br \/>\nSo,<br \/>\n| 6 &#8211; (-2) | = | 6 + 2 |<br \/>\n= | 8 | = 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the given absolute value expression is: 8<\/p>\n<p>Question 6.<br \/>\n|5 &#8211; (- 1)|<br \/>\nAnswer:<br \/>\nThe given absolute value expression is:<br \/>\n| 5 &#8211; (-1) |<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| -x | = x for x &gt; 0<br \/>\nSo,<br \/>\n| 5 &#8211; (-1) | = | 5 + 1 |<br \/>\n= | 6 | = 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the given absolute value expression is: 6<\/p>\n<p>Question 7.<br \/>\n|- 8 &#8211; (- 7)|<br \/>\nAnswer:<br \/>\nThe given absolute value expression is:<br \/>\n| -8 &#8211; (-7) |<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| -x | = x for x &gt; 0<br \/>\nSo,<br \/>\n| -8 &#8211; (-7) | = | -8 + 7 |<br \/>\n= | -1 | = 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the given absolute value expression is: 1<\/p>\n<p>Question 8.<br \/>\n|8 &#8211; 13|<br \/>\nAnswer:<br \/>\nThe given absolute value expression is:<br \/>\n| 8 &#8211; 13 |<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| -x | = x for x &gt; 0<br \/>\nSo,<br \/>\n| 8 &#8211; 13 | = | -5 | = 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the given absolute value expression is: 5<\/p>\n<p>Question 9.<br \/>\n|- 14 &#8211; 3|<br \/>\nAnswer:<br \/>\nThe given absolute value expression is:<br \/>\n| -14 &#8211; 3 |<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| -x | = x for x &gt; 0<br \/>\nSo,<br \/>\n| -14 &#8211; 3 | = | -17 | = 17<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the given absolute value expression is: 17<\/p>\n<p>Find the area of the triangle.<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35415\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1\" width=\"77\" height=\"113\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35415\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1\" width=\"77\" height=\"113\" \/><br \/>\nWe know that,<br \/>\nThe area of the triangle (A) is given as:<br \/>\nA = 1\/2 \u00d7Base \u00d7 Height<br \/>\nSo,<br \/>\nThe area of the given triangle is:<br \/>\nA = 1\/2 \u00d7 14m \u00d7 22m<br \/>\n= 11 \u00d7 14<br \/>\n= 154 m\u00b2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the given triangle is: 154 m\u00b2<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35414\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-2.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 2\" width=\"156\" height=\"61\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35414\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-2.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 2\" width=\"156\" height=\"61\" \/><br \/>\nWe know that,<br \/>\nThe area of the triangle (A) is given as:<br \/>\nA = \\(\\frac{1}{2}\\) \u00d7Base \u00d7 Height<br \/>\nSo,<br \/>\nThe area of the given triangle is:<br \/>\nA = \\(\\frac{1}{2}\\) \u00d7 7yd \u00d7 24yd<br \/>\n= \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{24}{1}\\) \u00d7 7<br \/>\n= 12 \u00d7 7<br \/>\n= 84 yd\u00b2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the given triangle is: 84 yd\u00b2<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35413\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 3\" width=\"175\" height=\"101\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35413\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 3\" width=\"175\" height=\"101\" \/><br \/>\nWe know that,<br \/>\nThe area of the triangle (A) is given as:<br \/>\nA = \\(\\frac{1}{2}\\) \u00d7Base \u00d7 Height<br \/>\nSo,<br \/>\nThe area of the given triangle is:<br \/>\nA = \\(\\frac{1}{2}\\) \u00d7 16 in \u00d7 25 in<br \/>\n= \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{16}{1}\\) \u00d7 25<br \/>\n= 8 \u00d7 25<br \/>\n= 200 in\u00b2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the given triangle is: 200 in\u00b2<\/p>\n<p>Question 13.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nDescribe the possible values for x and y when |x &#8211; y| &gt; 0. What does it mean when |x &#8211; y| = 0 ? Can |x &#8211; y| &lt; 0? Explain your reasoning.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe value of the absolute expression must be\u00a0 greater than or equal to 0 but not less than 0<br \/>\nSo,<br \/>\nThe values for | x &#8211; y | do not exist<br \/>\nNow,<br \/>\nThe possible values of | x &#8211; y | &gt; 0 should be greater than 0 and maybe x &gt; y and x &lt; y<br \/>\nThe possible values of | x &#8211; y | = 0 should be only one value i.e., 0 as x and y must be equal to make the difference value 0<\/p>\n<h3><a id=\"Basics_of_Geometry_Mathematical_Practices\"><\/a>Basics of Geometry Mathematical Practices<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nFind the area of the polygon using the specified units. Round your answer to the nearest hundredth.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35412\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-4.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 4\" width=\"196\" height=\"182\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35412\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-4.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 4\" width=\"196\" height=\"182\" \/><br \/>\nWe know that,<br \/>\nArea of the triangle = \\(\\frac{1}{2}\\) \u00d7 Base \u00d7 Height<br \/>\nSo,<br \/>\nFrom the figure,<br \/>\nThe value of the Base is: 2 cm<br \/>\nThe value of Height is: 2 cm<br \/>\nWe know that,<br \/>\n1 cm = \\(\\frac{25}{64}\\) inch = 0.3937 inch<br \/>\nSo,<br \/>\n2cm = \\(\\frac{25}{32}\\) inch = 0.7874 inch<br \/>\nSo,<br \/>\nThe area of the given triangle = \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{25}{32}\\) \u00d7 \\(\\frac{25}{32}\\)<br \/>\n= \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{625}{1024}\\)<br \/>\n= \\(\\frac{625}{2,048}\\) inch\u00b2<br \/>\n= 0.3051 inch\u00b2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the given triangle in square inches is: 0.3051 inch\u00b2<\/p>\n<p>Question 2.<br \/>\nparallelogram (square centimeters)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35411\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 5\" width=\"207\" height=\"147\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35411\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 5\" width=\"207\" height=\"147\" \/><br \/>\nWE know hat,<br \/>\nThe area of the parallelogram = Base \u00d7 Height<br \/>\nSo,<br \/>\nFrom the given figure,<br \/>\nThe base of the parallelogram is: 2.5 in<br \/>\nThe height of the parallelogram = 2 in<br \/>\nWe know that,<br \/>\n1 inch = 2.54 cm<br \/>\nSo,<br \/>\n2 inch = 2.08 cm<br \/>\n2.5 inch = 6.35 cm<br \/>\nSo,<br \/>\nThe area of the given parallelogram = 2.08 \u00d7 6.35<br \/>\n= 13.208 cm\u00b2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the given parallelogram in square cm is: 13.208 cm\u00b2<\/p>\n<p>Question 3.<br \/>\nThe distance between the two cities is 120 miles. What is the distance in kilometers? Round your answer to the nearest whole number.<br \/>\nAnswer:<br \/>\nIt is given that the distance between the two cities is 120 miles.<br \/>\nNow,<br \/>\nWe know that,<br \/>\n1 mile = 1.609 kilometer<br \/>\nSo,<br \/>\nThe distance between the two cities in kilometers = 120 \u00d7 1.609<br \/>\n= 193 kilometers<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance between the two cities in kilometers is: 193 kilometers<\/p>\n<h3><a id=\"1.1_Points,_Lines,_and_Planes\"><\/a>1.1 Points, Lines, and Planes<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Using Dynamic Geometry Software<\/p>\n<p>Work with a partner: Use dynamic geometry software to draw several points. Also draw some lines, line segments, and rays. What is the difference between a line, a line segment, and a ray?<br \/>\nSample<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35410\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-6.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 6\" width=\"268\" height=\"214\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-68692\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1.png\" alt=\"\" width=\"622\" height=\"305\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1.png 622w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-300x147.png 300w\" sizes=\"(max-width: 622px) 100vw, 622px\" \/><br \/>\nFrom the above,<br \/>\nThe differences between a line, a ray, and a line segment are:<br \/>\nA Ray has no starting and ending points<br \/>\nA line has a starting point but no ending point<br \/>\nA line segment has both starting point and an ending point<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Intersections of Lines and Planes<\/p>\n<p>Work with a partner:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35409\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-7.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 7\" width=\"246\" height=\"235\" \/><br \/>\na. Describe and sketch the ways in which two lines can intersect or not intersect. Give examples of each using the lines formed by the walls. floor. and ceiling in your classroom.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-68695\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-1.png\" alt=\"\" width=\"707\" height=\"359\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-1.png 707w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-1-300x152.png 300w\" sizes=\"(max-width: 707px) 100vw, 707px\" \/><br \/>\nExamples of non-intersecting lines are: Floor and ceiling<br \/>\nExamples of intersecting lines are: Walls and floor<\/p>\n<p>b. Describe and sketch the ways in which a line and a plane can intersect or not intersect. Give examples of each using the walls. floor, and ceiling in your classroom.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-68699\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1.jpg\" alt=\"\" width=\"740\" height=\"432\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1.jpg 740w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-300x175.jpg 300w\" sizes=\"(max-width: 740px) 100vw, 740px\" \/><br \/>\nExamples of the intersection of a plane and a line are: Walls and ceiling<br \/>\nExamples of the non-intersection of a plane and a line are:\u00a0 Floor and a blackboard<\/p>\n<p>c. Describe and sketch the ways in which two planes can intersect or not intersect. Give examples of each using the walls. floor, and ceiling in your classroom.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-68702\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-2.png\" alt=\"\" width=\"798\" height=\"402\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-2.png 798w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-2-300x151.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-2-768x387.png 768w\" sizes=\"(max-width: 798px) 100vw, 798px\" \/><br \/>\nExamples of the intersection of planes are: Floor and benches<br \/>\nExamples of the non-intersection of planes are: Floor and ceiling<\/p>\n<p><strong>Exploration 3<\/strong><\/p>\n<p>Exploring Dynamic Geometry Software<\/p>\n<p><strong>UNDERSTANDING MATHEMATICAL TERMS<\/strong><br \/>\n<strong>To be proficient in math, you need to understand definitions and previously established results. An appropriate tool, such as a software package, can sometimes help.<\/strong><\/p>\n<p>Work with a partner. Use dynamic geometry software to explore geometry. Use the software to find a term or concept that is unfamiliar to you. Then use the capabilities of the software to determine the meaning of the term or concept.<br \/>\nAnswer:<br \/>\nThe dynamic geometry software used is &#8220;GeoGebra&#8221;<br \/>\nThe URL for &#8220;GeoGebra &#8211; Geometry&#8221; is:<br \/>\n<a href=\"https:\/\/www.geogebra.org\/calculator\">https:\/\/www.geogebra.org\/calculator<br \/>\n<\/a>So,<br \/>\nUsing the above URL,<br \/>\nCheck the term that you are unfamiliar\u00a0 to you and find the meaning of that term using the above URL<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 4.<br \/>\nHow can you use dynamic geometry software to visualize geometric concepts?<br \/>\nAnswer:<br \/>\nSome of the uses dynamic geometry software to visualize geometric concepts are:<br \/>\na. Request dispatching for cheap energy prices in cloud data centers<br \/>\nb. Springerlink training kit<br \/>\nc. Luminosity measurements at Hadron colliders<br \/>\nd. From word embeddings to document distances<\/p>\n<h3><a id=\"Lesson_1.1_Points,_Lines,_and_Planes\"><\/a>Lesson 1.1 Points, Lines, and Planes<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nUse the diagram in Example 1. Give two other names for <img loading=\"lazy\" class=\"alignnone size-full wp-image-35408\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-8.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 8\" width=\"41\" height=\"30\" \/>. Name a point that is not coplanar with points Q. S, and T.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35407\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-9.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 9\" width=\"273\" height=\"170\" \/><br \/>\nAnswer:<br \/>\nThe given plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35407\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-9.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 9\" width=\"273\" height=\"170\" \/><br \/>\nThe definition of a ray is:<br \/>\nA ray has no starting and ending points<br \/>\nSo,<br \/>\nThe other names for \\(\\overline{S T}\\) are: Line m and \\(\\overline{T S}\\)<br \/>\nWe know that,<br \/>\n&#8220;Co-planar points&#8221; are the points if all of them lie in the same plane<br \/>\nHence, among the points Q, S, and T,<br \/>\nS and T are co-planar since they lie in the same plane and Q is not co-planar<\/p>\n<p>Question 2.<br \/>\nGive another name for \\(\\overline{K L}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35406\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-10.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 10\" width=\"152\" height=\"138\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35406\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-10.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 10\" width=\"152\" height=\"138\" \/><br \/>\nSo,<br \/>\nThe other name of \\(\\overline{K L}\\) is: \\(\\overline{L K}\\)<\/p>\n<p>Question 3.<br \/>\nAre \\(\\vec{K}\\)P and \\(\\vec{P}\\)K the same ray? Are \\(\\vec{N}\\)P and \\(\\vec{N}\\)M the same ray? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35406\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-10.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 10\" width=\"152\" height=\"138\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35406\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-10.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 10\" width=\"152\" height=\"138\" \/><br \/>\nSo,<br \/>\nFrom the above figure,<br \/>\nWe can observe that<br \/>\n\\(\\vec{K}\\)P and \\(\\vec{P}\\)K are not the same ray<br \/>\nReason:<br \/>\n\\(\\overline{K L}\\) is the ray and KP is the line segment<br \/>\nNow,<br \/>\nWe can also observe that<br \/>\n\\(\\vec{N}\\)P and \\(\\vec{N}\\)M are in the same ray<br \/>\nReason:<br \/>\nSince the points N, P, and M are collinear, the ray \\(\\vec{N}\\)M and \\(\\vec{N}\\)P are in the same plane<\/p>\n<p>Question 4.<br \/>\nSketch two different lines that intersect a plane at the same point.<br \/>\nAnswer:<br \/>\nThe representation of the two different lines that intersect a plane at the same point is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-68999\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-3.png\" alt=\"\" width=\"482\" height=\"243\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-3.png 482w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-3-300x151.png 300w\" sizes=\"(max-width: 482px) 100vw, 482px\" \/><\/p>\n<p>Question 5.<br \/>\nName the intersection of <img loading=\"lazy\" class=\"alignnone size-full wp-image-35705\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-11.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 11\" width=\"36\" height=\"32\" \/>\u00a0and line k.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35704\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-12.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 12\" width=\"212\" height=\"169\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35704\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-12.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 12\" width=\"212\" height=\"169\" \/><br \/>\nFrom the above figure,<br \/>\nWe can observe that the intersection of \\(\\overline{P Q}\\) and line k is: M<\/p>\n<p>Question 6.<br \/>\nName the intersection of plane A and plane B.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35704\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-12.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 12\" width=\"212\" height=\"169\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35704\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-12.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 12\" width=\"212\" height=\"169\" \/><br \/>\nFrom the above figure,<br \/>\nWe can observe that the intersection of plane A and plane B is: Line k<\/p>\n<p>Question 7.<br \/>\nName the intersection of line k and plane A.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35704\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-12.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 12\" width=\"212\" height=\"169\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35704\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-12.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 12\" width=\"212\" height=\"169\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that the intersection of line k and plane A is: Line k<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Use the diagram that shows a molecule of phosphorus pentachloride.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35703\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-13.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 13\" width=\"240\" height=\"273\" \/><\/p>\n<p>Question 8.<br \/>\nName two different planes that contain line s.<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35703\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-13.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 13\" width=\"240\" height=\"273\" \/><br \/>\nWe know that,<br \/>\nA &#8216;Plane&#8221; can be formed by using any three non-collinear points on the same plane<br \/>\nNow,<br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nThe different planes that contain line s are: JHG and KLI<\/p>\n<p>Question 9.<br \/>\nName three different planes that contain point K.<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35703\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-13.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 13\" width=\"240\" height=\"273\" \/><br \/>\nFrom the above figure,<br \/>\nThe three different planes that contain pint K are: HGK, HKL, and KLI<\/p>\n<p>Question 10.<br \/>\nName two different planes that contain \\(\\vec{H}\\)J.<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35703\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-13.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 13\" width=\"240\" height=\"273\" \/><br \/>\nFrom the above figure,<br \/>\nWe can say that<br \/>\nThe 2 different planes that contain \\(\\vec{H}\\)J are: HJI and HJL<\/p>\n<h3><a id=\"Exercise_1.1_Points,_Lines,_and_Planes\"><\/a>Exercise 1.1 Points, Lines, and Planes<\/h3>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nCompare collinear points and coplanar points.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48046\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-1.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 1\" width=\"576\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-1.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-1-300x30.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WHICH ONE DOES DOESN\u2019T BELONG?<\/strong><br \/>\nWhich term does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35701\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-14.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 14\" width=\"401\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-14.png 401w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-14-300x43.png 300w\" sizes=\"(max-width: 401px) 100vw, 401px\" \/><br \/>\nAnswer:<br \/>\nThe given expressions are:<br \/>\na. \\(\\overline{A B}\\)<br \/>\nb. plane CDE<br \/>\nc. \\(\\vec{FG}\\)<br \/>\nd. \\(\\vec{H}\\)I<br \/>\nSo,<br \/>\nFrom the above four expressions,<br \/>\nWe can observe that the three expressions are 2-dimensional geometrical expressions whereas 1 figure is a 3-dimensional geometrical expression<br \/>\nThe 2-dimensional geometrical expressions from the given expressions are: a), c), and d)<br \/>\nHence, from the above,<br \/>\nWe can conclude that expression c. does not belong with the other three<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3 &#8211; 6, use the diagram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35700\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-15.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 15\" width=\"229\" height=\"105\" \/><\/p>\n<p>Question 3.<br \/>\nName four points.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48047\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-3.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 3\" width=\"456\" height=\"36\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-3.png 456w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-3-300x24.png 300w\" sizes=\"(max-width: 456px) 100vw, 456px\" \/><\/p>\n<p>Question 4.<br \/>\nName two lines.<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35700\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-15.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 15\" width=\"229\" height=\"105\" \/><br \/>\nHence,<br \/>\nFrom the above figure,<br \/>\nWe can conclude that the two lines are: \\(\\vec{B}\\)C and \\(\\vec{D}\\)E<\/p>\n<p>Question 5.<br \/>\nName the plane that contains points A, B, and C.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48048\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-5.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 5\" width=\"347\" height=\"34\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-5.png 347w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-5-300x29.png 300w\" sizes=\"(max-width: 347px) 100vw, 347px\" \/><\/p>\n<p>Question 6.<br \/>\nName the plane that contains points A, D, and E.<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35700\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-15.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 15\" width=\"229\" height=\"105\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that there are 2 planes. They are:<br \/>\na. plane S b. plane T<br \/>\nHence,<br \/>\nFrom the above figure,<br \/>\nWe can conclude that points A, D, and E lie in Plane T<\/p>\n<p>In Exercises 7 &#8211; 10. use the diagram. (See Example 1.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35699\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-16.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 16\" width=\"291\" height=\"165\" \/><\/p>\n<p>Question 7.<br \/>\nGive two other names for <img loading=\"lazy\" class=\"alignnone size-full wp-image-35698\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-17.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 17\" width=\"37\" height=\"35\" \/>.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48049\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-7.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 7\" width=\"424\" height=\"41\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-7.png 424w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-7-300x29.png 300w\" sizes=\"(max-width: 424px) 100vw, 424px\" \/><\/p>\n<p>Question 8.<br \/>\nGive another name or plane V.<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35699\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-16.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 16\" width=\"291\" height=\"165\" \/><br \/>\nWe know that,<br \/>\nA plane is also named by a group of 3 or more co-planar points<br \/>\nHence, from the above,<br \/>\nWe can conclude that another name for plane V is: plane QRT<\/p>\n<p>Question 9.<br \/>\nName three points that are collinear. Then name a fourth point that is not collinear with these three points.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48050\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-9.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 9\" width=\"571\" height=\"54\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-9.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-9-300x28.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 10.<br \/>\nName a point that is not coplanar with R, S, and T.<br \/>\nAnswer:<br \/>\nThe given\u00a0 figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35699\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-16.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 16\" width=\"291\" height=\"165\" \/><br \/>\nWe know that,<br \/>\nThe points that are present in the same plane are called &#8220;Co-planar points&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that the point that is co-planar with R, S, and T is: W<\/p>\n<p>In Exercises 11 &#8211; 16, use the diagram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35697\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-18.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 18\" width=\"275\" height=\"183\" \/><\/p>\n<p>Question 11.<br \/>\nWhat is another name for \\(\\overline{B D}\\)?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48051\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-11.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 11\" width=\"278\" height=\"40\" \/><\/p>\n<p>Question 12.<br \/>\nWhat is another name for \\(\\overline{A C}\\)?<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35697\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-18.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 18\" width=\"275\" height=\"183\" \/><br \/>\nWe know that,<br \/>\nThe line segment is the same from both sides if we can consider any point starting or ending point<br \/>\nEx: \\(\\overline{A B}\\) is the same as \\(\\overline{B A}\\)<br \/>\nbecause we can consider here either starting point A or starting point B, then the ending points will be either B or A<br \/>\nHence, from the above,<br \/>\nWe can conclude that the other name for \\(\\overline{A C}\\) is: \\(\\overline{C A}\\)<\/p>\n<p>Question 13.<br \/>\nWhat is another name for ray \\(\\vec{A}\\)E?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48052\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-13.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 13\" width=\"271\" height=\"35\" \/><\/p>\n<p>Question 14.<br \/>\nName all rays with endpoint E.<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35697\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-18.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 18\" width=\"275\" height=\"183\" \/><br \/>\nHence, from the above figure,<br \/>\nWe can conclude that the rays with endpoint E are: s and t<\/p>\n<p>Question 15.<br \/>\nName two pairs of opposite rays.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48053\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-15.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 15\" width=\"552\" height=\"40\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-15.png 552w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-15-300x22.png 300w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><\/p>\n<p>Question 16.<br \/>\nName one pair of rays that are not opposite rays.<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35697\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-18.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 18\" width=\"275\" height=\"183\" \/><br \/>\nWe know that &#8220;opposite&#8221; means &#8220;Opposite direction&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that the pair of rays that are not opposite rays are:<br \/>\n\\(\\vec{E}\\)B and\\(\\vec{E}\\)C<\/p>\n<p>In Exercises 17 &#8211; 24, sketch the figure described.<\/p>\n<p>Question 17.<br \/>\nplane P and line l intersecting at one point<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48054\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-17.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 17\" width=\"197\" height=\"144\" \/><\/p>\n<p>Question 18.<br \/>\nplane K and line m intersecting at all points on line m<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nplane K and line m intersecting at all points on line m<br \/>\nHence,<br \/>\nThe representation of the given statement is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-69605\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-4.png\" alt=\"\" width=\"597\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-4.png 597w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-4-300x106.png 300w\" sizes=\"(max-width: 597px) 100vw, 597px\" \/><\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35696\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-19.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 19\" width=\"80\" height=\"30\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48055\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-19.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 19\" width=\"177\" height=\"152\" \/><\/p>\n<p>Question 20.<br \/>\n\\(\\vec{M}\\)N and \\(\\vec{N}\\)X<br \/>\nAnswer:<br \/>\nThe given vectors are:<br \/>\n\\(\\vec{M}\\)N and \\(\\vec{N}\\)X<br \/>\nHence,<br \/>\nThe representation of vectors along with their direction is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-69606\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-5.png\" alt=\"\" width=\"293\" height=\"108\" \/><\/p>\n<p>Question 21.<br \/>\nplane M and \\(\\vec{N}\\)B intersecting at B<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48056\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-21.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 21\" width=\"201\" height=\"135\" \/><\/p>\n<p>Question 22.<br \/>\nplane M and \\(\\vec{N}\\)B intersecting at A<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nplane M and \\(\\vec{N}\\)B intersecting at A<br \/>\nHence,<br \/>\nThe representation of the given statement is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-69608\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-6.png\" alt=\"\" width=\"316\" height=\"187\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-6.png 316w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-6-300x178.png 300w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><\/p>\n<p>Question 23.<br \/>\nplane A and plane B not intersecting<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48057\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-23.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 23\" width=\"190\" height=\"184\" \/><\/p>\n<p>Question 24.<br \/>\nplane C and plane D intersecting at <img loading=\"lazy\" class=\"alignnone size-full wp-image-35695\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-20.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 20\" width=\"38\" height=\"24\" \/><br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nplane C and plane D intersecting at <img loading=\"lazy\" class=\"alignnone size-full wp-image-35695\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-20.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 20\" width=\"38\" height=\"24\" \/><br \/>\nHence,<br \/>\nThe representation of the given statement is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-69609\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-7.png\" alt=\"\" width=\"348\" height=\"304\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-7.png 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-7-300x262.png 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p><strong>ERROR ANALYSIS<\/strong><br \/>\nIn Exercises 25 and 26, describe and correct the error in naming opposite rays in the diagram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35694\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-21.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 21\" width=\"270\" height=\"185\" \/><\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35693\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-22.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 22\" width=\"241\" height=\"53\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48058\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-25.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 25\" width=\"572\" height=\"92\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-25.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-25-300x48.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35692\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-23.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 23\" width=\"224\" height=\"65\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35694\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-21.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 21\" width=\"270\" height=\"185\" \/><br \/>\nFrom the above,<br \/>\nWe can observe that \\(\\vec{Y}\\)C and \\(\\vec{Y}\\)E are the opposite rays because Y, C, and E are the collinear points and Y is in between C and E<\/p>\n<p>In Exercises 27 &#8211; 34. use the diagram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35691\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-24.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 24\" width=\"215\" height=\"204\" \/><\/p>\n<p>Question 27.<br \/>\nName a point that is collinear with points E and H.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48059\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-27.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 27\" width=\"286\" height=\"28\" \/><\/p>\n<p>Question 28.<br \/>\nName a point that is collinear with points B and I<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35691\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-24.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 24\" width=\"215\" height=\"204\" \/><br \/>\nHence, from the above figure,<br \/>\nWe can conclude that C is collinear with B and I<\/p>\n<p>Question 29.<br \/>\nName a p0int that is not collinear with points E and H.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-29.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 29\" width=\"510\" height=\"31\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-29.png 510w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-29-300x18.png 300w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><\/p>\n<p>Question 30.<br \/>\nName a point that is not collinear with points B and I.<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35691\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-24.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 24\" width=\"215\" height=\"204\" \/><br \/>\nWe know that,<br \/>\nThe points that are in the same line are called &#8220;Collinear points&#8221;<br \/>\nHence, from the above figure,<br \/>\nWe can conclude that A, D, E, F, G, H, J are not collinear with points B and I<\/p>\n<p>Question 31.<br \/>\nName a point that is coplanar with points D, A, and B.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48061\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-31.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 31\" width=\"386\" height=\"32\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-31.png 386w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-31-300x25.png 300w\" sizes=\"(max-width: 386px) 100vw, 386px\" \/><\/p>\n<p>Question 32.<br \/>\nName a point that is coplanar with points C, G, and F.<br \/>\nAnswer:<br \/>\nThe given figure is;<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35691\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-24.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 24\" width=\"215\" height=\"204\" \/><br \/>\nWe know that,<br \/>\nThe points that are in the same plane are called &#8220;Co-planar points&#8221;<br \/>\nFrom the above figure,<br \/>\nWe can observe that CGFB is a plane<br \/>\nHence, from the above figure,<br \/>\nWe can conclude that B and I are co-planar with points C, G, and F<\/p>\n<p>Question 33.<br \/>\nName the intersection of plane AEH and plane FBE.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48062\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-33.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 33\" width=\"502\" height=\"37\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-33.png 502w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-33-300x22.png 300w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/><\/p>\n<p>Question 34.<br \/>\nName the intersection of plane BGF and plane HDG.<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35691\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-24.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 24\" width=\"215\" height=\"204\" \/><br \/>\nHence, from the above figure,<br \/>\nWe can conclude that the intersection of plane BGF and plane HDG is: \\(\\overline{C G}\\)<\/p>\n<p>In Exercises 35 &#8211; 38, name the geometric term modeled by the object.<\/p>\n<p>Question 35.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35690\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-25.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 25\" width=\"134\" height=\"154\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48063\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-35.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 35\" width=\"106\" height=\"33\" \/><\/p>\n<p>Question 36.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35689\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-26.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 26\" width=\"218\" height=\"166\" \/><br \/>\nAnswer:<br \/>\nThe given object is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35689\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-26.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 26\" width=\"218\" height=\"166\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that the geometric term modeled by the object is: Plane<\/p>\n<p>Question 37.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35688\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-27.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 27\" width=\"90\" height=\"197\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48064\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-37.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 37\" width=\"111\" height=\"29\" \/><\/p>\n<p>Question 38.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35687\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-28.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 28\" width=\"120\" height=\"188\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35687\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-28.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 28\" width=\"120\" height=\"188\" \/><br \/>\nHence, from the above figure,<br \/>\nWe can conclude that the geometric term modeled from the given object is: Line<\/p>\n<p>In Exercises 39 &#8211; 44. use the diagram to name all the points that are not coplanar with the given points.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35686\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-29.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 29\" width=\"217\" height=\"214\" \/><br \/>\nQuestion 39.<br \/>\nN, K, and L<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48065\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-39.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 39\" width=\"471\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-39.png 471w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-39-300x21.png 300w\" sizes=\"(max-width: 471px) 100vw, 471px\" \/><\/p>\n<p>Question 40.<br \/>\nP, Q, and N<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35686\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-29.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 29\" width=\"217\" height=\"214\" \/><br \/>\nHence, from the above figure,<br \/>\nWe can conclude that R, S, L, and K are not co-planar\u00a0 with P, Q, and N<\/p>\n<p>Question 41.<br \/>\nP, Q, and R<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-41.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 41\" width=\"469\" height=\"31\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-41.png 469w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-41-300x20.png 300w\" sizes=\"(max-width: 469px) 100vw, 469px\" \/><\/p>\n<p>Question 42.<br \/>\nR, K, and N<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35686\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-29.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 29\" width=\"217\" height=\"214\" \/><br \/>\nHence, from the above figure,<br \/>\nWe can conclude that P, S, L, and M are not co-planar with R, K, and N<\/p>\n<p>Question 43.<br \/>\nP, S, and K<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48067\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-43.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 43\" width=\"463\" height=\"36\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-43.png 463w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-43-300x23.png 300w\" sizes=\"(max-width: 463px) 100vw, 463px\" \/><\/p>\n<p>Question 44.<br \/>\nQ, K, and L<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35686\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-29.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 29\" width=\"217\" height=\"214\" \/><br \/>\nHence, from the above figure,<br \/>\nWe can conclude that R, M, P, and S are not co-planar with Q, K, and L<\/p>\n<p>Question 45.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nGiven two points on a line and a third point not on the line. is it possible to draw<br \/>\na plane that includes the line and the third point? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48068\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-45.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 45\" width=\"573\" height=\"71\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-45.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-45-300x37.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nIs it possible for one point to be in two different planes? Explain your reasoning.<br \/>\nAnswer:<br \/>\nYes, it is\u00a0possible for one point to be in two different planes. This can be explained in the following way:<br \/>\nThe Intersection of two planes is a line.<br \/>\nHence,<br \/>\nyes, one point or an Infinite number of points can be common between two different planes.<\/p>\n<p>Question 47.<br \/>\n<strong>REASONING<\/strong><br \/>\nExplain why a four-legged chair may rock from side to side even if the floor is level. Would a three-legged chair on the same level floor rock from side to side? Why or why not?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48069\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-47.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 47\" width=\"560\" height=\"116\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-47.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-47-300x62.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nYou are designing the living room of an apartment. Counting the floor, walls, and ceiling, you want the design to contain at least eight different planes. Draw a diagram of your design. Label each plane in your design.<br \/>\nAnswer:<br \/>\nIt is given that you are designing the living room of an apartment and you want the design to contain at least eight different planes which include the floor, walls, and ceiling<br \/>\nHence,<br \/>\nThe representation of the design that contain floor, walls, and ceiling is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-69614\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-8.png\" alt=\"\" width=\"339\" height=\"252\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-8.png 339w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-8-300x223.png 300w\" sizes=\"(max-width: 339px) 100vw, 339px\" \/><\/p>\n<p>Question 49.<br \/>\n<strong>LOOKING FOR STRUCTURE<\/strong><br \/>\nTwo coplanar intersecting lines will always intersect at one point. What is the greatest number of intersection points that exist if you draw tour coplanar lines? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48070\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-49.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 49\" width=\"574\" height=\"207\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-49.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-49-300x108.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 50.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nYou and your friend walk in opposite directions, forming opposite rays. You were originally on the comer of Apple Avenue and Cherry Court.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35685\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-30.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 30\" width=\"297\" height=\"202\" \/><br \/>\na. Name two possibilities of the road and direction you and your friend may have traveled.<br \/>\nAnswer:<br \/>\nIt is given that you are at the corner of Apple Avenue and Cherry court<br \/>\nHence, from the above,<br \/>\nThe 2 possibilities that you and your friend travel in the opposite directions are:<br \/>\ni)<br \/>\nIf you traveled from the corner of Apple Avenue and Cherry court i.e., towards the east, then your friend will travel from the corner of Apple Avenue and Rose Rd. i.e., towards the west<br \/>\nii).<br \/>\nIf you traveled from the corner of Apple Avenue and Cherry court i.e., towards the west, then your friend will travel from the corner of Apple Avenue and Rose Rd. i.e., towards the east<\/p>\n<p>b. Your friend claims he went north on Cherry Court. and you went east on Apple Avenue. Make an argument as to why you know this could not have happened.<br \/>\nAnswer:<br \/>\nIt is given that your friend claims he went north on Cherry Court. and you went east on Apple Avenue<br \/>\nBut, from the above,<br \/>\nIt is given that you and your friend have to travel in the opposite directions<br \/>\nBut, according to the given statement,<br \/>\nYou and your friend travels in the perpendicular directions<br \/>\nHence,<br \/>\nWe can conclude that the claim of your friend is not possible<\/p>\n<p><strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nIn Exercises 51 &#8211; 54. graph the inequality on a number line. Tell whether the graph is a segment a ray or rays. a point, or a line.<\/p>\n<p>Question 51.<br \/>\nx \u2264 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48071\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-51.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 51\" width=\"472\" height=\"43\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-51.png 472w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-51-300x27.png 300w\" sizes=\"(max-width: 472px) 100vw, 472px\" \/><\/p>\n<p>Question 52.<br \/>\n&#8211; 7 \u2264 x \u2264 4<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-7 \u2264 x \u2264 4<br \/>\nHence,<br \/>\nThe representation of the given inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-69646\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-9.png\" alt=\"\" width=\"551\" height=\"157\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-9.png 551w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-9-300x85.png 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><br \/>\nHence, from the above number line,<br \/>\nWe can conclude that the given inequality represents a line segment in the number line<\/p>\n<p>Question 53.<br \/>\nx \u2265 5 or x \u2264 &#8211; 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48072\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-53.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 53\" width=\"559\" height=\"47\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-53.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-53-300x25.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 54.<br \/>\n|x| \u2264 0<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n| x | \u2264 0<br \/>\nHence,<br \/>\nThe representation of the given inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-69660\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-10.png\" alt=\"\" width=\"479\" height=\"494\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-10.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-10-291x300.png 291w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nHence, from the above number line,<br \/>\nWe can conclude that the given inequality represents the plane in the number line<\/p>\n<p>Question 55.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nUse the diagram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35684\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-31.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 31\" width=\"323\" height=\"265\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-31.png 323w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-31-300x246.png 300w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><br \/>\na. Name two points that arc collinear with P.<br \/>\nb. Name two planes that contain J.<br \/>\nc. Name all the points that are in more than One plane.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48073\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-55.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 55\" width=\"572\" height=\"126\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-55.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-55-300x66.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p><strong>CRITICAL THINKING<\/strong><br \/>\nIn Exercises 56 &#8211; 63. complete the<br \/>\nstatement with always, sometimes, or never. Explain your reasoning.<\/p>\n<p>Question 56.<br \/>\nA line ________________ has endpoints.<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nA line ________________ has endpoints.<br \/>\nHence,<br \/>\nThe completed statement is:<br \/>\nA line never has endpoints.<\/p>\n<p>Question 57.<br \/>\nA line and a point _________________ intersect<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48074\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-57.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 57\" width=\"407\" height=\"30\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-57.png 407w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-57-300x22.png 300w\" sizes=\"(max-width: 407px) 100vw, 407px\" \/><\/p>\n<p>Question 58.<br \/>\nA plane and a point ________________ intersect.<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nA plane and a point ________________ intersect.<br \/>\nHence,<br \/>\nThe completed statement is:<br \/>\nA plane and a point sometimes intersect.<\/p>\n<p>Question 59.<br \/>\nTwo planes _________________ intersect in a line.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48075\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-59.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 59\" width=\"402\" height=\"32\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-59.png 402w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-59-300x24.png 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><\/p>\n<p>Question 60.<br \/>\nTwo points ____________________ determine a line.<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nTwo points ____________________ determine a line.<br \/>\nHence,<br \/>\nThe completed statement is:<br \/>\nTwo points always determine a line.<\/p>\n<p>Question 61.<br \/>\nAny three points ____________________ determine a plane.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48076\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-61.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 61\" width=\"565\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-61.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-61-300x32.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 62.<br \/>\nAny three points not on the same line ____________________ determine a plane.<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nAny three points not on the same line ____________________ determine a plane.<br \/>\nHence,<br \/>\nThe completed statement is:<br \/>\nAny three points not on the same line always determine a plane.<\/p>\n<p>Question 63.<br \/>\nTwo lines that are not parallel _________________ intersect.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48077\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-63.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 63\" width=\"586\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-63.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-63-300x30.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 64.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nIs it possible for three planes to never intersect? intersect in one line? intersect in one point? Sketch the possible situations.<br \/>\nAnswer:<br \/>\ncase (1):<br \/>\nIt is not possible for three planes to intersect when the three planes are parallel<br \/>\nSo,<br \/>\nThe representation of this case is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-69726\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-11.png\" alt=\"\" width=\"619\" height=\"153\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-11.png 619w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-11-300x74.png 300w\" sizes=\"(max-width: 619px) 100vw, 619px\" \/><br \/>\ncase (2):<br \/>\nTo intersect in 1 line, the two planes must be perpendicular and the third plane should pass through that line<br \/>\nSo,<br \/>\nThe representation of this case is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-69734\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-12.png\" alt=\"\" width=\"380\" height=\"218\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-12.png 380w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-12-300x172.png 300w\" sizes=\"(max-width: 380px) 100vw, 380px\" \/><br \/>\ncase (3):<br \/>\nTo intersect in 1 point, the two planes must be intersected with a line and the third plane passes through a point of that line<br \/>\nSo,<br \/>\nThe representation of this case is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-69738\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-13.png\" alt=\"\" width=\"352\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-13.png 352w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-13-300x242.png 300w\" sizes=\"(max-width: 352px) 100vw, 352px\" \/><\/p>\n<p>Maintaining Mathematical Proficiency<br \/>\nFind the absolute value.<br \/>\nQuestion 65.<br \/>\n|6 + 2|<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48078\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-65.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 65\" width=\"200\" height=\"38\" \/><\/p>\n<p>Question 66.<br \/>\n|3 &#8211; 9|<br \/>\nAnswer:<br \/>\nThe given absolute value expression is:<br \/>\n| 3 &#8211; 9 |<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| -x | = x for x &gt; 0<br \/>\nSo,<br \/>\n| 3 &#8211; 9 | = | -6 | = 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the given absolute value expression is: 6<\/p>\n<p>Question 67.<br \/>\n|- 8 &#8211; 2|<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48079\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-67.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 67\" width=\"411\" height=\"38\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-67.png 411w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-67-300x28.png 300w\" sizes=\"(max-width: 411px) 100vw, 411px\" \/><\/p>\n<p>Question 68.<br \/>\n|7 &#8211; 11|<br \/>\nAnswer:<br \/>\nThe given absolute value expression is:<br \/>\n| 7 &#8211; 11 |<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| -x | = x for x &gt; 0<br \/>\nSo,<br \/>\n| 7 &#8211; 11 | = | -4 | = 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the given absolute value expression is: 4<\/p>\n<p>Solve the equation<\/p>\n<p>Question 69.<br \/>\n18 + x = 43<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48080\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-69.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 69\" width=\"179\" height=\"99\" \/><\/p>\n<p>Question 70.<br \/>\n36 + x = 20<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n36 + x = 20<br \/>\nSo,<br \/>\nx = 20 &#8211; 36<br \/>\nx = -16<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: -16<\/p>\n<p>Question 71.<br \/>\nx &#8211; 15 = 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48081\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-1.1-a-71.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 1.1 a 71\" width=\"173\" height=\"97\" \/><\/p>\n<p>Question 72.<br \/>\nx &#8211; 23 = 19<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\nx &#8211; 23 = 19<br \/>\nSo,<br \/>\nx = 19 + 23<br \/>\nx = 42<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 42<\/p>\n<h3><a id=\"1.2_Measuring_and_Constructing_Segments\"><\/a>1.2 Measuring and Constructing Segments<\/h3>\n<p>Essential Question<br \/>\nHow can you measure and construct a line segment?<br \/>\nAnswer:<br \/>\nThe steps used to measure a line segment are:<br \/>\na. Pick up a scale to measure the length of a line segment.<br \/>\nb. Identify the line segment you want to measure<br \/>\nc. Place the tip of the ruler at the starting of the line segment<\/p>\n<p>The steps used to construct a line segment are:<br \/>\na. Place the compass at one end of the line<br \/>\nb. Adjust the compass to slightly longer than half of the line&#8217;s length<br \/>\nc. Draw arcs above and below the line<br \/>\nd. Keeping the same compass width, draw arcs from the other end of the line<br \/>\ne. Place ruler where the arcs cross and draw the line segment<\/p>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Measuring Line Segments Using Nonstandard Units<\/p>\n<p>Work with a partner.<\/p>\n<p>a. Draw a line segment that has a length of 6 inches.<br \/>\nAnswer:<br \/>\nWe will use a ruler to draw a line segment and the ruler we use generally is the &#8220;Centimeter ruler&#8221;<br \/>\nBut,<br \/>\nIt is given that we have to draw a line segment that has a length of 6 inches<br \/>\nBut, it is not possible<br \/>\nSo,<br \/>\nConvert inches into centimeters<br \/>\nWe know that,<br \/>\n1 inch = 2.54 centimeters<br \/>\nSo,<br \/>\n6 inches = 15.24 cm<br \/>\nHence,<br \/>\nThe representation of the line segment that has the length of 6 inches in terms of cm is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-70108\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-14.png\" alt=\"\" width=\"736\" height=\"53\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-14.png 736w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-14-300x22.png 300w\" sizes=\"(max-width: 736px) 100vw, 736px\" \/><\/p>\n<p>b. Use a standard-sized paper clip to measure the length of the line segment. Explain how you measured the line segment in \u201cpaper clips.\u201d<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35682\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-32.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 32\" width=\"257\" height=\"261\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35681\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-33.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 33\" width=\"96\" height=\"32\" \/><br \/>\nAnswer:<br \/>\nTake a standard-sized paper clip and measure the length of the paper clip using a ruler<br \/>\nSo,<br \/>\nUsing a standard-sized paper clip, the length of the line segment is: 3.4925 cm or 3.5 cm<br \/>\nHence,<br \/>\nThe representation of the length of the line segment that is measured in the paper clip is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-70111\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-16.png\" alt=\"\" width=\"319\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-16.png 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-16-300x82.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><\/p>\n<p>c. Write conversion factors from paper clips to inches and vice versa.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35680\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-34.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 34\" width=\"156\" height=\"61\" \/><br \/>\nAnswer:<br \/>\nFrom part (b),<br \/>\nWe know that<br \/>\nThe length of a paper clip is: 3.5 cm<br \/>\nWe know that,<br \/>\n1 cm = 0.393 inches<br \/>\nSo,<br \/>\n3.5 cm = 1.377 inches<br \/>\nHence,<br \/>\n1 paper clip = 1.377 in<br \/>\nNow,<br \/>\nWe know that,<br \/>\n1 inch = 2.54 cm<br \/>\nHence,<br \/>\n1 inch = 2.54 paperclip<br \/>\nHence, from the above,<br \/>\nWe can conclude that the conversion of paper clips into inches and vice-versa is:<br \/>\n1 paperclip = 1.377 inch<br \/>\n1 inch = 2.54 paperclip<\/p>\n<p>d. A straightedge is a tool that you can use to draw a straight line. An example of a straightedge is a ruler. Use only a pencil, straightedge, paper clip, and paper to draw another line segment that is 6 inches long. Explain your process.<br \/>\nAnswer:<br \/>\nThe process using a pencil, a straightedge, paperclip, and paper to draw a line segment of 6 inches is:<br \/>\nStep 1:<br \/>\nAttach a paper to the paperclip and verify that the paper sets correctly in the paperclip<br \/>\nStep 2:<br \/>\nNow, use a straightedge tool like a ruler to draw a line segment on the paper<br \/>\nStep 3:<br \/>\nThe line segment must start from the starting of the ruler i.e, 0. Mark the point at 0 as A<br \/>\nStep 4:<br \/>\nContinue the line segment from 0 to 6 on the ruler and make the endpoint at 6 and label it as B<br \/>\nHence, from the above steps,<br \/>\nWe draw the lines segment AB of length 6 inches<br \/>\nBut,<br \/>\nWe know that,<br \/>\nA ruler consists of the only cm.<br \/>\nSo, convert inches into cm<br \/>\nSo,<br \/>\n1 inch = 2.54cm<br \/>\nSo,<br \/>\n6 inches = 15.24 cm<br \/>\nHence,<br \/>\nThe representation of the line segment AB of 6 inches long is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-70108\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-14.png\" alt=\"\" width=\"736\" height=\"53\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-14.png 736w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-14-300x22.png 300w\" sizes=\"(max-width: 736px) 100vw, 736px\" \/><\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Measuring Line Segments Using Nonstandard Units<\/p>\n<p>Work with a partner.<\/p>\n<p>a. Fold a 3-inch by 5-inch index card on one of its diagonals.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35679\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-35.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 35\" width=\"249\" height=\"149\" \/><br \/>\nAnswer:<br \/>\nThe given index card is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35679\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-35.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 35\" width=\"249\" height=\"149\" \/><br \/>\nWhen we fold the given index card,<br \/>\nWe can only see the right-angled triangle<br \/>\nHence,<br \/>\nThe representation of the folded index card at its diagonal is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-70186\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-17.png\" alt=\"\" width=\"289\" height=\"225\" \/><\/p>\n<p>b. Use the Pythagoras Theorem to algebraically determine the length of the diagonal in inches. Use a ruler to check your answer.<br \/>\nAnswer:<br \/>\nFrom part (a),<br \/>\nThe index card folded at its diagonal is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-70186\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-17.png\" alt=\"\" width=\"289\" height=\"225\" \/><br \/>\nWe know that,<br \/>\nAccording to Pythagoras theorem,<br \/>\nHypotenuse\u00b2 = Side\u00b2 + Side\u00b2<br \/>\nWhere,<br \/>\nThe hypotenuse is the longest side in a right-angled triangle<br \/>\nSo,<br \/>\nIn the given triangle,<br \/>\nAB and BC are the sides<br \/>\nAC is the hypotenuse<br \/>\nSo,<br \/>\nAC\u00b2 = 3\u00b2 + 5\u00b2<br \/>\nAC\u00b2 = 9 + 25<br \/>\nAC\u00b2 = 34<br \/>\nAC = \u221a34 \u2245 6 in<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of the diagonal is approximately equal to 6 inches<\/p>\n<p>c. Measure the length and width of the index card in paper clips.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe length of the index card in paper clips is: 4 cm (Approximately )<br \/>\nThe width of the index card in the paper clips is: 1 cm<\/p>\n<p>d. Use the Pythagoras Theorem to algebraically determine the length of the diagonal in paper clips. Then check your answer by measuring the length of the diagonal in paper clips. Does the Pythagorean Theorem work for any unit of measure? Justify your answer.<br \/>\nAnswer:<br \/>\nThe representation of the length and width of the paper clips is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-70239\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-18.png\" alt=\"\" width=\"292\" height=\"215\" \/><br \/>\nWe know that,<br \/>\nAccording to Pythagoras theorem,<br \/>\nHypotenuse\u00b2 = Side\u00b2 + Side\u00b2<br \/>\nWhere,<br \/>\nThe hypotenuse is the longest side in a right-angled triangle<br \/>\nSo,<br \/>\nIn the given triangle,<br \/>\nAB and BC are the sides<br \/>\nAC is the hypotenuse<br \/>\nSo,<br \/>\nAC\u00b2 = 4\u00b2 + 1\u00b2<br \/>\nAC\u00b2 = 16 + 1<br \/>\nAC\u00b2 = 17<br \/>\nAC = \u221a17 \u2245 4 cm<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of the diagonal in paper clips is: 4 cm<br \/>\nYes, the Pythagoras work for any unit of measure but it is applicable only for the right-angled triangles<\/p>\n<p><strong>Exploration 3<\/strong><\/p>\n<p>Measuring Heights Using Nonstandard Units<\/p>\n<p>Work with a partner.<\/p>\n<p>Consider a unit of length that is equal to the length of the diagonal you found in Exploration 2. Call this length \u201c1 diag.\u201d How tall are you in diags? Explain how you obtained your answer.<br \/>\nAnswer:<br \/>\nFrom Exploration 2,<br \/>\nThe length of the diagonal we have found is approximately equal to 6 inches<br \/>\nSo,<br \/>\nAccording to the given problem,<br \/>\n1 diag = 6 inches<br \/>\nWe know that,<br \/>\nThe height can be measured in the foot<br \/>\nSo,<br \/>\n1 inch = 0.08 feet<br \/>\nSo,<br \/>\n63.6 inch = 5.3 feet<br \/>\nSo,<br \/>\nIn terms of diags,<br \/>\n63.6inches = 60 + 3.6 inches<br \/>\n= 10 (6 inches) + 6 (0.6 inches)<br \/>\n= 10 diags + 0.6 diags<br \/>\n= 10.6 diags<br \/>\nHence, from the above,<br \/>\nWe can conclude that you are 10.6 diags tall<\/p>\n<p>Communicate Your Answer:<\/p>\n<p>Question 4.<br \/>\nHow can you measure and construct a line segment?<br \/>\nAnswer:<br \/>\nThe steps used to measure a line segment are:<br \/>\na. Pick up a scale to measure the length of a line segment.<br \/>\nb. Identify the line segment you want to measure<br \/>\nc. Place the tip of the ruler at the starting of the line segment<\/p>\n<p>The steps used to construct a line segment are:<br \/>\na. Place the compass at one end of line<br \/>\nb. Adjust the compass to slightly longer than half of the line&#8217;s length<br \/>\nc. Draw arcs above and below the line<br \/>\nd. Keeping the same compass width, draw arcs from the other end of line<br \/>\ne. Place ruler where the arcs cross and draw the line segment<\/p>\n<h3><a id=\"Lesson_1.2_Measuring_and_Constructing_Segments\"><\/a>Lesson 1.2 Measuring and Constructing Segments<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Use a ruler to measure the length of the segment.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35678\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-36.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 36\" width=\"226\" height=\"36\" \/><br \/>\nAnswer:<br \/>\nThe length of the given segment in cm is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-70556\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-21.png\" alt=\"\" width=\"229\" height=\"44\" \/><\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35677\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-37.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 37\" width=\"192\" height=\"36\" \/><br \/>\nAnswer:<br \/>\nThe length of the given line segment in cm is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-70555\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-20.png\" alt=\"\" width=\"199\" height=\"44\" \/><\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35676\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-38.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 38\" width=\"137\" height=\"36\" \/><br \/>\nAnswer:<br \/>\nThe length of the given line segment in cm is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-70559\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-22.png\" alt=\"\" width=\"138\" height=\"46\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35675\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-39.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 39\" width=\"182\" height=\"40\" \/><br \/>\nAnswer:<br \/>\nThe length of the given line segment in cm is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-70560\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-23.png\" alt=\"\" width=\"182\" height=\"48\" \/><\/p>\n<p>Question 5.<br \/>\nPlot A(- 2, 4), B(3, 4), C(0, 2), and D(0, &#8211; 2) in a coordinate plane. Then<br \/>\ndetermine whether \\(\\overline{A B}\\) and \\(\\overline{C D}\\) are congruent.<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nA (-2, 4), B (3, 4), C (0, 2), and D (0, -2)<br \/>\nWe know that,<br \/>\nThe distance between 2 points is:<br \/>\nd = \u221a(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2<br \/>\nNow,<br \/>\nThe representation of the given points in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-70563\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-24.png\" alt=\"\" width=\"491\" height=\"504\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-24.png 491w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-24-292x300.png 292w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><br \/>\nNow,<br \/>\nThe distance between AB = \u221a(4 &#8211; 4)\u00b2 + (3 + 2)\u00b2<br \/>\n= \u221a0 + 5\u00b2<br \/>\n= \u221a5\u00b2 = 5<br \/>\nThe distance between CD = \u221a(0 &#8211; 0)\u00b2 + (-2 &#8211; 2)\u00b2<br \/>\n= \u221a0 + 4\u00b2<br \/>\n= \u221a4\u00b2 = 4<br \/>\nSince the distance between \\(\\overline{A B}\\) and \\(\\overline{C D}\\) are not same,<br \/>\n\\(\\overline{A B}\\) is not congruent to \\(\\overline{C D}\\)<br \/>\nHence,<br \/>\n\\(\\overline{A B}\\) \u2260 \\(\\overline{C D}\\)<\/p>\n<p>Question 6.<br \/>\nUse the Segment Addition Postulate to find XZ.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35674\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-40.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 40\" width=\"164\" height=\"91\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35674\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-40.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 40\" width=\"164\" height=\"91\" \/><br \/>\nWe know that,<br \/>\n&#8220;The Segment Addition Postulate&#8221; states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation<br \/>\nAB + BC = AC<br \/>\nSo,<br \/>\nFrom the above figure,<br \/>\nXZ = XY + YZ<br \/>\nXZ = 23 + 50<br \/>\nXZ = 73<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of XZ is: 73<\/p>\n<p>Question 7.<br \/>\nIn the diagram. WY = 30. Can you use the Segment Addition Postulate to find the distance between points W and Z? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35674\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-40.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 40\" width=\"164\" height=\"91\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35674\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-40.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 40\" width=\"164\" height=\"91\" \/><br \/>\nWe know that,<br \/>\n&#8220;The Segment Addition Postulate&#8221; states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation<br \/>\nAB + BC = AC<br \/>\nIt is also given that<br \/>\nWY = 30<br \/>\nNow,<br \/>\nTo find the distance between the points W and Z, we have to use the &#8220;Segment Addition Postulate&#8221;<br \/>\nSo,<br \/>\nWZ = WY + YZ<br \/>\nWZ = 30 + 50<br \/>\nWZ = 80<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance between points W and Z is: 80<\/p>\n<p>Question 8.<br \/>\nUse the diagram at the left to find KL.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35673\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-41.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 41\" width=\"192\" height=\"50\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35673\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-41.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 41\" width=\"192\" height=\"50\" \/><br \/>\nWe know that,<br \/>\nBy using the Segment Addition Postulate,<br \/>\nIf we have three points A, B, and C and we know the distance AB and AC, then the value of AC is given as:<br \/>\nThe total distance (AC) = Segment distance 1 (AB) + Segment distance 2 (BC)<br \/>\nSo,<br \/>\nJL = JK + KL<br \/>\n144 = 37 + KL<br \/>\nKL = 144 &#8211; 37<br \/>\nKL = 107<br \/>\nHence, from the above,<br \/>\nWE can conclude that the value of KL is: 107<\/p>\n<p>Question 9.<br \/>\nThe cities shown on the map lie approximately in a straight line. Find the distance from Albuquerque. New Mexico. to Provo. Utah.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35672\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-42.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 42\" width=\"362\" height=\"265\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-42.png 362w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-42-300x220.png 300w\" sizes=\"(max-width: 362px) 100vw, 362px\" \/><br \/>\nAnswer:<br \/>\nFrom the given map,<br \/>\nIt is given that<br \/>\nThe distance between Albuquerque and Carlsbad is: 231mi<br \/>\nThe distance between Carlsbad and Provo is: 680mi<br \/>\nNow,<br \/>\nLet the distance between Albuquerque and Provo be x<br \/>\nSo,<br \/>\nNow,<br \/>\nBy using the &#8220;Segment Addition Postulate&#8221;,<br \/>\nThe distance between Carlsbad and Provo = (The distance between Albuquerque and Carlsbad) + (The distance between Albuquerque and Provo)<br \/>\n680 = 231 + x<br \/>\nx = 680 &#8211; 231<br \/>\nx = 449<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance between Albuquerque and Provo is: 449 mi<\/p>\n<h3><a id=\"Exercise_1.2_Measuring_and_Constructing_Segments\"><\/a>Exercise 1.2 Measuring and Constructing Segments<\/h3>\n<p>Question 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how \\(\\overline{X Y}\\) and XY arc different.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48082\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 1\" width=\"535\" height=\"76\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-1.png 535w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-1-300x43.png 300w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>DIFFERENT WORDS. SAME QUESTION<\/strong><br \/>\nWhich is different? Find \u201cboth&#8221; answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35671\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-43.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 43\" width=\"267\" height=\"67\" \/><br \/>\nFind AC + CB<br \/>\nFind BC &#8211; AC<br \/>\nFind AB<br \/>\nFind CA + BC.<br \/>\nAnswer:<br \/>\nThe given line segment is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35671\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-43.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 43\" width=\"267\" height=\"67\" \/><br \/>\nFrom the given line segment,<br \/>\nAC = 3 and CB = 7<br \/>\nNow,<br \/>\na.<br \/>\nAC + CB =3 + 7 = 10<br \/>\nb.<br \/>\nBC &#8211; AC = 7 &#8211; 3 = 4<br \/>\nc.<br \/>\nAB = AC + CB (By using the Segment Addition Postulate)<br \/>\nSo,<br \/>\nAB = 3 + 7 = 10<br \/>\nd.<br \/>\nCA + BC = 3 + 7 = 10<br \/>\nHence, from the above,<br \/>\nWe can conclude that the expressions a, c, and d are the same<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3 &#8211; 6, use a ruler to measure the length of the segment to the nearest tenth of a centimeter.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35670\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-44.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 44\" width=\"176\" height=\"26\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48083\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 3\" width=\"112\" height=\"26\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35669\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-45.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 45\" width=\"297\" height=\"22\" \/><br \/>\nAnswer:<br \/>\nThe length of the given line segment in cm is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-70768\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-25.png\" alt=\"\" width=\"290\" height=\"36\" \/><\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35668\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-46.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 46\" width=\"231\" height=\"28\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48084\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 5\" width=\"106\" height=\"24\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35666\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-47.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 47\" width=\"340\" height=\"29\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-47.png 340w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-47-300x26.png 300w\" sizes=\"(max-width: 340px) 100vw, 340px\" \/><br \/>\nAnswer:<br \/>\nThe length of the given line segment is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-70769\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-26.png\" alt=\"\" width=\"328\" height=\"32\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-26.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-26-300x29.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><\/p>\n<p><strong>CONSTRUCTION<\/strong><br \/>\nIn Exercises 7 and 8. use a compass and straightedge to construct a copy of the segment.<br \/>\nQuestion 7.<br \/>\nCopy the segment in Exercise 3.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48085\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-7.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 7\" width=\"584\" height=\"332\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-7.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-7-300x171.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 8.<br \/>\nCopy the segment in Exercise 4.<br \/>\nAnswer:<br \/>\nUsing a straightedge, draw a ray where the left endpoint will be the beginning of the segment.<br \/>\nWith a compass, measure the segment in Exercise 4 by placing the point of the compass on the segment endpoint on the left and the pencil point on the segment endpoint on the right<br \/>\nWithout changing the compass setting, place the point of the compass on the endpoint on the left of the ray you drew and mark the ray with an arc<br \/>\nWhere the arc and ray intersect is the right endpoint of the segment in Exercise 4.<br \/>\nHence,<br \/>\nThe segment in Exercise 4 is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35669\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-45.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 45\" width=\"297\" height=\"22\" \/><\/p>\n<p>In Exercises 9 &#8211; 14, plot the points in a coordinate plane. Then determine whether \\(\\overline{A B}\\) and \\(\\overline{C D}\\) are congruent.<br \/>\nQuestion 9.<br \/>\nA(- 4, 5), B(- 4, 8), C(2, &#8211; 3), D(2, 0)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48086\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-9.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 9\" width=\"495\" height=\"331\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-9.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-9-300x201.png 300w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><\/p>\n<p>Question 10.<br \/>\nA(6, &#8211; 1), B(1, &#8211; 1), C(2, &#8211; 3), D(4, &#8211; 3)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nA (6, -1), B (1, -1), C (2, -3), and D (4, -3)<br \/>\nLet the points be represented as:<br \/>\nA (x1, y1), B (x2, y2), C (x3, y3), and D (x4, y4)<br \/>\nWe know that,<br \/>\nThe distance between points A and B is:<br \/>\nD = \u221a(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2<br \/>\nSo,<br \/>\n\\(\\overline{A B}\\) = \u221a(1 &#8211; 6)\u00b2 + (-1 + 1)\u00b2<br \/>\n= \u221a(-5)\u00b2<br \/>\n= 5<br \/>\nThe distance between points C and D is:<br \/>\n\\(\\overline{C D}\\) = \u221a(x4 &#8211; x3)\u00b2 + (y4 &#8211; y3)\u00b2<br \/>\n= \u221a(4 &#8211; 2)\u00b2 + (-3 + 3)\u00b2<br \/>\n= \u221a2\u00b2<br \/>\n= 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\overline{A B}\\) is not congruent with \\(\\overline{C D}\\)<br \/>\nThe representation of the given points in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-70771\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-27.png\" alt=\"\" width=\"484\" height=\"498\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-27.png 484w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-27-292x300.png 292w\" sizes=\"(max-width: 484px) 100vw, 484px\" \/><\/p>\n<p>Question 11.<br \/>\nA(8, 3), B(- 1, 3), C(5, 10), D(5, 3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48087\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-11.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 11\" width=\"327\" height=\"433\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-11.png 327w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-11-227x300.png 227w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><\/p>\n<p>Question 12.<br \/>\nA(6, &#8211; 8), B(6, 1), C(7, &#8211; 2), D(- 2, &#8211; 2)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nA (6, -8), B (6, 1), C (7, -2), and D (-2, -2)<br \/>\nLet the points be represented as:<br \/>\nA (x1, y1), B (x2, y2), C (x3, y3), and D (x4, y4)<br \/>\nWe know that,<br \/>\nThe distance between points A and B is:<br \/>\nD = \u221a(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2<br \/>\nSo,<br \/>\n\\(\\overline{A B}\\) = \u221a(6 &#8211; 6)\u00b2 + (8 + 1)\u00b2<br \/>\n= \u221a(9)\u00b2<br \/>\n= 9<br \/>\nThe distance between points C and D is:<br \/>\n\\(\\overline{C D}\\) = \u221a(x4 &#8211; x3)\u00b2 + (y4 &#8211; y3)\u00b2<br \/>\n= \u221a(-7 &#8211; 2)\u00b2 + (-2 + 2)\u00b2<br \/>\n= \u221a(-9)\u00b2<br \/>\n= 9<br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\overline{A B}\\) is congruent with \\(\\overline{C D}\\)<br \/>\nThe representation of the given points in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-70772\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-28.png\" alt=\"\" width=\"487\" height=\"506\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-28.png 487w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-28-289x300.png 289w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><\/p>\n<p>Question 13.<br \/>\nA(- 5, 6), B(- 5, &#8211; 1), C(- 4, 3), D(3, 3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48088\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-13.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 13\" width=\"484\" height=\"261\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-13.png 484w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-13-300x162.png 300w\" sizes=\"(max-width: 484px) 100vw, 484px\" \/><\/p>\n<p>Question 14.<br \/>\nA(10, &#8211; 4), B(3, &#8211; 4), C(- 1, 2), D(- 1, 5)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nA (10, -4), B (3, -4), C (-1, 2), and D (-1, 5)<br \/>\nLet the points be represented as:<br \/>\nA (x1, y1), B (x2, y2), C (x3, y3), and D (x4, y4)<br \/>\nWe know that,<br \/>\nThe distance between points A and B is:<br \/>\nD = \u221a(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2<br \/>\nSo,<br \/>\n\\(\\overline{A B}\\) = \u221a(3 &#8211; 10)\u00b2 + (-4 + 4)\u00b2<br \/>\n= \u221a(-7)\u00b2<br \/>\n= 7<br \/>\nThe distance between points C and D is:<br \/>\n\\(\\overline{C D}\\) = \u221a(x4 &#8211; x3)\u00b2 + (y4 &#8211; y3)\u00b2<br \/>\n= \u221a(1 &#8211; 1)\u00b2 + (-2 + 5)\u00b2<br \/>\n= \u221a3\u00b2<br \/>\n= 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\overline{A B}\\) is not congruent with \\(\\overline{C D}\\)<br \/>\nThe representation of the given points in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-70773\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-29.png\" alt=\"\" width=\"495\" height=\"503\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-29.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-29-295x300.png 295w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><\/p>\n<p>In Exercises 15 &#8211; 22. find FH.<br \/>\nQuestion 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35665\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-48.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 48\" width=\"258\" height=\"105\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48089\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-15.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 15\" width=\"177\" height=\"102\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35663\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-49.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 49\" width=\"254\" height=\"94\" \/><br \/>\nAnswer:<br \/>\nThe given line segment is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35663\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-49.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 49\" width=\"254\" height=\"94\" \/><br \/>\nBy using the Segment Addition Postulate,<br \/>\nFH = FG + GH<br \/>\nFH = 19 + 7<br \/>\nFH = 26<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of FH is: 26<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35662\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-50.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 50\" width=\"249\" height=\"80\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48090\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-17.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 17\" width=\"192\" height=\"99\" \/><\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35661\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-51.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 51\" width=\"238\" height=\"114\" \/><br \/>\nAnswer:<br \/>\nThe given line segment is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35661\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-51.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 51\" width=\"238\" height=\"114\" \/><br \/>\nBy using the Segment Addition Postulate,<br \/>\nFH = FG + GH<br \/>\nFH = 4 + 15<br \/>\nFH = 19<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of FH is: 19<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35660\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-52.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 52\" width=\"253\" height=\"87\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48091\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-19.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 19\" width=\"184\" height=\"97\" \/><\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35659\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-53.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 53\" width=\"252\" height=\"56\" \/><br \/>\nAnswer:<br \/>\nThe given line segment is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35659\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-53.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 53\" width=\"252\" height=\"56\" \/><br \/>\nBy using the Segment Addition Postulate,<br \/>\nFG = FH + HG<br \/>\nFG = FH + 15<br \/>\n22 = FH + 15<br \/>\nFH = 22 &#8211; 15<br \/>\nFH = 7<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of FH is: 7<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35658\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-54.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 54\" width=\"236\" height=\"139\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48092\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-21.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 21\" width=\"176\" height=\"98\" \/><\/p>\n<p>Question 22.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35657\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-55.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 55\" width=\"227\" height=\"151\" \/><br \/>\nAnswer:<br \/>\nThe given line segment is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35657\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-55.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 55\" width=\"227\" height=\"151\" \/><br \/>\nBy using the Segment Addition Postulate,<br \/>\nFG = FH + HG<br \/>\n53 = FH + 40<br \/>\nFH = 53 &#8211; 40<br \/>\nFH = 13<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of FH is: 13<\/p>\n<p><strong>ERROR ANALYSIS<\/strong><br \/>\nIn Exercises 23 and 24, describe and correct the error in finding the length of \\(\\overline{A B}\\).<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-35656\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-56.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 56\" width=\"306\" height=\"74\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-56.png 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-56-300x73.png 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35655\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-57.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 57\" width=\"314\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-57.png 314w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-57-300x83.png 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48093\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-23.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 23\" width=\"405\" height=\"65\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-23.png 405w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-23-300x48.png 300w\" sizes=\"(max-width: 405px) 100vw, 405px\" \/><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35654\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-58.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 58\" width=\"316\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-58.png 316w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-58-300x85.png 300w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\n| -x | = x for x &gt; 0<br \/>\nSo,<br \/>\nThe distance between points A and B is:<br \/>\n| AB| = | 1 &#8211; 4.5| or | 4.5 &#8211; 1|<br \/>\nHence,<br \/>\n| AB | = 3.5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance between the points A and B is: 3.5<\/p>\n<p>Question 25.<br \/>\n<strong>ATTENDING TO PRECISION<\/strong><br \/>\nThe diagram shows an insect called a walking stick. Use the ruler to estimate the length of the abdomen and the length of the thorax to the nearest \\(\\frac{1}{4}\\) inch. How much longer is the walking stick\u2019s abdomen than its thorax? How many times longer is its abdomen than its thorax?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35653\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-59.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 59\" width=\"338\" height=\"170\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-59.png 338w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-59-300x151.png 300w\" sizes=\"(max-width: 338px) 100vw, 338px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48094\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-25.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 25\" width=\"547\" height=\"251\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-25.png 547w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-25-300x138.png 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nIn 2003, a remote-controlled model airplane became the first-ever to fly nonstop across the Atlantic Ocean. The map shows the airplane\u2019s position at three different points during its flight. Point A represents Cape Spear. New foundland. point B represents the approximate position after 1 day, and point C represents Mannin Bay\u2019 Ireland. The airplane left Cape Spear and landed in Mannin Bay.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35652\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-60.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 60\" width=\"394\" height=\"157\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-60.png 394w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-60-300x120.png 300w\" sizes=\"(max-width: 394px) 100vw, 394px\" \/><br \/>\na. Find the total distance the model airplane flew.<br \/>\nAnswer:<br \/>\nIt is given that a remote-controlled airplane flies from Cape Spear to Mannin Bay that is located across the Atlantic Ocean<br \/>\nNow,<br \/>\nThe total distance traveled by the model airplane is represented as the total distance from A to C on the map<br \/>\nNow,<br \/>\nFrom the map,<br \/>\nAC represents the total distance traveled by the model airplane<br \/>\nAB represents the distance traveled by model airplane from Cape Spear and it is in flight mode after 1 day and it represents as B<br \/>\nBC represents the distance traveled from the middle of the flight to Mannin Bay<br \/>\nSo,<br \/>\nNow,<br \/>\nBy using the Segment Addition Postulate,<br \/>\nAC = AB + BC<br \/>\nSo,<br \/>\nAC = 1281 miles + 601 miles<br \/>\nAC = 1881 miles<br \/>\nHence, from the above,<br \/>\nWe can conclude that the total distance traveled by the model airplane is: 1881 miles<\/p>\n<p>b. The model airplane\u2019s flight lasted nearly 38 hours. Estimate the airplane\u2019s average speed in miles per hour.<br \/>\nAnswer:<br \/>\nFrom part (a),<br \/>\nWe observed that,<br \/>\nThe total distance traveled by the model airplane is: 1881 miles<br \/>\nIt is given that<br \/>\nThe model airplane&#8217;s flight lasted nearly 38 hours<br \/>\nWe know that,<br \/>\nAverage speed = \\(\\frac{Total distance}{Total time}\\)<br \/>\nSo,<br \/>\nAverage speed = \\(\\frac{1881}{38}\\)<br \/>\n= 49.5 miles per hour<br \/>\nHence, from the above,<br \/>\nWe can conclude that the average speed of the airplane is: 49.5 miles per hour<\/p>\n<p>Question 27.<br \/>\n<strong>USING STRUCTURE<\/strong><br \/>\nDetermine whether the statements are true or False. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35651\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-61.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 61\" width=\"268\" height=\"135\" \/><br \/>\na. B is between A and C.<br \/>\nb. C is between B and E.<br \/>\nc. D is between A and H.<br \/>\nd. E is between C and F.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48095\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-27.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 27\" width=\"369\" height=\"140\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-27.png 369w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-27-300x114.png 300w\" sizes=\"(max-width: 369px) 100vw, 369px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nWrite an expression for the length of the segment.<br \/>\na. \\(\\overline{A C}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35650\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-62.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 62\" width=\"227\" height=\"38\" \/><br \/>\nAnswer:<br \/>\nThe given line segment is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35650\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-62.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 62\" width=\"227\" height=\"38\" \/><br \/>\nSo,<br \/>\nBy using the Segment Addition Postulate,<br \/>\n\\(\\overline{A C}\\) = \\(\\overline{A B}\\) + \\(\\overline{B C}\\)<br \/>\n\\(\\overline{A C}\\) = (x + 2) + (7x &#8211; 3)<br \/>\n\\(\\overline{A C}\\) = 8x &#8211; 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the expression of the given line segment is: (8x &#8211; 1)<\/p>\n<p>b. \\(\\overline{Q R}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35649\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-63.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 63\" width=\"234\" height=\"54\" \/><br \/>\nAnswer:<br \/>\nThe given line segment is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35649\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-63.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 63\" width=\"234\" height=\"54\" \/><br \/>\nSo,<br \/>\nBy using the Segment Addition Postulate,<br \/>\n\\(\\overline{P R}\\) = \\(\\overline{P Q}\\) + \\(\\overline{Q R}\\)<br \/>\n13y + 25 = (8y + 5) + \\(\\overline{Q R}\\)<br \/>\n\\(\\overline{Q R}\\) = 13y + 25 &#8211; 8y &#8211; 5<br \/>\n\\(\\overline{Q R}\\) = 5y + 20<br \/>\nHence, from the above,<br \/>\nWe can conclude that the expression of the given line segment is: (5y + 20)<\/p>\n<p>Question 29.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nPoint S is between points R and T on \\(\\overline{R T}\\). Use the information to write an equation in term of x. Then Solve the equation and find RS, ST, and RT.<br \/>\na. RS = 2x + 10<br \/>\nST = x &#8211; 4<br \/>\nRT = 21<\/p>\n<p>b. RS = 3x &#8211; 16<br \/>\nST = 4x &#8211; 8<br \/>\nRT = 60<\/p>\n<p>c. RS = 4x &#8211; 9<br \/>\nST=11<br \/>\nRTx+IO<\/p>\n<p>d. RS = 4x &#8211; 9<br \/>\nST = 19<br \/>\nRT = 8x &#8211; 14<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48096\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-29.1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 29.1\" width=\"524\" height=\"518\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-29.1.png 524w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-29.1-300x297.png 300w\" sizes=\"(max-width: 524px) 100vw, 524px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48097\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-29.2.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 29.2\" width=\"529\" height=\"413\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-29.2.png 529w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-29.2-300x234.png 300w\" sizes=\"(max-width: 529px) 100vw, 529px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nIs it possible to design a table where no two legs have the same length? Assume that the endpoints of the legs must all lie in the same plane. Include a diagram as part o! your answer.<br \/>\nAnswer:<br \/>\nIt is possible to design a table where no two legs have the same length and that the endpoints of the legs all lie in the same plane. They just have to be attached to the table at different angles as seen in the below figure:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-70810\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-30.png\" alt=\"\" width=\"545\" height=\"225\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-30.png 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-30-300x124.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Question 31.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou have w walk from Room 103 to Room 117.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35648\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-64.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 64\" width=\"336\" height=\"146\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-64.png 336w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-64-300x130.png 300w\" sizes=\"(max-width: 336px) 100vw, 336px\" \/><br \/>\na. How many feet do you travel from Room 103 to Room 117?<br \/>\nb. You can walk 4.4 feet per second. How many minutes will it take you to get to Room 117?<br \/>\nc. Why might it take you longer than the time in Part (b)?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48098\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-31.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 31\" width=\"529\" height=\"121\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-31.png 529w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-31-300x69.png 300w\" sizes=\"(max-width: 529px) 100vw, 529px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend and your Cousin discuss measuring with a ruler. Your friend says that you must always line up objects at the zero on a ruler. Your cousin says it does not matter. Decide who is correct and explain your reasoning.<br \/>\nAnswer:<br \/>\nYour cousin is correct<\/p>\n<p>Explanation:<br \/>\nIt is given that,<br \/>\nYour friend said that you must always line up objects at the zero on a ruler and your cousin said that it does not matter<br \/>\nNow,<br \/>\nWe just have to deduce the endpoint length from the start point length on the ruler<br \/>\nExample:<br \/>\nIf you measure a segment that is 5 cm long, it is the same if you put zero on the start point or 5 on the start point, then 10 is on the endpoint<br \/>\nRemember that the starting point will be any number on the ruler and the ending point will be n units away from that number<br \/>\nSo,<br \/>\n5 &#8211; 0 = 5 is same as 10 &#8211; 5 = 5<\/p>\n<p>Question 33.<br \/>\n<strong>REASONING<\/strong><br \/>\nYou travel twin City X to City Y. You know that the round-trip distance is 647 miles. City Z, a city you pass on the way, is 27 miles from City X. Find the distance from City Z to City Y. Justify your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48099\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-33.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 33\" width=\"320\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-33.png 320w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-33-300x198.png 300w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe bar graph shows the win-loss record for a lacrosse team over a period of three years. Explain how you can apply the Ruler Postulate (Post. 1.1) and the Segment Addition Postulate (Post. 1.2) when interpreting a stacked bar graph like the one shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35647\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-65.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 65\" width=\"294\" height=\"200\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nRuler Postulate:<br \/>\nThe points on a line can be put into a one-to-one correspondence (paired) with the real numbers. The distance between any two points is represented by the absolute value of the difference between the numbers.<br \/>\nSegment Addition Postulate:<br \/>\nThe Segment Addition Postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation<br \/>\nAB + BC = AC<br \/>\nHence,<br \/>\nBy using the ruler and Segment Addition Postulates,<br \/>\nWe can conclude that the number of games is equal to the number of wins and the number of losses<\/p>\n<p>Question 35.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nThe points (a,b) and (c, b) from a segment, and the points (d, e) and (d, f ) from a segment. Create an equation assuming the segments are congruent. Are there any letters not used in the equation? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48100\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-35.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 35\" width=\"579\" height=\"232\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-35.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-35-300x120.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nIn the diagram, \\(\\overline{A B}\\) \u2245 \\(\\overline{B C}\\), \\(\\overline{A C}\\) \u2245 \\(\\overline{C D}\\), and AD = 12. Find the lengths of all segments in the diagram. Suppose you choose one of the segments at random. What is the probability that the measure of the segment is greater than 3? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35646\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-66.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 66\" width=\"220\" height=\"66\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35646\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-66.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 66\" width=\"220\" height=\"66\" \/><br \/>\nIt is given that,<br \/>\n\\(\\overline{A B}\\) \u2245 \\(\\overline{B C}\\)<br \/>\n\\(\\overline{A C}\\) \u2245 \\(\\overline{C D}\\)<br \/>\n\\(\\overline{A D}\\) = 12<br \/>\nNow,<br \/>\nBy using the Segment Addition Postulate,<br \/>\nAD = AB + BC + CD<br \/>\n12 = AB + BC + CD<br \/>\nNow,<br \/>\nAD = AC + CD<br \/>\nAD = 2CD<br \/>\nCD = \\(\\frac{12}{2}\\)<br \/>\nCD = 6<br \/>\nSo,<br \/>\nAC = 6<br \/>\nNow,<br \/>\nFro the given line segment,<br \/>\nAC = AB + BC<br \/>\nAC = 2BC<br \/>\nBC = \\(\\frac{6}{2}\\)<br \/>\nBC = 3<br \/>\nHenc,<br \/>\nAB = 3<br \/>\nNow,<br \/>\nWe know that,<br \/>\nProbability = \\(\\frac{The number of favorable cases}{The total number of cases}\\)<br \/>\nSo,<br \/>\nThe probability of getting the segment that the length is greater than 3 is:<br \/>\nP = \\(\\frac{The number of segments that the length is greater than 3}{The number of total segments}\\)<br \/>\nP = 3 \/ 6<br \/>\nP = 0.5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the probability of getting the length of the line segments greater than 3 is: 0.5<\/p>\n<p>Question 37.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nIs it possible to use the Segment Addition Postulate (Post. 1.2) to show FB &gt; CB or that AC &gt; DB? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35645\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-67.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 67\" width=\"308\" height=\"38\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-67.png 308w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-67-300x37.png 300w\" sizes=\"(max-width: 308px) 100vw, 308px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48101\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-37.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 37\" width=\"577\" height=\"201\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-37.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-37-300x105.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Maintaining Mathematical Proficiency<\/p>\n<p>Simplify.<\/p>\n<p>Question 38.<br \/>\n\\(\\frac{-4+6}{2}\\)<br \/>\nAnswer:<br \/>\nThe given expression is: \\(\\frac{-6 + 4}{2}\\)<br \/>\nSo,<br \/>\n\\(\\frac{-4+6}{2}\\) = \\(\\frac{2}{2}\\)<br \/>\n= \\(\\frac{1}{1}\\)<br \/>\n= 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the given expression is: 1<\/p>\n<p>Question 39.<br \/>\n\\(\\sqrt{20+5}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48102\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-39.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 39\" width=\"231\" height=\"31\" \/><\/p>\n<p>Question 40.<br \/>\n\\(\\sqrt{25+9}\\)<br \/>\nAnswer:<br \/>\nThe given expression is: \\(\\sqrt{25 + 9}\\)<br \/>\nSo,<br \/>\n\\(\\sqrt{25+9}\\) = \\(\\sqrt{34}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the given expression is: \\(\\sqrt{34}\\)<\/p>\n<p>Question 41.<br \/>\n\\(\\frac{7+6}{2}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48103\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-41.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 41\" width=\"144\" height=\"55\" \/><\/p>\n<p>Solve the equation.<\/p>\n<p>Question 42.<br \/>\n5x + 7 = 9x &#8211; 17<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n5x + 7 = 9x &#8211; 17<br \/>\nSo,<br \/>\n5x &#8211; 9x = -17 &#8211; 7<br \/>\n-4x = -24<br \/>\n4x = 24<br \/>\nx = \\(\\frac{24}{4}[\/larex]<br \/>\nx = 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x for the given equation is: 6<\/p>\n<p>Question 43.<br \/>\n[latex]\\frac{3+y}{2}=6\\) = 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48104\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-43.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 43\" width=\"134\" height=\"120\" \/><\/p>\n<p>Question 44.<br \/>\n\\(\\frac{-5+x}{2}\\) = &#8211; 9<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n\\(\\frac{-5+x}{2}\\) = &#8211; 9<br \/>\nSo,<br \/>\n-5 + x = -9 (2)<br \/>\n-5 + x = -18<br \/>\nx = -18 + 5<br \/>\nx = -13<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x for the given equation is: -13<\/p>\n<p>Question 45.<br \/>\n&#8211; 6x &#8211; 13 = &#8211; x = 23<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48105\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-1.2-a-45.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 1.2 a 45\" width=\"228\" height=\"131\" \/><\/p>\n<h3><a id=\"1.3_Using_Midpoint_and_Distance_Formulas\"><\/a>1.3 Using Midpoint and Distance Formulas<\/h3>\n<p>EssentiaI Question<br \/>\nHow can you find the midpoint and length of a line segment in a coordinate plane?<br \/>\nAnswer:<br \/>\nLet the line segment is formed by the points A (x1, y1), B (x2, y2)<br \/>\nSo,<br \/>\nThe coordinates of the midpoint of the line segment are given as:<br \/>\nM = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nThe length of the line segment in a coordinate plane is given as:<br \/>\nD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<\/p>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Finding the Midpoint of a Line Segment<\/p>\n<p>Work with a partner.<\/p>\n<p>Use centimeter graph paper.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35644\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-68.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 68\" width=\"246\" height=\"249\" \/><br \/>\na.\u00a0 Graph \\(\\overline{A B}\\), where the points A and B are as shown.<br \/>\nAnswer:<br \/>\nFrom the given graph,<br \/>\nThe given points are:<br \/>\nA (3, 4), B (-5, -2)<br \/>\nCompare the given points with<br \/>\nA (x1, y1), B (x2, y2)<br \/>\nSo,<br \/>\nThe distance between points A and B is given as:<br \/>\nD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nD = \\(\\sqrt{(-5 &#8211; 3)\u00b2 + (-2 &#8211; 4)\u00b2}\\)<br \/>\nD = \\(\\sqrt{(-8)\u00b2 + (-6)\u00b2}\\)<br \/>\nD = \\(\\sqrt{64 + 36}\\)<br \/>\nD = \\(\\sqrt{100}\\)<br \/>\nD = 10 cm<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of \\(\\overline{A B}\\) is: 10cm<br \/>\nThe representation of \\(\\overline{A B}\\) is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-71140\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-31.png\" alt=\"\" width=\"524\" height=\"53\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-31.png 524w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-31-300x30.png 300w\" sizes=\"(max-width: 524px) 100vw, 524px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>b. Explain how to bisect \\(\\overline{A B}\\), that is, to divide AB into two congruent line segments. Then<br \/>\nbisects \\(\\overline{A B}\\) and use the result to find the midpoint M of \\(\\overline{A B}\\).<br \/>\nAnswer:<br \/>\nThe steps to find the bisector of \\(\\overline{A B}\\) is:<br \/>\na. Place the compass at one end of the line segment<br \/>\nb. Adjust the compass to slightly longer than half of the line segment length<br \/>\nc. Draw arcs above and below the line<br \/>\nd. Keeping the same compass width, draw arcs from the other end of line<br \/>\ne. Place ruler where the arcs cross and draw the line segment<br \/>\nNow,<br \/>\nFrom part (a),<br \/>\nThe representation of \\(\\overline{A B}\\) is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-71140\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-31.png\" alt=\"\" width=\"524\" height=\"53\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-31.png 524w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-31-300x30.png 300w\" sizes=\"(max-width: 524px) 100vw, 524px\" \/><br \/>\nNow,<br \/>\nThe representation of the perpendicular bisector and the midpoint M of \\(\\overline{A B}\\) is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-71185\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-32.png\" alt=\"\" width=\"544\" height=\"149\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-32.png 544w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-32-300x82.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><br \/>\nHence, from the above figure,<br \/>\nThe midpoint of \\(\\overline{A B}\\) is: 5 cm<\/p>\n<p>c. What are the coordinates of the midpoint M?<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe coordinates of the midpoint of the line segment are given as:<br \/>\nM = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nSo,<br \/>\nM = (\\(\\frac{3 &#8211; 5}{2}\\),\\(\\frac{4 &#8211; 2}{2}\\))<br \/>\nM = (\\(\\frac{-2}{2}\\),\\(\\frac{2}{2}\\))<br \/>\nM = (-1, 1)<br \/>\nHence,<br \/>\nThe coordinates of the midpoint M is: (-1, 1)<\/p>\n<p>d. Compare the x-coordinates of A, B, and M. Compare the y-coordinates of A, B, and M. How arc the coordinates of the 4 midpoints M related to the coordinates of A and B?<br \/>\nAnswer:<br \/>\nThe coordinates of A, B, and M are:<br \/>\nA (3, 4), B (-5, -2), and M (-1, 1)<br \/>\nCompare the given coordinates with<br \/>\nA (x1, y1), B (x2, y2), C (x3, y3)<br \/>\nHence,<br \/>\nThe x-coordinates and y-coordinates of M are related to the coordinates of A and B are:<br \/>\nM= (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}[\/latex}<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Finding the Length of a Line Segment work with a partner. Use centimeter graph paper.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35642\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-70.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 70\" width=\"295\" height=\"293\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-70.png 295w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-70-150x150.png 150w\" sizes=\"(max-width: 295px) 100vw, 295px\" \/><br \/>\na. Add point C to your graph as shown.<br \/>\nAnswer:<br \/>\nFrom the graph,<br \/>\nThe given points are:<br \/>\nA (3, 4), B (-5, -2), and C (3, 2)<br \/>\nCompare the given points with<br \/>\nA (x1, y1), B (x2, y2), and C (x3, y3)<br \/>\nSo,<br \/>\nThe coordinates of the length between points A and B is:<br \/>\nD = ( |x2 + x1|, |y2 + y1| )<br \/>\nSo,<br \/>\nD = ( |-5 + 3|, |-2 + 4| )<br \/>\nD = ( |-2|, |2| )<br \/>\nD = (-2, 2)<br \/>\nNow,<br \/>\nThe length between AB and C is:<br \/>\nD = ( |x2 + x1|, |y2 + y1| )<br \/>\nSo,<br \/>\nD = ( |-2 + 3|, |2 + 3| )<br \/>\nD = ( |1|, |5| )<br \/>\nD = ( 1, 5)<br \/>\nHence, frm the above,<br \/>\nWe can conclude that the coordinates of the total length by adding point C is: (1, 5)<\/p>\n<p>b. Use the Pythagorean Theorem to find the length of AB.<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nA (3, 4), B (-5, -2), and C (3, 2)<br \/>\nCompare the given points with<br \/>\nA (x1, y1), B (x2, y2), and C (x3, y3)<br \/>\nWe know that,<br \/>\nThe length of a segment is:<br \/>\nD = [latex]\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nSo,<br \/>\n\\(\\overline{B C}\\) = \\(\\sqrt{(-5 + 3)\u00b2 + (-2 + 2)\u00b2}\\)<br \/>\n= \\(\\sqrt{(-2)\u00b2 + (0)\u00b2}\\)<br \/>\n= \\(\\sqrt{4 + 0}\\)<br \/>\n=\\(\\sqrt{4}\\) = 2<br \/>\n\\(\\overline{A C}\\) = \\(\\sqrt{(-3 + 3)\u00b2 + (-2 + 4)\u00b2}\\)<br \/>\n= \\(\\sqrt{0\u00b2 + 2\u00b2}\\)<br \/>\n= \\(\\sqrt{2\u00b2}\\) = 2<br \/>\nNow,<br \/>\nAccording to Pythagoras theorem,<br \/>\nHypotenuse\u00b2 = Side\u00b2 + Side\u00b2<br \/>\nSo,<br \/>\nFrom the graph,<br \/>\nAB represents the hypotenuse<br \/>\nAC represents the side<br \/>\nBC represents the side<br \/>\nSo,<br \/>\nAB\u00b2 = AC\u00b2 + BC\u00b2<br \/>\nAB\u00b2 = 2\u00b2 + 2\u00b2<br \/>\nAB\u00b2 = 4 + 4<br \/>\nAB\u00b2 = 8<br \/>\nAB = \\(\\sqrt{8}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of AB is: \\(\\sqrt{8}\\)<\/p>\n<p>c. Use a centimeter ruler to verify the length you found in part (b).<br \/>\n<strong>MAKING SENSE OF PROBLEMS<\/strong><br \/>\nTo be proficient in math, you need to check your answers and continually ask yourself, \u201cDoes this make sense?\u2019<br \/>\nAnswer:<br \/>\nFrom part (b),<br \/>\nWe found the length of \\(\\overline{A B}\\) as: \\(\\sqrt{8}\\)<br \/>\nNow,<br \/>\nTo verify the length of \\(\\overline{A B}\\), use the &#8220;Distance formula&#8221;<br \/>\nWe know that,<br \/>\nThe distance beween 2 points of a line segment is given as:<br \/>\nD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nSo,<br \/>\n\\(\\overline{A B}\\) = \\(\\sqrt{(-5 + 3)\u00b2 + (-2 + 4)\u00b2}\\)<br \/>\n= \\(\\sqrt{(-2)\u00b2 + (2)\u00b2}\\)<br \/>\n= \\(\\sqrt{4 + 4}\\)<br \/>\n=\\(\\sqrt{8}\\)<\/p>\n<p>d. Use the Pythagorean Theorem and point M from Exploration 1 to find the lengths of \\(\\overline{A M}\\) and \\(\\overline{M B}\\). What can you conclude?<br \/>\nAnswer:<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 3.<br \/>\nHow can you find the midpoint and length ola line segment in a coordinate plane?<br \/>\nAnswer:<br \/>\nLet the line segment is formed by the points A (x1, y1), B (x2, y2)<br \/>\nSo,<br \/>\nThe coordinates of the midpoint of the line segment are given as:<br \/>\nM = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nThe length of the line segment in a coordinate plane is given as:<br \/>\nD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<\/p>\n<p>Question 4.<br \/>\nFind the coordinates of the midpoint M and the length of the line segment whose endpoints are given.<br \/>\na. D(- 10, &#8211; 4), E(14, 6)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nD (-10, -4), E (14, 6)<br \/>\nWe know that,<br \/>\nThe coordinates of the midpoint of the line segment are given as:<br \/>\nM = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nSo,<br \/>\nM = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nM = (\\(\\frac{14 &#8211; 10}{2}\\), \\(\\frac{6 &#8211; 4}{2}\\))<br \/>\nM = (\\(\\frac{4}{2}\\), \\(\\frac{2}{2}\\))<br \/>\nM = (2, 1)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the coordinates of the midpoint of the given points are: (2, 1)<\/p>\n<p>b. F(- 4, 8), G(9, 0)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nF (-4, 8), G (9, 0)<br \/>\nWe know that,<br \/>\nM = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nSo,<br \/>\nM = (\\(\\frac{9 &#8211; 4}{2}\\), \\(\\frac{8 + 0}{2}\\))<br \/>\nM = (\\(\\frac{5}{2}\\), \\(\\frac{8}{2}\\))<br \/>\nM = (\\(\\frac{5}{2}\\), 4)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the coordinates of the midpoint of the given points are: (\\(\\frac{5}{2}\\), 4)<\/p>\n<h3><a id=\"Lesson_1.3_Using_Midpoint_and_Distance_Formulas\"><\/a>Lesson 1.3 Using Midpoint and Distance Formulas<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Identify the segment, bisector of \\(\\overline{P Q}\\). Then find PQ.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35641\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-71.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 71\" width=\"173\" height=\"77\" \/><br \/>\nAnswer:<br \/>\nThe given line segment is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35641\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-71.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 71\" width=\"173\" height=\"77\" \/><br \/>\nWe know that,<br \/>\nA segment has a starting point and an ending point<br \/>\nSo,<br \/>\nFrom the above figure,<br \/>\nWe can observe that<br \/>\n\\(\\overline{P Q}\\) is a &#8220;Segment&#8221;<br \/>\nWe know that,<br \/>\nA &#8220;Bisector&#8221; is a line that divides a line segment into two congruent (or) equal parts<br \/>\nSo,<br \/>\nFrom the above figure,<br \/>\nWe can observe that<br \/>\nThe bisector of \\(\\overline{P Q}\\) is: MN<br \/>\nNow,<br \/>\nFrom the above figure,<br \/>\nThe bisector divided the given line segment into 2 equal parts and given the length of 1 part<br \/>\nSo,<br \/>\nIt is given that,<br \/>\n\\(\\overline{P M}\\) = 1\\(\\frac{7}{8}\\)<br \/>\nHence,<br \/>\nThe length of \\(\\overline{P Q}\\) = \\(\\overline{P M}\\) + \\(\\overline{M Q}\\)<br \/>\n= 2 \u00d7 1\\(\\frac{7}{8}\\)<br \/>\n= 2 \u00d7 \\(\\frac{15}{8}\\)<br \/>\n= \\(\\frac{2}{1}\\) \u00d7 \\(\\frac{15}{8}\\)<br \/>\n= \\(\\frac{15}{4}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of \\(\\overline{p Q} \\) is: \\(\\frac{15}{4}\\)<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35640\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-72.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 72\" width=\"172\" height=\"47\" \/><br \/>\nAnswer:<br \/>\nThe given line segment is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35640\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-72.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 72\" width=\"172\" height=\"47\" \/><br \/>\nWe know that,<br \/>\nA segment has a starting point and an ending point<br \/>\nSo,<br \/>\nFrom the above figure,<br \/>\nWe can observe that<br \/>\n\\(\\overline{P Q}\\) is a &#8220;Segment&#8221;<br \/>\nWe know that,<br \/>\nA &#8220;Bisector&#8221; is a line that divides a line segment into two congruent (or) equal parts<br \/>\nSo,<br \/>\nFrom the above figure,<br \/>\nWe can observe that<br \/>\nThe bisector of \\(\\overline{P Q}\\) is: M<br \/>\nNow,<br \/>\nFrom the above figure,<br \/>\nThe bisector divided the given line segment into 2 equal parts and given the length of 1 part<br \/>\nSo,<br \/>\nIt is given that,<br \/>\n\\(\\overline{M Q}\\) = 2\\(\\frac{2}{7}\\)<br \/>\nHence,<br \/>\nThe length of \\(\\overline{P Q}\\) = \\(\\overline{P M}\\) + \\(\\overline{M Q}\\)<br \/>\n= 2 \u00d7 2\\(\\frac{2}{7}\\)<br \/>\n= 2 \u00d7 \\(\\frac{16}{7}\\)<br \/>\n= \\(\\frac{2}{1}\\) \u00d7 \\(\\frac{16}{7}\\)<br \/>\n= \\(\\frac{32}{7}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of \\(\\overline{P Q} \\) is: \\(\\frac{32}{7}\\)<\/p>\n<p>Question 3.<br \/>\nIdentify the segment bisector of \\(\\overline{P Q}\\). Then find MQ.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34453\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-73.png\" alt=\"Big Ideas Math Geometry Solutions 73\" width=\"220\" height=\"85\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34453\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-73.png\" alt=\"Big Ideas Math Geometry Solutions 73\" width=\"220\" height=\"85\" \/><br \/>\nWe know that,<br \/>\nA &#8220;Bisector&#8221; is a line that divides a line segment into 2 congruent (or) equal parts<br \/>\nSo,<br \/>\nThe bisector of \\(\\overline{P Q}\\) is: line l<br \/>\nWe know that,<br \/>\nDue to a Bisector,<br \/>\nIn \\(\\overline{P Q}\\),<br \/>\n\\(\\overline{P M}\\) = \\(\\overline{M Q}\\)<br \/>\nSo,<br \/>\n5x &#8211; 3 = 11 &#8211; 2x<br \/>\n5x + 2x = 11 + 3<br \/>\n7x = 14<br \/>\nx = \\(\\frac{14}{7}\\)<br \/>\nx = 2<br \/>\nSo,<br \/>\nMQ = 11 &#8211; 2x<br \/>\nMQ = 11 &#8211; 2 (2)<br \/>\nMQ = 11 &#8211; 4<br \/>\nMQ = 7<br \/>\nHence, from theabove,<br \/>\nWe can conclude that the value of MQ is:7<\/p>\n<p>Question 4.<br \/>\nIdentify the segment bisector or \\(\\overline{R S}\\). Then find RS.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35639\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-73.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 73\" width=\"220\" height=\"85\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nThe endpoints of \\(\\overline{A B}\\) are A (1, 2) and B(7, 8). Find the coordinates of the midpoint M.<br \/>\nAnswer:<br \/>\nThe given endpoints of \\(\\overline{A B}\\) are:<br \/>\nA (1, 2), B (7, 8)<br \/>\nWe know that,<br \/>\nM = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nSo,<br \/>\nM = (\\(\\frac{1 + 7}{2}\\), \\(\\frac{8 + 2}{2}\\))<br \/>\nM = (\\(\\frac{8}{2}\\), \\(\\frac{10}{2}\\))<br \/>\nM = (4, 5)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the coordinates of the midpoint of \\(\\overline{A B}\\) are: (4, 5)<\/p>\n<p>Question 6.<br \/>\nThe endpoints of \\(\\overline{C D}\\) are C( &#8211; 4, 3) and D(6, 5). Find the coordinates of the midpoint M.<br \/>\nAnswer:<br \/>\nThe given endpoints of \\(\\overline{C D}\\) are:<br \/>\nC (-4, 3), D (6, 5)<br \/>\nWe know that,<br \/>\nM = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nSo,<br \/>\nM = (\\(\\frac{6 &#8211; 4}{2}\\), \\(\\frac{5 + 3}{2}\\))<br \/>\nM = (\\(\\frac{2}{2}\\), \\(\\frac{8}{2}\\))<br \/>\nM = (1, 4)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the coordinates of the midpoint of \\(\\overline{C D}\\) are: (1, 4)<\/p>\n<p>Question 7.<br \/>\nThe midpoint of \\(\\overline{T U}\\) is M(2, 4). One endpoint is T(1, 1). Find the coordinates of endpoint U.<br \/>\nAnswer:<br \/>\nThe given points of \\(\\overline{T U}\\) are:<br \/>\nM (2, 4), T (1, 1)<br \/>\nLet the one endpoint be T<br \/>\nWe know that,<br \/>\nM = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nSo,<br \/>\n(2, 4) = (\\(\\frac{x1 + 1}{2}\\), \\(\\frac{y1 + 1}{2}\\))<br \/>\nSo,<br \/>\n\\(\\frac{x1 + 1}{2}\\) = 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \\(\\frac{y1 + 1}{2}\\) = 4<br \/>\nx1 + 1 = 2 (2)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 y1 + 1 = 4 (2)<br \/>\nx1 = 4 &#8211; 1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0y1 = 8 &#8211; 1<br \/>\nx1 = 3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0y1 = 7<br \/>\nHence, from the above,<br \/>\nWe can conclude that the other endpoint of \\(\\overline{T U}\\) is: (3, 7)<\/p>\n<p>Question 8.<br \/>\nThe midpoint of \\(\\overline{V W}\\) is M (- 1, &#8211; 2). One endpoint is W(4, 4). Find the coordinates of endpoint V.<br \/>\nAnswer:<br \/>\nThe given points of \\(\\overline{V W}\\) are:<br \/>\nM (-1, -2), W (4, 4)<br \/>\nWe know that,<br \/>\nM = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nSo,<br \/>\n(-1, -2) = (\\(\\frac{x1 + 4}{2}\\), \\(\\frac{y1 + 4}{2}\\))<br \/>\nSo,<br \/>\n\\(\\frac{x1 + 4}{2}\\) = -1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \\(\\frac{y1 + 4}{2}\\) = -2<br \/>\nx1 + 4 = -1 (2)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 y1 + 4 = -2 (2)<br \/>\nx1 = -2 &#8211; 4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 y1 = -4 &#8211; 4<br \/>\nx1 = -6\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0y1 = -8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the other endpoint V is: (-6, -8)<\/p>\n<p>Question 9.<br \/>\nIn Example 4, a park is 3 miles east and 4 miles south of your apartment. Find the distance between the park and your school.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Exercise_1.3_Using_Midpoint_and_Distance_Formulas\"><\/a>Exercise 1.3 Using Midpoint and Distance Formulas<\/h3>\n<p>Question 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nIf a point ray, line, line segment, or plane intersects a segment at its midpoint, then what does it do to the segment?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48106\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-1.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 1\" width=\"608\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-1.png 608w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-1-300x29.png 300w\" sizes=\"(max-width: 608px) 100vw, 608px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nTo find the length of \\(\\overline{A B}\\), with endpoints A(- 7, 5) and B(4, &#8211; 6). you can use the _________ .<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nTo find the length with two endpoints, we use the &#8220;Distance formula&#8221;<br \/>\nThe distance between the 2 endpoints is given as:<br \/>\nD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nTo find the length of \\(\\overline{A B}\\), with endpoints A(- 7, 5) and B(4, &#8211; 6). you can use the &#8221; Distance formula &#8221;<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3 &#8211; 6. identify the segment bisector of \\(\\overline{R S}\\). Then find RS.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35637\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-75.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 75\" width=\"291\" height=\"75\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48107\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-3.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 3\" width=\"271\" height=\"70\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35636\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-76.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 76\" width=\"287\" height=\"79\" \/><br \/>\nAnswer:<br \/>\nThe given line segment is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35636\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-76.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 76\" width=\"287\" height=\"79\" \/><br \/>\nWe know that,<br \/>\nA &#8220;Bisector&#8221; is a line that divides a line segment into 2 equal parts<br \/>\nSo,<br \/>\nThe bisector of \\(\\overline{R S}\\) is: line A<br \/>\nFrom the given figure,<br \/>\nIt is given that<br \/>\n\\(\\overline{M S}\\) = 9<br \/>\nHence,<br \/>\n\\(\\overline{R S}\\) = 9 (2)<br \/>\n\\(\\overline{R S}\\) = 18<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of \\(\\overline{R S}\\) is: 18<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35635\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-77.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 77\" width=\"289\" height=\"50\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48108\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-5.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 5\" width=\"219\" height=\"68\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35634\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-78.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 78\" width=\"290\" height=\"113\" \/><br \/>\nAnswer:<br \/>\nThe given line segment is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35634\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-78.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 78\" width=\"290\" height=\"113\" \/><br \/>\nWe know that,<br \/>\nA &#8220;Bisector&#8221; is a line that divides a line segment into 2 equal parts<br \/>\nSo,<br \/>\nThe bisector of \\(\\overline{R S}\\) is: line s<br \/>\nFrom the given figure,<br \/>\nIt is given that<br \/>\n\\(\\overline{R M}\\) = 12<br \/>\nHence,<br \/>\n\\(\\overline{R S}\\) = 12 (2)<br \/>\n\\(\\overline{R S}\\) = 24<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of \\(\\overline{R S}\\) is: 24<\/p>\n<p>In Exercises 7 and 8, identify the segment bisector of \\(\\overline{J K}\\). Then find JM.<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35633\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-79.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 79\" width=\"262\" height=\"49\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48109\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-7.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 7\" width=\"363\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-7.png 363w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-7-300x112.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35632\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-80.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 80\" width=\"264\" height=\"146\" \/><br \/>\nAnswer:<br \/>\nThe given line segment is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35632\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-80.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 80\" width=\"264\" height=\"146\" \/><br \/>\nFrom the above figure,<br \/>\nA &#8220;Bisector&#8221; is a line that divides a line segment into 2 equal parts<br \/>\nSo,<br \/>\nThe bisector of \\(\\overline{J K}\\) is: line l<br \/>\nSince the 2 parts are equal,<br \/>\n\\(\\overline{J M}\\) = \\(\\overline{M K}\\)<br \/>\nSo,<br \/>\n3x + 15 = 8x + 25<br \/>\n3x &#8211; 8x = 25 &#8211; 15<br \/>\n-5x = 10<br \/>\nx = \\(\\frac{10}{-5}\\)<br \/>\nx = -2<br \/>\nSo,<br \/>\nJM = 3x + 15<br \/>\nJM = 3 (-2) + 15<br \/>\nJM = -6 + 15<br \/>\nJM = 9<br \/>\nHence, from he above,<br \/>\nWe can conclude that the length of JM is: 9<\/p>\n<p>In Exercises 9 and 10. identify the segment bisector of \\(\\overline{X Y}\\). Then find XY.<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35842\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-81.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 81\" width=\"263\" height=\"99\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48110\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-9.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 9\" width=\"516\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-9.png 516w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-9-300x123.png 300w\" sizes=\"(max-width: 516px) 100vw, 516px\" \/><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35841\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-82.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 82\" width=\"263\" height=\"112\" \/><br \/>\nAnswer:<br \/>\nThe given line segment is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35841\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-82.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 82\" width=\"263\" height=\"112\" \/><br \/>\nFrom the above figure,<br \/>\nA &#8220;Bisector&#8221; is a line that divides a line segment into 2 equal parts<br \/>\nSo,<br \/>\nThe bisector of \\(\\overline{X Y}\\) is: line n<br \/>\nSince the 2 parts are equal,<br \/>\n\\(\\overline{X M}\\) = \\(\\overline{M Y}\\)<br \/>\nSo,<br \/>\n5x + 8 = 9x + 12<br \/>\n5x &#8211; 9x = 12 &#8211; 8<br \/>\n-4x = 4<br \/>\nx = \\(\\frac{-4}{4}\\)<br \/>\nx = -1<br \/>\nSo,<br \/>\nXY = XM + MY<br \/>\nXY = 5x + 8 + 9x + 12<br \/>\nXY = 14x + 20<br \/>\nXY = 14 (-1) + 20<br \/>\nXY = 20 &#8211; 14<br \/>\nXY = 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of XY is: 6<\/p>\n<p><strong>CONSTRUCTION<\/strong><br \/>\nIn Exercises 11 &#8211; 14, copy the segment and construct a segment bisector by paper folding. Then label the midpoint M.<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35840\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-83.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 83\" width=\"259\" height=\"34\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48111\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-11.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 11\" width=\"566\" height=\"102\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-11.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-11-300x54.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35839\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-84.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 84\" width=\"328\" height=\"39\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-84.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-84-300x36.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\nAnswer:<br \/>\nThe given line segment is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35839\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-84.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 84\" width=\"328\" height=\"39\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-84.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-84-300x36.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\nWe know that,<br \/>\nA &#8220;Bisector&#8221; is a line or point that divides a line segment into 2 equal parts<br \/>\nHence,<br \/>\nThe representation of the bisector along with midpoint M of the given segment is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-71929\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-33.png\" alt=\"\" width=\"325\" height=\"54\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-33.png 325w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-33-300x50.png 300w\" sizes=\"(max-width: 325px) 100vw, 325px\" \/><\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35838\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-85.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 85\" width=\"233\" height=\"68\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48112\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-13.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 13\" width=\"548\" height=\"216\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-13.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-13-300x118.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35837\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-86.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 86\" width=\"314\" height=\"185\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-86.png 314w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-86-300x177.png 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><br \/>\nAnswer:<br \/>\nThe given line segment is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35837\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-86.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 86\" width=\"314\" height=\"185\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-86.png 314w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-86-300x177.png 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><br \/>\nWe know that,<br \/>\nA &#8220;Bisector&#8221; is a line or point that divides a line segment into 2 equal parts<br \/>\nHence,<br \/>\nThe representation of the bisector along with midpoint M of the given segment is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-71930\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-34.png\" alt=\"\" width=\"330\" height=\"180\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-34.png 330w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-34-300x164.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><\/p>\n<p>In Exercises 15 &#8211; 18, the endpoints of \\(\\overline{C D}\\) are given. Find the coordinates of the midpoint M.<br \/>\nQuestion 15.<br \/>\nC (3, &#8211; 5) and D (7, 9)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48113\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-15.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 15\" width=\"379\" height=\"179\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-15.png 379w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-15-300x142.png 300w\" sizes=\"(max-width: 379px) 100vw, 379px\" \/><\/p>\n<p>Question 16.<br \/>\nC (4, 7) and D (0, &#8211; 3)<br \/>\nAnswer:<br \/>\nThe given endpoints of \\(\\overline{C D}\\) are:<br \/>\nC (4, 7), D (0, -3)<br \/>\nWe know that,<br \/>\nM = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nSo,<br \/>\nM = (\\(\\frac{4 + 0}{2}\\), \\(\\frac{7 &#8211; 3}{2}\\))<br \/>\nM = (\\(\\frac{4}{2}\\), \\(\\frac{4}{2}\\))<br \/>\nM = (2, 2)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the coordinates of the midpoint of \\(\\overline{C D}\\) are: (2, 2)<\/p>\n<p>Question 17.<br \/>\nC (- 2, 0) and D (4, 9)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48114\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-17.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 17\" width=\"389\" height=\"212\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-17.png 389w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-17-300x163.png 300w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><\/p>\n<p>Question 18.<br \/>\nC (- 8, &#8211; 6) and D (- 4, 10)<br \/>\nAnswer:<br \/>\nThe given endpoints of \\(\\overline{C D}\\) are:<br \/>\nC (-8, -6), D (-4, 10)<br \/>\nWe know that,<br \/>\nM = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nSo,<br \/>\nM = (\\(\\frac{-8 &#8211; 4}{2}\\), \\(\\frac{10 &#8211; 6}{2}\\))<br \/>\nM = (\\(\\frac{-12}{2}\\), \\(\\frac{4}{2}\\))<br \/>\nM = (-6, 2)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the coordinates of the midpoint of \\(\\overline{C D}\\) are: (-6, 2)<\/p>\n<p>In Exercises 19 &#8211; 22. the midpoint M and one endpoint of \\(\\overline{G H}\\) are given. Find the coordinates of the other endpoint.<\/p>\n<p>Question 19.<br \/>\nG (5, &#8211; 6) and M (4, 3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48115\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-19.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 19\" width=\"345\" height=\"243\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-19.png 345w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-19-300x211.png 300w\" sizes=\"(max-width: 345px) 100vw, 345px\" \/><\/p>\n<p>Question 20.<br \/>\nH (- 3, 7) and M (- 2, 5)<br \/>\nAnswer:<br \/>\nThe given points of \\(\\overline{G H}\\) are:<br \/>\nM (-2, 5), H (-3, 7)<br \/>\nLet the point G be: (x1, y1)<br \/>\nWe know that,<br \/>\nM = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nSo,<br \/>\n(-2, 5) = (\\(\\frac{x1 -3}{2}\\), \\(\\frac{y1 + 7}{2}\\))<br \/>\nSo,<br \/>\n\\(\\frac{x1 &#8211; 3}{2}\\) = -2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \\(\\frac{y1 + 7}{2}\\) = 5<br \/>\nx1 &#8211; 3 = -2 (2)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 y1 + 7 = 5 (2)<br \/>\nx1 = -4 &#8211; 3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 y1 = 10 &#8211; 7<br \/>\nx1 = -7\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0y1 = 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the other endpoint G is: (-7, 3)<\/p>\n<p>Question 21.<br \/>\nH ( &#8211; 2, 9) and M(8, 0)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48116\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-21.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 21\" width=\"355\" height=\"245\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-21.png 355w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-21-300x207.png 300w\" sizes=\"(max-width: 355px) 100vw, 355px\" \/><\/p>\n<p>Question 22.<br \/>\nG (- 4, 1) and M (- \\(\\frac{13}{2}\\), &#8211; 6)<br \/>\nAnswer:<br \/>\nThe given points of \\(\\overline{G H}\\) are:<br \/>\nM (- \\(\\frac{13}{2}\\), &#8211; 6), G (-4, 1)<br \/>\nLet the other endpoint be H (x2, y2)<br \/>\nWe know that,<br \/>\nM = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nSo,<br \/>\n(- \\(\\frac{13}{2}\\), &#8211; 6) = (\\(\\frac{x2 &#8211; 4}{2}\\), \\(\\frac{y2 + 1}{2}\\))<br \/>\nSo,<br \/>\n\\(\\frac{x2 &#8211; 4}{2}\\) = &#8211; \\(\\frac{13}{2}\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\\(\\frac{y2 + 1}{2}\\) = -6<br \/>\nx2 &#8211; 4 = &#8211; \\(\\frac{13}{2}\\) (2)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0y2 + 1 = -6 (2)<br \/>\nx1 = -13 + 4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0y2 = -12 &#8211; 1<br \/>\nx1 = -9\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 y1 = -13<br \/>\nHence, from the above,<br \/>\nWe can conclude that the other endpoint H is: (-9, -13)<\/p>\n<p>In Exercises 23 &#8211; 30, find the distance between the two points.<\/p>\n<p>Question 23.<br \/>\nA (13, 2) and B (7, 10)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48117\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-23.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 23\" width=\"317\" height=\"238\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-23.png 317w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-23-300x225.png 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><\/p>\n<p>Question 24.<br \/>\nC (- 6, 5) and D (- 3, 1)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nC (-6, 5), D (-3, 1)<br \/>\nCompare the given points with<br \/>\nA (x1, y1), B (x2, y2)<br \/>\nSo,<br \/>\nThe distance between points C and D is given as:<br \/>\nD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nD = \\(\\sqrt{(6 &#8211; 3)\u00b2 + (1 &#8211; 5)\u00b2}\\)<br \/>\nD = \\(\\sqrt{(3)\u00b2 + (-4)\u00b2}\\)<br \/>\nD = \\(\\sqrt{9 + 16}\\)<br \/>\nD = \\(\\sqrt{25}\\)<br \/>\nD = 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance between 2 given points is: 5<\/p>\n<p>Question 25.<br \/>\nE (3, 7) and F (6, 5)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48118\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-25.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 25\" width=\"310\" height=\"227\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-25.png 310w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-25-300x220.png 300w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><\/p>\n<p>Question 26.<br \/>\nG (- 5, 4) and H (2, 6)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nG (-5, 4), H (2, 6)<br \/>\nCompare the given points with<br \/>\nA (x1, y1), B (x2, y2)<br \/>\nSo,<br \/>\nThe distance between points A and B is given as:<br \/>\nD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nD = \\(\\sqrt{(2 + 5)\u00b2 + (6 &#8211; 4)\u00b2}\\)<br \/>\nD = \\(\\sqrt{(7)\u00b2 + (2)\u00b2}\\)<br \/>\nD = \\(\\sqrt{49 + 4}\\)<br \/>\nD = \\(\\sqrt{53}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance between 2 given points is: \\(\\sqrt{53}\\)<\/p>\n<p>Question 27.<br \/>\nJ (- 8, 0) and K (1, 4)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48119\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-27.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 27\" width=\"328\" height=\"276\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-27.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-27-300x252.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><\/p>\n<p>Question 28.<br \/>\nL (7, &#8211; 1) and M (- 2, 4)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nL (7, -1), M (-2, 4)<br \/>\nCompare the given points with<br \/>\nA (x1, y1), B (x2, y2)<br \/>\nSo,<br \/>\nThe distance between points A and B is given as:<br \/>\nD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nD = \\(\\sqrt{(-2 &#8211; 7)\u00b2 + (4 + 1)\u00b2}\\)<br \/>\nD = \\(\\sqrt{(-9)\u00b2 + (5)\u00b2}\\)<br \/>\nD = \\(\\sqrt{81 + 25}\\)<br \/>\nD = \\(\\sqrt{106}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance between 2 given points is: \\(\\sqrt{106}\\)<\/p>\n<p>Question 29.<br \/>\nR (0, 1) and S (6, 3.5)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48120\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-29.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 29\" width=\"325\" height=\"238\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-29.png 325w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-29-300x220.png 300w\" sizes=\"(max-width: 325px) 100vw, 325px\" \/><\/p>\n<p>Question 30.<br \/>\nT (13, 1.6) and V (5.4, 3.7)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nT (13, 1.6), V (5.4, 3.7)<br \/>\nCompare the given points with<br \/>\nA (x1, y1), B (x2, y2)<br \/>\nSo,<br \/>\nThe distance between points A and B is given as:<br \/>\nD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nD = \\(\\sqrt{(13 &#8211; 5.4)\u00b2 + (1.6 &#8211; 3.7)\u00b2}\\)<br \/>\nD = \\(\\sqrt{(7.6)\u00b2 + (2.1)\u00b2}\\)<br \/>\nD = \\(\\sqrt{57.76 + 4.41}\\)<br \/>\nD = \\(\\sqrt{62.17}\\)<br \/>\nD = 7.884<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance between 2 given points is: 7.884<\/p>\n<p><strong>ERROR ANALYSIS<\/strong><br \/>\nIn Exercises 31 and 32, describe and correct the error in finding the distance between A(6, 2) and 8(1, &#8211; 4).<\/p>\n<p>Question 31.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35836\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-87.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 87\" width=\"329\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-87.png 329w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-87-300x111.png 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48121\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-31.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 31\" width=\"380\" height=\"179\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-31.png 380w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-31-300x141.png 300w\" sizes=\"(max-width: 380px) 100vw, 380px\" \/><\/p>\n<p>Question 32.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35835\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-88.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 88\" width=\"335\" height=\"150\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-88.png 335w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-88-300x134.png 300w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><br \/>\nAnswer:<br \/>\nIn the above figure,<br \/>\nThe distance between A and B is given by using the formula:<br \/>\nD = \\(\\sqrt{(x1 &#8211; y1)\u00b2 + (x2 &#8211; y2)\u00b2}\\)<br \/>\nBut,<br \/>\nThe used formula is wrong<br \/>\nNow,<br \/>\nThe given points are:<br \/>\nA (6, 2), B (1, -4)<br \/>\nCompare the given points with<br \/>\nA (x1, y1), B (x2, y2)<br \/>\nSo,<br \/>\nThe distance between points A and B is given as:<br \/>\nD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nD = \\(\\sqrt{(6 &#8211; 1)\u00b2 + (2 + 4)\u00b2}\\)<br \/>\nD = \\(\\sqrt{(5)\u00b2 + (6)\u00b2}\\)<br \/>\nD = \\(\\sqrt{25 + 36}\\)<br \/>\nD = \\(\\sqrt{61}\\)<br \/>\nD = 7.8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance between A and B is: 7.8<\/p>\n<p><strong>COMPARING SEGMENTS<\/strong><br \/>\nIn Exercises 33 and 34, the endpoints of two segments are given. Find each segment length. Tell whether the segments are congruent. If they are not congruent, a state which segment length is greater.<\/p>\n<p>Question 33.<br \/>\n\\(\\overline{A B}\\): A(0, 2), B(- 3, 8) and \\(\\overline{C D}\\): C(- 2, 2), D(0, &#8211; 4)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48122\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-33.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 33\" width=\"449\" height=\"411\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-33.png 449w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-33-300x275.png 300w\" sizes=\"(max-width: 449px) 100vw, 449px\" \/><\/p>\n<p>Question 34.<br \/>\n\\(\\overline{E F}\\): E(1, 4),F(5, 1) and \\(\\overline{G H}\\): G(-3, 1), H(1, 6)<br \/>\nAnswer:<br \/>\nThe given points of \\(\\overline{E F}\\) are:<br \/>\nE (1, 4), F (5, 1)<br \/>\nCompare the given points with<br \/>\nA (x1, y1), B (x2, y2)<br \/>\nSo,<br \/>\nThe distance between points E and F is given as:<br \/>\nD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nD = \\(\\sqrt{(5 &#8211; 1)\u00b2 + (1 &#8211; 4)\u00b2}\\)<br \/>\nD = \\(\\sqrt{(4)\u00b2 + (-3)\u00b2}\\)<br \/>\nD = \\(\\sqrt{16 + 9}\\)<br \/>\nD = \\(\\sqrt{25}\\)<br \/>\nD = 5<br \/>\nNow,<br \/>\nThe given points are:<br \/>\nG (-3, 1), H (1, 6)<br \/>\nCompare the given points with<br \/>\nA (x1, y1), B (x2, y2)<br \/>\nSo,<br \/>\nThe distance between points G and H is given as:<br \/>\nD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nD = \\(\\sqrt{(-1 &#8211; 3)\u00b2 + (1 &#8211; 6)\u00b2}\\)<br \/>\nD = \\(\\sqrt{(-4)\u00b2 + (-5)\u00b2}\\)<br \/>\nD = \\(\\sqrt{16 + 25}\\)<br \/>\nD = \\(\\sqrt{41}\\)<br \/>\nD = 6.4<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe lengths of \\(\\overline{E F}\\) and \\(\\overline{G H}\\) are not congruent<br \/>\nThe comparison of the lengths is:<br \/>\n\\(\\overline{E F}\\) &lt; \\(\\overline{G H}\\)<\/p>\n<p>Question 35.<br \/>\n<strong>WRITING<\/strong><br \/>\nYour friend is having trouble understanding the Midpoint Formula.<br \/>\na. Explain how to find the midpoint when given the two endpoints in your own words.<br \/>\nb. Explain how to tind the other endpoint when given one endpoint and the midpoint in your own words.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48123\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-35.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 35\" width=\"580\" height=\"287\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-35.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-35-300x148.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>PROBLEM-SOLVING<\/strong><br \/>\nIn baseball, the strike zone is the region a baseball needs to pass through for the umpire to declare it a strike when the butler does not swing. The top of the strike zone is a horizontal plane passing through the midpoint in the top of the batter\u2019s shoulders and the top of the uniform pants when the player is in a batting stance. Find the height of T. (Note: All heights are in inches.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35834\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-89.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 89\" width=\"219\" height=\"281\" \/><br \/>\nAnswer:<br \/>\nIt is given that the strike zone is the region a baseball needs to pass through for the umpire to declare it a strike when the butler does not swing. The top of the strike zone is a horizontal plane passing through the midpoint in the top of the batter\u2019s shoulders and the top of the uniform pants when the player is in a batting stance.<br \/>\nSo,<br \/>\nFrom the figure,<br \/>\nwe can observe that the height of T lies between 60 and 42<br \/>\nSo,<br \/>\nWhen we find the mid value of 60 and 42, we will get the height of T<br \/>\nSo,<br \/>\nT = \\(\\frac{60 + 42}{2}\\)<br \/>\nT = \\(\\frac{102}{2}\\)<br \/>\nT = 51<br \/>\nHence, from he above,<br \/>\nWe can conclude that the height of T is: 51 inches<\/p>\n<p>Question 37.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe figure shows the position of three players during part of a water polo match. Player A throws the ball to Player B. who then throws the ball to Player C.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35833\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-90.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 90\" width=\"344\" height=\"243\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-90.png 344w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-90-300x212.png 300w\" sizes=\"(max-width: 344px) 100vw, 344px\" \/><br \/>\na. Ho far did Player A throw the hail? Player B?<br \/>\nb. How far would Player A have to throw the ball to throw it directly to Player C?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48124\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-37.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 37\" width=\"550\" height=\"645\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-37.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-37-256x300.png 256w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYour school is 20 blocks east and 12 blocks south of your house. The mall is 10 blocks north and 7 blocks west of our house. You plan on going to the mall right after school. Find the distance between your school and the mall assuming there is a road directly connecting the school and the mall. One block is 0.1 mile.<br \/>\nAnswer:<br \/>\nThe representation of the coordinates of school and Mall in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-72061\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-35.png\" alt=\"\" width=\"310\" height=\"228\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-35.png 310w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-35-300x221.png 300w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><br \/>\nFrom the above graph,<br \/>\nThe coordinates of the school and Mall are:<br \/>\nS (20, -12), M (-7, 10)<br \/>\nCompare the given points with<br \/>\nA (x1, y), B (x2, y2)<br \/>\nSo,<br \/>\nThe distance between the schoola and Mall is given as:<br \/>\nSM = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nSo,<br \/>\nSM = \\(\\sqrt{(-7 &#8211; 20)\u00b2 + (10 + 12)\u00b2}\\)<br \/>\nSM = \\(\\sqrt{(-27)\u00b2 +(22)\u00b2}\\)<br \/>\nSM = \\(\\sqrt{1213}\\)<br \/>\nSM = 34.8 miles<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance between the school and the Mall is: 34.8 miles<\/p>\n<p>Question 39.<br \/>\n<strong>PROBLEM-SOLVING<\/strong><br \/>\nA path goes around a triangular park, as shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35832\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-91.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 91\" width=\"250\" height=\"186\" \/><br \/>\na. Find the distance around the park to the nearest yard.<br \/>\nb. A new path and a bridge are constructed from point Q to the midpoint M of \\(\\overline{P R}\\). Find QM to the nearest yard.<br \/>\nc. A man jogs from P to Q to M Lo R to Q and back to P at an average speed of 150 yards per minute. About how many minutes does it take? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48125\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-39.1.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 39.1\" width=\"475\" height=\"586\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-39.1.png 475w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-39.1-243x300.png 243w\" sizes=\"(max-width: 475px) 100vw, 475px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48126\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-39.2.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 39.2\" width=\"514\" height=\"603\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-39.2.png 514w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-39.2-256x300.png 256w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims there is an easier way to find the length of a segment than the Distance Formula when the x-coordinates of the endpoints are equal. He claims all you have to do is subtract the y-coordinates. Do you agree with his statement? Explain your reasoning.<br \/>\nAnswer:<br \/>\nYes, your friend is correct<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nDistance between 2 points = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nIt is given that the x-coordinates are equal<br \/>\nSo,<br \/>\nx1 = x2 = 0<br \/>\nSo,<br \/>\nDistance between 2 points = y2 &#8211; y1<br \/>\nHence, from the above,<br \/>\nWe can conclude that your friend is correct<\/p>\n<p>Question 41.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nTwo points are located at (a, c) and (b, c). Find the midpoint and the distance between the two points.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48127\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-41.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 41\" width=\"537\" height=\"97\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-41.png 537w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-41-300x54.png 300w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\n\\(\\overline{A B}\\) contains midpoint M and points C and D. as shown. Compare the lengths. If you cannot draw a conclusion. write impossible to tell. Explain your reasoning.<br \/>\na. AM and MB<br \/>\nb. AC and MB<br \/>\nc. MC and MD<br \/>\nd. MB and DB<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nUse the diagram in Exercise 42. The points on \\(\\overline{A B}\\) represent locations you pass on your commute to work. You travel from your home at location A to location M before realizing that your left your lunch at home. You could turn around to get your lunch and then continue to work at location B. Or you could go to work and go to location D for lunch today. You want to choose the option that involves the least distance you must travel. which option should you choose? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48128\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-43.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 43\" width=\"581\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-43.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-43-300x58.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nDescribe three ways to divide a rectangle into two congruent regions. Do the regions have to he triangles? Use a diagram to support your answer.<br \/>\nAnswer:<br \/>\nThe division of triangles into 2 congruent regions don&#8217;t have to be a triangle<br \/>\nNow,<br \/>\ncase (i):<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-72077\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-36.png\" alt=\"\" width=\"262\" height=\"200\" \/><br \/>\nIn the above case,<br \/>\nThe 2 regions are rectangles<br \/>\ncase (ii):<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-72082\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-37.png\" alt=\"\" width=\"266\" height=\"203\" \/><br \/>\nIn the above case,<br \/>\nThe 2 regions are triangles<br \/>\ncase (iii):<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-72086\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-38.png\" alt=\"\" width=\"275\" height=\"212\" \/><br \/>\nIn the above case,<br \/>\nThe 2 regions are squares<\/p>\n<p>Question 45.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nThe length of \\(\\overline{X Y}\\) is 24 centimeters. The midpoint of \\(\\overline{X Y}\\) is M. and C is on \\(\\overline{X M}\\) so that XC is \\(\\frac{2}{3}\\) of XM. Point D is on \\(\\overline{M Y}\\) so that MD is \\(\\frac{3}{4}\\) of MY. What is the length of \\(\\overline{C D}\\)?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48129\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-45.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 45\" width=\"357\" height=\"274\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-45.png 357w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-45-300x230.png 300w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/><\/p>\n<p>Maintaining Mathematical Proficiency<\/p>\n<p>Find the perimeter and area of the figure.<\/p>\n<p>Question 46.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35831\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-92.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 92\" width=\"115\" height=\"129\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35831\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-92.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 92\" width=\"115\" height=\"129\" \/><br \/>\nThe above figure is: Square<br \/>\nSo,<br \/>\nWe know that,<br \/>\nThe perimeter of a square = 4 \u00d7 Side<br \/>\nThe area of a square = Side\u00b2<br \/>\nFrom the above figure,<br \/>\nThe length of the side = 5 cm<br \/>\nSo,<br \/>\nThe perimeter of a square = 4 (5) = 20 cm<br \/>\nThe area of a square = 5\u00b2 = 25 cm\u00b2<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe perimeter of a square is: 20 cm<br \/>\nThe area of a square is: 25 cm\u00b2<\/p>\n<p>Question 47.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35830\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-93.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 93\" width=\"74\" height=\"129\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48130\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-47.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 47\" width=\"204\" height=\"97\" \/><\/p>\n<p>Question 48.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35829\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-94.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 94\" width=\"147\" height=\"108\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35829\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-94.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 94\" width=\"147\" height=\"108\" \/><br \/>\nFrom the above,<br \/>\nThe given figure is: Triangle<br \/>\nWe know that,<br \/>\nThe perimeter of triangle = The sum of all the sides of the given triangle<br \/>\nThe area of triangle = \\(\\frac{1}{2}\\) \u00d7 Base \u00d7 Height<br \/>\nSo,<br \/>\nThe perimeter of triangle = 3 + 4 + 5 = 12 m<br \/>\nThe area of triangle = \\(\\frac{1}{2}\\) \u00d7 3 \u00d7 4<br \/>\n= \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{4}{1}\\) \u00d7 3<br \/>\n= 6 m\u00b2<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe perimeter of triangle is: 12 m<br \/>\nThe area oftriangle is: 6 m\u00b2<\/p>\n<p>Question 49.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35828\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-95.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 95\" width=\"122\" height=\"127\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48131\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-49.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 49\" width=\"275\" height=\"141\" \/><\/p>\n<p>Solve the inequality. Graph the solution.<\/p>\n<p>Question 50.<br \/>\na + 18 &lt; 7<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\na + 18 &lt; 7<br \/>\nSo,<br \/>\na &lt; 7 &#8211; 18<br \/>\na &lt; -11<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is: a &lt; -11<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-72094\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-39.png\" alt=\"\" width=\"569\" height=\"46\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-39.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-39-300x24.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 51.<br \/>\ny &#8211; 5 \u2265 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48132\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-51.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 51\" width=\"557\" height=\"64\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-51.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-51-300x34.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 52.<br \/>\n&#8211; 3x &gt; 24<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-3x &gt; 24<br \/>\nx &lt; &#8211;\\(\\frac{24}{3}\\)<br \/>\nx &lt; -8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is: x &lt; -8<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-72097\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-40.png\" alt=\"\" width=\"563\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-40.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-40-300x32.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 53.<br \/>\n\\(\\frac{z}{4}\\) \u2264 12<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48133\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-53.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 1.3 a 53\" width=\"557\" height=\"78\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-53.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-1.3-a-53-300x42.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<h3><a id=\"Study_Skills:_Keeping_Your_Mind_Focused\"><\/a>Study Skills: Keeping Your Mind Focused<\/h3>\n<p><strong>1.1 &#8211; 1.3 What did you learn<\/strong><\/p>\n<p>Mathematical Practices<\/p>\n<p>Question 1.<br \/>\nSketch an example of the situation described in Exercise 49 on page 10. Label your figure.<br \/>\nAnswer:<br \/>\nThe representation of the example of the situation described in Exercise 49 on page 10 is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-78560\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-55.png\" alt=\"\" width=\"205\" height=\"141\" \/><\/p>\n<p>Question 2.<br \/>\nExplain how you arrived at your answer for Exercise 35 on page 18.<br \/>\nAnswer:<br \/>\nwe arrived at the answer for Exercise 35 on page 18 by using the distance formula between 2 points.<br \/>\nWe know that,<br \/>\nThe distance between the 2 points = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<\/p>\n<p>Question 3.<br \/>\nWhat assumptions did you make when solving Exercise 43 0n page 26?<br \/>\nAnswer:<br \/>\nThe assumptions we make when solving Exercise 43 on page 26 is:<br \/>\nAll the lengths between the 2 points in the segment are equal<\/p>\n<h3><a id=\"1.1_-_1.3_Quiz\"><\/a>1.1 &#8211; 1.3 Quiz<\/h3>\n<p>Use the diagram<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-35827\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-96.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 96\" width=\"194\" height=\"144\" \/><\/p>\n<p>Question 1.<br \/>\nName four points.<br \/>\nAnswer:<br \/>\nFrom the above figure,<br \/>\nThe four points are: A, L, B, and K<\/p>\n<p>Question 2.<br \/>\nName three collinear points.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe points that lie in the same line are called\u00a0 &#8220;Collinear points&#8221;<br \/>\nHence, from the above figure,<br \/>\nThe three collinear points are: A, L, and B<\/p>\n<p>Question 3.<br \/>\nName two lines.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nA line has a starting point but no ending point<br \/>\nFrom the above figure,<br \/>\nThe lines are GHF, ALB<\/p>\n<p>Question 4.<br \/>\nName three coplanar points.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe points that are present in the same plane are called &#8220;Co-planar points&#8221;<br \/>\nHence, from the above figure,<br \/>\nThe coplanar points are: G, H, and F<\/p>\n<p>Question 5.<br \/>\nName the plane that is shaded green.<br \/>\nAnswer:<br \/>\nFrom the above figure,<br \/>\nThe plane that is shaded green is named as Plane GHF<\/p>\n<p>Question 6.<br \/>\nGive two names for the plane that is shaded blue.<br \/>\nAnswer:<br \/>\nFrom the figure,<br \/>\nThe two names for the plane that is shaded blue are: Plane AKL, Plane BCD<\/p>\n<p>Question 7.<br \/>\nName three line segments.<br \/>\nAnswer:<br \/>\nFrom the figure,<br \/>\nThe 3 line segments are: CD, HG, DE<\/p>\n<p>Question 8.<br \/>\nName three rays.<br \/>\nAnswer:<br \/>\nFrom the figure,<br \/>\nThe names of the 3 rays are: Ray GHF, ray CDE, Ray ALB<\/p>\n<p>Sketch the figure described.<\/p>\n<p>Question 9.<br \/>\n\\(\\vec{Q}\\)R and <img loading=\"lazy\" class=\"alignnone size-full wp-image-35826\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-97.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 97\" width=\"35\" height=\"25\" \/><br \/>\nAnswer:<br \/>\nThe representation of \\(\\vec{Q}\\)R and QS is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-73118\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-41.png\" alt=\"\" width=\"387\" height=\"168\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-41.png 387w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-41-300x130.png 300w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><\/p>\n<p>Question 10.<br \/>\nplane P intersecting <img loading=\"lazy\" class=\"alignnone size-full wp-image-35825\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-98.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 98\" width=\"33\" height=\"28\" \/>\u00a0at Z<br \/>\nAnswer:<br \/>\nThe representation of plane P intersecting YZ at z is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-73120\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-42.png\" alt=\"\" width=\"385\" height=\"195\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-42.png 385w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-42-300x152.png 300w\" sizes=\"(max-width: 385px) 100vw, 385px\" \/><\/p>\n<p>Plot the points in a coordinate plane. Then determine whether \\(\\overline{A B}\\) and \\(\\overline{C D}\\) are congruent.<\/p>\n<p>Question 11.<br \/>\nA(- 3, 3), B( 1, 3), C(3, 2), D(3, &#8211; 2)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nA (-3, 3), B (1, 3), C (3, 2), D (3, -2)<br \/>\nCompare any 2 points with (x1, y1), (x2, y2)<br \/>\nWe know that,<br \/>\nThe distance can be calculated by using:<br \/>\nD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nSo,<br \/>\n\\(\\overline{A B}\\) = \\(\\sqrt{(1 + 3)\u00b2 + (3 &#8211; 3)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4)\u00b2}\\) = 4<br \/>\n\\(\\overline{C D}\\) = \\(\\sqrt{(3 &#8211; 3)\u00b2 + (2 + 2)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4)\u00b2}\\) = 4<br \/>\nSo, from the above,<br \/>\n\\(\\overline{A B}\\) is congruent to \\(\\overline{C D}\\) since both the lengths are the same<br \/>\nHence, from the above,<br \/>\nThe representation of the given points in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-73122\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-43.png\" alt=\"\" width=\"493\" height=\"504\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-43.png 493w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-43-293x300.png 293w\" sizes=\"(max-width: 493px) 100vw, 493px\" \/><br \/>\n\\(\\overline{A B}\\) is congruent to \\(\\overline{C D}\\)<\/p>\n<p>Question 12.<br \/>\nA(- 8, 7), B(1, 7), C(- 3, &#8211; 6), D(5, &#8211; 6)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nA (-8, 7), B (1, 7), C (-3, -6), D (5, -6)<br \/>\nCompare any 2 points with (x1, y1), (x2, y2)<br \/>\nWe know that,<br \/>\nThe distance can be calculated by using:<br \/>\nD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nSo,<br \/>\n\\(\\overline{A B}\\) = \\(\\sqrt{(1 + 8)\u00b2 + (7 &#8211; 7)\u00b2}\\)<br \/>\n= \\(\\sqrt{(9)\u00b2}\\) = 9<br \/>\n\\(\\overline{C D}\\) = \\(\\sqrt{(5 + 3)\u00b2 + (6 &#8211; 6)\u00b2}\\)<br \/>\n= \\(\\sqrt{(8)\u00b2}\\) = 8<br \/>\nSo, from the above,<br \/>\n\\(\\overline{A B}\\) is not congruent to \\(\\overline{C D}\\) since both the lengths are not the same<br \/>\nHence, from the above,<br \/>\nThe representation of the given points in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-73148\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-44.png\" alt=\"\" width=\"489\" height=\"506\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-44.png 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-44-290x300.png 290w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><br \/>\n\\(\\overline{A B}\\) is not congruent to \\(\\overline{C D}\\)<\/p>\n<p>Find AC. (Section 1.2)<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35824\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-99.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 99\" width=\"320\" height=\"31\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-99.png 320w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-99-300x29.png 300w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><br \/>\nAnswer:<br \/>\nThe given line segment is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35824\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-99.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 99\" width=\"320\" height=\"31\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-99.png 320w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-99-300x29.png 300w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><br \/>\nSo,<br \/>\nFrom the Segment Addition Postulate,<br \/>\n\\(\\overline{A C}\\) = \\(\\overline{A B}\\) + \\(\\overline{B C}\\)<br \/>\n\\(\\overline{A C}\\) = 13 + 26<br \/>\n\\(\\overline{A C}\\) = 39<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of \\(\\overline{A C}\\) is: 39<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35823\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-100.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 100\" width=\"314\" height=\"55\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-100.png 314w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-100-300x53.png 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><br \/>\nAnswer:<br \/>\nThe given line segment is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35823\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-100.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 100\" width=\"314\" height=\"55\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-100.png 314w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-100-300x53.png 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><br \/>\nSo,<br \/>\nFrom the Segment Addition Postulate,<br \/>\n\\(\\overline{A B}\\) = \\(\\overline{A C}\\) + \\(\\overline{B C}\\)<br \/>\n62 = \\(\\overline{A C}\\) + 11<br \/>\n\\(\\overline{A C}\\) = 62 &#8211; 11<br \/>\n\\(\\overline{A C}\\) = 51<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of \\(\\overline{A C}\\) is: 51<\/p>\n<p>Find the coordinates of the midpoint M and the distance between the two points.<\/p>\n<p>Question 15.<br \/>\nJ(4, 3) and K(2, &#8211; 3)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nJ (4, 3), K (2, -3)<br \/>\nWe know that,<br \/>\nM = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nSo,<br \/>\nM = (\\(\\frac{4 + 2}{2}\\), \\(\\frac{3 &#8211; 3}{2}\\))<br \/>\nM = (\\(\\frac{6}{2}\\), \\(\\frac{0}{2}\\))<br \/>\nM = (3, 0)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the coordinates of the midpoint are: (3, 0)<\/p>\n<p>Question 16.<br \/>\nL(- 4, 5) and N(5, &#8211; 3)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nL (-4, 5), N (5, -3)<br \/>\nWe know that,<br \/>\nM = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nSo,<br \/>\nM = (\\(\\frac{-4 + 5}{2}\\), \\(\\frac{5 &#8211; 3}{2}\\))<br \/>\nM = (\\(\\frac{1}{2}\\), \\(\\frac{2}{2}\\))<br \/>\nM = (\\(\\frac{1}{2}\\), 1)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the coordinates of the midpoint are: (\\(\\frac{1}{2}\\), 1)<\/p>\n<p>Question 17.<br \/>\nP(- 6, &#8211; 1) and Q(1, 2)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nP (-6, -1), Q (1, 2)<br \/>\nWe know that,<br \/>\nM = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nSo,<br \/>\nM = (\\(\\frac{-6 + 1}{2}\\), \\(\\frac{2 &#8211; 1}{2}\\))<br \/>\nM = (\\(\\frac{-5}{2}\\), \\(\\frac{1}{2}\\))<br \/>\nM = (-\\(\\frac{5}{2}\\), \\(\\frac{1}{2}\\))<br \/>\nHence, from the above,<br \/>\nWe can conclude that the coordinates of the midpoint are: (-\\(\\frac{5}{2}\\), \\(\\frac{1}{2}\\))<\/p>\n<p>Question 18.<br \/>\nIdentify the segment bisector of \\(\\overline{R S}\\). Then find RS.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35822\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-101.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 101\" width=\"309\" height=\"50\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-101.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-101-300x49.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><br \/>\nAnswer:<br \/>\nThe given line segment is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35822\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-101.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 101\" width=\"309\" height=\"50\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-101.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-101-300x49.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><br \/>\nWe know that,<br \/>\nA bisector is a point or a line that divides a line segment into 2 congruent parts<br \/>\nSo,<br \/>\nFrom the above figure,<br \/>\nM is the bisector of \\(\\overline{R S}\\)<br \/>\nSo,<br \/>\n6x &#8211; 2 = 3x + 7<br \/>\n6x &#8211; 3x = 7 + 2<br \/>\n3x = 9<br \/>\nx = \\(\\frac{9}{3}\\)<br \/>\nx = 3<br \/>\nSo,<br \/>\n\\(\\overline{R S}\\) = 6x &#8211; 2 + 3x + 7<br \/>\n= 9x + 5<br \/>\n= 9 (3) + 5<br \/>\n= 27 + 5<br \/>\n= 32<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of [altex]\\overline{R S}[\/latex] is: 32<\/p>\n<p>Question 19.<br \/>\nThe midpoint of \\(\\overline{J K}\\) is M(0, 1). One endpoint is J(- 6, 3). Find the coordinates of endpoint K.<br \/>\nAnswer:<br \/>\nThe given points of \\(\\overline{J K}\\) are:<br \/>\nM (0, 1), H (-6, 3)<br \/>\nLet the point G be: (x1, y1)<br \/>\nWe know that,<br \/>\nM = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nSo,<br \/>\n(0, 1) = (\\(\\frac{x1 -6}{2}\\), \\(\\frac{y1 + 3}{2}\\))<br \/>\nSo,<br \/>\n\\(\\frac{x1 &#8211; 6}{2}\\) = 0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \\(\\frac{y1 + 3}{2}\\) = 1<br \/>\nx1 &#8211; 12 = 0 (2)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 y1 + 7 = 1 (2)<br \/>\nx1 = 0 + 12\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0y1 = 2 &#8211; 7<br \/>\nx1 = 12\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 y1 = -5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the other endpoint G is: (12, -5)<\/p>\n<p>Question 20.<br \/>\nYour mom asks you to run some errands on your way home from school. She wants you to Stop at the post office and the grocery store, which is both on the same straight road between your school and your house. The distance from your school to the post office is 376 yards. the distance from the post office to your house is 929 yards. and the distance from the grocery store to your house is 513 yards.<br \/>\na. Where should you stop first?<br \/>\nAnswer:<br \/>\nIt is given that your mom asks you to run some errands on your way home from school. She wants you to stop at the post office and the grocery store, which is both on the same straight road between your school and your house.<br \/>\nHence, from the above,<br \/>\nWe can conclude that you should first stop at the post office<\/p>\n<p><span style=\"font-size: 16px;\">b. What is the distance from the post office to the grocery store?<br \/>\n<\/span>Answer:<br \/>\nIt is given that the distance from your school to the post office is 376 yards. the distance from the post office to your house is 929 yards. and the distance from the grocery store to your house is 513 yards.<br \/>\nSo,<br \/>\nThe distance from the post office to the grocery store = (The distance from the post office to your house) + (The distance from the grocery store to your house)<br \/>\n= 929 + 513<br \/>\n= 1442 yards<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance from the post office to the grocery store is: 1442 yards<\/p>\n<p>c. What is the distance from your school to your house?<br \/>\nAnswer:<br \/>\nIt is given that the distance from your school to the post office is 376 yards. the distance from the post office to your house is 929 yards. and the distance from the grocery store to your house is 513 yards.<br \/>\nSo,<br \/>\nThe distance from your school to your house = (The distance from your school to the post office) + (The distance from the post office to the grocery store)<br \/>\n= 376 + 1442<br \/>\n= 1818 yards<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance from your school to your house is: 1818 yards<\/p>\n<p>d. you walk at a speed of 75 yards per minute. How long does it take you to walk straight home from school? Explain your answer.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nTime = \\(\\frac{Distance}{Speed}\\)<br \/>\nFrom part (c),<br \/>\nThe total distance is: 1818 yards<br \/>\nThe given speed is: 75 yards per minute<br \/>\nSo,<br \/>\nTime = \\(\\frac{1818}{75}\\)<br \/>\nTime = 24.24 minutes<br \/>\nHence, from the above,<br \/>\nWe can conclude that the time taken for you to walk straight home from school is: 24.24 minutes<\/p>\n<p>Question 21.<br \/>\nThe figure shows a coordinate plane on a baseball held. The distance from home plate to first base is 90 feet. The pitching mound is the midpoint between home plate and second base. Find the distance from home plate to second base. Find the distance between the home plate and the pitching mound. Explain how you found our answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35821\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-102.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 102\" width=\"219\" height=\"215\" \/><br \/>\nAnswer:<br \/>\nFrom the figure,<br \/>\nThe coordinates to the home plate are: (0, 0), and (0, 6)<br \/>\nThe coordinates to the second plate are: (6, 6), and (6, 0)<br \/>\nThe coordinate of the pitching mound is: (3, 3)<br \/>\nNow,<br \/>\nThe length of the home plate is:<br \/>\nD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(0 &#8211; 0)\u00b2 + (6 &#8211; 6)\u00b2}\\)<br \/>\n= (0, 6)<br \/>\nThe length of the second plate is:<br \/>\nD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(6 &#8211; 6)\u00b2 + (6 &#8211; 0)\u00b2}\\)<br \/>\n= (0, 6)<br \/>\nNow,<br \/>\nThe distance from the home plate to the second base is:<br \/>\nD = (0, 6) &#8211; (0, 6)<br \/>\nD = (0, 0)<br \/>\nThe distance between the home plate and the pitching mound is:<br \/>\nD = (3, 3) &#8211; (0, 0)<br \/>\nD = (3, 3)<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe distance from the home plate to the second base is: (0, 0)<br \/>\nThe distance from the home plate to the pitching mound is: (3, 3)<\/p>\n<h3><a id=\"1.4_Perimeter_and_Area_in_the_Coordinate_Plane\"><\/a>1.4 Perimeter and Area in the Coordinate Plane<\/h3>\n<p><strong>Essential Question<\/strong><\/p>\n<p>How can you find the perimeter and area of a polygon in a coordinate plane?<br \/>\nAnswer:<br \/>\nWhen two-dimensional figures are shown on the\u00a0coordinate plane, a mix of counting and the Pythagorean Theorem can be used to\u00a0determine\u00a0the lengths of each side. Then add up the lengths to\u00a0determine\u00a0the\u00a0perimeter\u00a0or use the basic\u00a0area\u00a0formulas for triangles and rectangles to\u00a0determine\u00a0the\u00a0area\u00a0of the\u00a0figure.<\/p>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Finding the Perimeter and Area of a Quadrilateral<\/p>\n<p>Work with a partner<\/p>\n<p>a. On a piece of centimeter graph paper. draw quadrilateral ABCD in a coordinate plane. Label the points A(1, 4), B(- 3, 1) C(0, &#8211; 3), and D(4, 0).<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nA (1, 4), B (-3, 1), C (0, -3), and D (4, 0)<br \/>\nHence,<br \/>\nThe representation of the given points in the coordinate plane are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35820\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-103.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 103\" width=\"311\" height=\"310\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-103.png 311w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-103-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-103-150x150.png 150w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><\/p>\n<p>b. Find the perimeter of quadrilateral ABCD.<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nA (1, 4), B (-3, 1), C (0, -3), and D (4, 0)<br \/>\nWe know that,<br \/>\nThe perimeter is defined as the sum of all the sides of a polygon<br \/>\nSo,<br \/>\nIn a coordinate plane, the perimeter of the polygon can be found by finding the lengths of the given sides<br \/>\nWe know that,<br \/>\nThe length of the side of a polygon in a coordinate plane is:<br \/>\nD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nSo,<br \/>\nAB = \\(\\sqrt{(1 + 3)\u00b2 + (4 &#8211; 1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4)\u00b2 + (3)\u00b2}\\)<br \/>\n= \\(\\sqrt{16 + 9}\\)<br \/>\n= \\(\\sqrt{25}\\)<br \/>\n= 5 cm<br \/>\nBC = \\(\\sqrt{(0 + 3)\u00b2 + (1 + 3)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3)\u00b2 + (4)\u00b2}\\)<br \/>\n=\\(\\sqrt{9 + 16}\\)<br \/>\n= \\(\\sqrt{25}\\)<br \/>\n= 5 cm<br \/>\nCD = \\(\\sqrt{(4 &#8211; 0)\u00b2 + (0 + 3)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4)\u00b2 + (3)\u00b2}\\)<br \/>\n= \\(\\sqrt{(16 + 9}\\)<br \/>\n= \\(\\sqrt{25}\\)<br \/>\n= 5 cm<br \/>\nDA = \\(\\sqrt{(4 &#8211; 1)\u00b2 + (4 &#8211; 0)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3)\u00b2 + (4)\u00b2}\\)<br \/>\n= \\(\\sqrt{9 + 16}\\)<br \/>\n= \\(\\sqrt{25}\\)<br \/>\n= 5 cm<br \/>\nHence,<br \/>\nThe perimeter of the Quadrilateral ABCD = AB + BC + CD + DA<br \/>\n= 5 + 5 + 5 + 5<br \/>\n= 20 cm<\/p>\n<p>c. Are adjacent sides of quadrilateral ABCD perpendicular to each other? How can you tell?<br \/>\nAnswer:<br \/>\nFrom part (a),<br \/>\nThe lengths of all the sides of a quadrilateral are: 5 cm<br \/>\nWe know that,<br \/>\nFor a square, the lengths of all the sides are equal and the angle between all the sides of the square is 90\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the adjacent sides of quadrilateral ABCD are perpendicular to each other<\/p>\n<p>d. What is the definition of a square? Is quadrilateral ABCD a square? Justify your answer. Find the area of quadrilateral ABCD.<br \/>\nAnswer:<br \/>\nDefinition of the square:<br \/>\nA &#8220;Square&#8221; is a quadrilateral that has the length of all the sides equal and all the angles 90\u00b0<br \/>\nFrom part (b),<br \/>\nWe found out the lengths of all the sides are equal and all the angles are 90\u00b0<br \/>\nSo,<br \/>\nQuadrilateral ABCD is a square<br \/>\nSo,<br \/>\nArea of a square = Side\u00b2<br \/>\n= 5\u00b2<br \/>\n= 25 cm\u00b2<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Finding the Area of a Polygon Work with a partner.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-35819\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-104.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 104\" width=\"310\" height=\"308\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-104.png 310w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-104-300x298.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-104-150x150.png 150w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><\/p>\n<p>a. Partition quadrilateral ABCD into four right triangles and one square, as shown. Find the coordinates of the vertices for the five smaller polygons.<br \/>\nAnswer:<br \/>\nFrom the figure,<br \/>\nThe five smaller polygons are:<br \/>\n\u0394AQD, \u0394BPA, \u0394DRC, \u0394CSB, and square PQRS<br \/>\nNow,<br \/>\nThe coordinates for the given vertices polygons are:<br \/>\nThe coordinates of \u0394AQD are:<br \/>\nA (1, 4), Q (1, 0), and D (4, 0)<br \/>\nThe coordinates of \u0394BPA are:<br \/>\nB (-3, 1), P (1, 1), and A (1, 4)<br \/>\nThe coordinates of \u0394DRC are:<br \/>\nD (4, 0), R (0, 0), and C (0, -3)<br \/>\nThe coordinates of \u0394CSB are:<br \/>\nC (0, -3), S (0, 1), and B (-3, 1)<br \/>\nThe coordinates of square PQRS are:<br \/>\nP (1, 1), Q (1, 0), R (0, 0), and S (0, 1)<\/p>\n<p>b. Find the areas of the five smaller polygons.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35818\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-105.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 105\" width=\"196\" height=\"146\" \/><br \/>\nAnswer:<br \/>\nFrom part (a),<br \/>\nThe coordinates of \u0394AQD are:<br \/>\nA (1, 4), Q (1, 0), and D (4, 0)<br \/>\nThe coordinates of \u0394BPA are:<br \/>\nB (-3, 1), P (1, 1), and A (1, 4)<br \/>\nThe coordinates of \u0394DRC are:<br \/>\nD (4, 0), R (0, 0), and C (0, -3)<br \/>\nThe coordinates of \u0394CSB are:<br \/>\nC (0, -3), S (0, 1), and B (-3, 1)<br \/>\nThe coordinates of square PQRS are:<br \/>\nP (1, 1), Q (1, 0), R (0, 0), and S (0, 1)<br \/>\nNow,<br \/>\nThe area of \u0394 AQD:<br \/>\nThe length of AQ = \\(\\sqrt{(x2 &#8211; x1)\u00b2 +\u00a0 (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(1 &#8211; 1)\u00b2 +\u00a0 (4 &#8211; 0)\u00b2}\\)<br \/>\n= 4<br \/>\nThe length of QD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 +\u00a0 (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4 &#8211; 1)\u00b2 +\u00a0 (0 &#8211; 0)\u00b2}\\)<br \/>\n= 3<br \/>\nThe length of DA = \\(\\sqrt{(x2 &#8211; x1)\u00b2 +\u00a0 (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4 &#8211; 1)\u00b2 +\u00a0 (4 &#8211; 0)\u00b2}\\)<br \/>\n= 5<br \/>\nSo,<br \/>\nThe area of \u0394AQD = \\(\\frac{1}{2}\\) \u00d7 Base \u00d7 Height<br \/>\n= \\(\\frac{1}{2}\\) (4) (3)<br \/>\n= 6<\/p>\n<p>The area of \u0394 BPA:<br \/>\nThe length of BP = \\(\\sqrt{(x2 &#8211; x1)\u00b2 +\u00a0 (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(1 + 3)\u00b2 +\u00a0 (1 &#8211; 1)\u00b2}\\)<br \/>\n= 4<br \/>\nThe length of PA = \\(\\sqrt{(x2 &#8211; x1)\u00b2 +\u00a0 (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(1 &#8211; 1)\u00b2 +\u00a0 (4 &#8211; 1)\u00b2}\\)<br \/>\n= 3<br \/>\nThe length of BA = \\(\\sqrt{(x2 &#8211; x1)\u00b2 +\u00a0 (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4 &#8211; 1)\u00b2 +\u00a0 (1 + 3)\u00b2}\\)<br \/>\n= 5<br \/>\nSo,<br \/>\nThe area of \u0394BPA = \\(\\frac{1}{2}\\) \u00d7 Base \u00d7 Height<br \/>\n= \\(\\frac{1}{2}\\) (4) (3)<br \/>\n= 6<\/p>\n<p>The area of \u0394 DRC:<br \/>\nThe length of DR = \\(\\sqrt{(x2 &#8211; x1)\u00b2 +\u00a0 (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(0 &#8211; 0)\u00b2 +\u00a0 (4 &#8211; 0)\u00b2}\\)<br \/>\n= 4<br \/>\nThe length of RC = \\(\\sqrt{(x2 &#8211; x1)\u00b2 +\u00a0 (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3 + 0)\u00b2 +\u00a0 (0 &#8211; 0)\u00b2}\\)<br \/>\n= 3<br \/>\nThe length of CD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 +\u00a0 (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(0 + 3)\u00b2 +\u00a0 (4 &#8211; 0)\u00b2}\\)<br \/>\n= 5<br \/>\nSo,<br \/>\nThe area of \u0394DRC = \\(\\frac{1}{2}\\) \u00d7 Base \u00d7 Height<br \/>\n= \\(\\frac{1}{2}\\) (4) (3)<br \/>\n= 6<\/p>\n<p>The area of \u0394 CSB:<br \/>\nThe length of CS = \\(\\sqrt{(x2 &#8211; x1)\u00b2 +\u00a0 (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(0 &#8211; 0)\u00b2 +\u00a0 (1 + 3)\u00b2}\\)<br \/>\n= 4<br \/>\nThe length of SB = \\(\\sqrt{(x2 &#8211; x1)\u00b2 +\u00a0 (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(1 &#8211; 1)\u00b2 +\u00a0 (0 + 3)\u00b2}\\)<br \/>\n= 3<br \/>\nThe length of BC = \\(\\sqrt{(x2 &#8211; x1)\u00b2 +\u00a0 (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(1 + 3)\u00b2 +\u00a0 (0+ 3)\u00b2}\\)<br \/>\n= 5<br \/>\nSo,<br \/>\nThe area of \u0394CSB = \\(\\frac{1}{2}\\) \u00d7 Base \u00d7 Height<br \/>\n= \\(\\frac{1}{2}\\) (4) (3)<br \/>\n= 6<\/p>\n<p>The area of square PQRS:<br \/>\nThe length of PQ = \\(\\sqrt{(x2 &#8211; x1)\u00b2 +\u00a0 (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(1 &#8211; 1)\u00b2 +\u00a0 (1 &#8211; 0)\u00b2}\\)<br \/>\n= 1<br \/>\nThe length of QR = \\(\\sqrt{(x2 &#8211; x1)\u00b2 +\u00a0 (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(1 &#8211; 0)\u00b2 +\u00a0 (0 &#8211; 0)\u00b2}\\)<br \/>\n= 1<br \/>\nThe length of RS = \\(\\sqrt{(x2 &#8211; x1)\u00b2 +\u00a0 (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(1 &#8211; 0)\u00b2 +\u00a0 (0 &#8211; 0)\u00b2}\\)<br \/>\n= 1<br \/>\nThe length of PS = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(1 &#8211; 0)\u00b2 + (1 &#8211; 1)\u00b2}\\)<br \/>\n= 1<br \/>\nSo,<br \/>\nThe area of square PQRS = Side\u00b2<br \/>\n= 1<\/p>\n<p>c. Is the sum of the areas of the five smaller polygons equal to the area of quadrilateral ABCD? Justify your answer.<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nThe coordinates of the quadrilateral ABCD are:<br \/>\nA (1, 4), B(-3, 1), C (0, -3), and D (4, 0)<br \/>\nNow,<br \/>\nThe length of AB = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(1 + 3)\u00b2 + (4 &#8211; 1)\u00b2}\\)<br \/>\n= 5<br \/>\nThe length of BC = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(0 + 3)\u00b2 + (1 + 3)\u00b2}\\)<br \/>\n= 5<br \/>\nThe length of CD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(4 &#8211; 0)\u00b2 + (0 + 3)\u00b2}\\)<br \/>\n= 5<br \/>\nThe length of DA = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(4 &#8211; 0)\u00b2 + (4 &#8211; 1)\u00b2}\\)<br \/>\n= 5<br \/>\nSo, from the above<br \/>\nWe can observe that all the lengths of the sides are equal and the product of the slopes of the perpendicular sides is -1<br \/>\nHence,<br \/>\nThe area of quadrilateral ABCD = Side\u00b2<br \/>\n= 5\u00b2 = 25<br \/>\nNow,<br \/>\nThe sum of the areas of the five smaller polygons = 6 + 6 + 6 + 6 + 1<br \/>\n= 25<br \/>\nHence, from the above,<br \/>\nWe can conclude that the sum of the areas of the five smaller polygons equal to the area of quadrilateral ABCD<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 3.<br \/>\nHow can you find the perimeter and area of a polygon in a coordinate plane?<br \/>\nAnswer:<br \/>\nWhen two-dimensional figures are shown on the\u00a0coordinate plane, a mix of counting and the Pythagorean Theorem can be used to\u00a0determine\u00a0the lengths of each side. Then add up the lengths to\u00a0determine\u00a0the\u00a0perimeter\u00a0or use the basic\u00a0area\u00a0formulas for triangles and rectangles to\u00a0determine\u00a0the\u00a0area\u00a0of the\u00a0figure.<\/p>\n<p>Question 4.<br \/>\nRepeat Exploration 1 for quadrilateral EFGH. where the coordinates of the vertices are E(- 3, 6), F(- 7, 3), G(- 1, &#8211; 5), and H(3, &#8211; 2).<br \/>\nAnswer:<br \/>\nThe coordinates of the vertices of quadrilateral EFGH are:<br \/>\nE (-3, 6), F (-7, 3), G (-1, -5), and H (3, -2)<br \/>\nNow,<br \/>\nThe length of EF = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(7 &#8211; 3)\u00b2 + (6 &#8211; 3)\u00b2}\\)<br \/>\n= 5<br \/>\nThe length of FG = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(7 &#8211; 1)\u00b2 + (3 + 5)\u00b2}\\)<br \/>\n= 10<br \/>\nThe length of GH = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(3 + 1)\u00b2 + (5 &#8211; 2)\u00b2}\\)<br \/>\n= 5<br \/>\nThe length of HE = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(3 + 3)\u00b2 + (6 + 2)\u00b2}\\)<br \/>\n= 10<br \/>\nHence,<br \/>\nThe perimeter of quadrilateral EFGH = EF + FG + GH + HE<br \/>\n= 5 + 5 + 10 +\u00a0 10<br \/>\n= 30<br \/>\nFrom the lengths of the sides,<br \/>\nWe can observe that the opposite sides have the same lengths and the product of the slopes of the perpendicular sides is -1<br \/>\nSo,<br \/>\nThe figure is: Rectangle<br \/>\nWe know that,<br \/>\nThe area of a rectangle = Length \u00d7 Width<br \/>\nSo,<br \/>\nThe area of quadrilateral EFGH = 5 \u00d7 10 = 50<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe perimeter of quadrilateral EFGH is: 30<br \/>\nThe area of quadrilateral EFGH is: 50<\/p>\n<h3><a id=\"Lesson_1.4_Perimeter_and_Area_in_the_Coordinate_Plane\"><\/a>Lesson 1.4 Perimeter and Area in the Coordinate Plane<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Classify the polygon the number of sides. Tell whether it is convex or concave.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35817\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-106.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 106\" width=\"88\" height=\"62\" \/><br \/>\nAnswer:<br \/>\nThe given polygon is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35817\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-106.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 106\" width=\"88\" height=\"62\" \/><br \/>\nFrom the given polygon,<br \/>\nThe number of sides is: 5<br \/>\nSo,<br \/>\nThe given polygon is &#8220;Pentagon&#8221;<br \/>\nWe know that,<br \/>\nThe figure is concave if all the interior angles are greater than 180\u00b0<br \/>\nThe figure is convex if all the interior angles are less than 180\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given polygon is &#8220;Pentagon&#8221; and it is convex<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35816\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-107.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 107\" width=\"79\" height=\"81\" \/><br \/>\nAnswer:<br \/>\nThe given polygon is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35816\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-107.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 107\" width=\"79\" height=\"81\" \/><br \/>\nFrom the above polygon,<br \/>\nWe can observe that<br \/>\nThe number of sides is: 6<br \/>\nSo,<br \/>\nThe given polygon is: Hexagon<br \/>\nWe know that,<br \/>\nThe figure is concave if all the interior angles are greater than 180\u00b0<br \/>\nThe figure is convex if all the interior angles are less than 180\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given polygon is &#8220;Hexagon&#8221; and it is convex<\/p>\n<p>Find the perimeter of the polygon with the given vertices.<\/p>\n<p>Question 3.<br \/>\nD(- 3, 2), E(4, 2), F(4, &#8211; 3)<br \/>\nAnswer:<br \/>\nThe given vertices are:<br \/>\nD (-3, 2), E (4, 2), F (4, -3)<br \/>\nNow,<br \/>\nThe length of DE = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(4 + 3)\u00b2 + (2 &#8211; 2)\u00b2}\\)<br \/>\n= 7<br \/>\nThe length of EF = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(4 &#8211; 4)\u00b2 + (3 + 2)\u00b2}\\)<br \/>\n= 5<br \/>\nThe length of FD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(4 + 3)\u00b2 + (2 + 3)\u00b2}\\)<br \/>\n= 8.60<br \/>\nSo,<br \/>\nThe perimeter of the given vertices = 7 + 5 + 8.60<br \/>\n= 20.60<br \/>\nHence, from the above,<br \/>\nWe can conclude that the perimeter of the given vertices is: 20.60<\/p>\n<p>Question 4.<br \/>\nG(- 3, 2), H(2, 2), J(- 1, &#8211; 3)<br \/>\nAnswer:<br \/>\nThe given vertices are:<br \/>\nG (-3, 2), H (2, 2), I (-1, -3)<br \/>\nNow,<br \/>\nThe length of GH = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(2 + 3)\u00b2 + (2 &#8211; 2)\u00b2}\\)<br \/>\n= 5<br \/>\nThe length of HI = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(2 + 1)\u00b2 + (3 + 2)\u00b2}\\)<br \/>\n= 5.8<br \/>\nThe length of IG = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(3 &#8211; 1)\u00b2 + (2 + 3)\u00b2}\\)<br \/>\n= 5.3<br \/>\nSo,<br \/>\nThe perimeter of the given vertices = 5 + 5.8 + 5.3<br \/>\n= 16.1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the perimeter of the given vertices is: 16.1<\/p>\n<p>Question 5.<br \/>\nK( &#8211; 1, 1), L(4, 1), M(2, &#8211; 2), N(- 3, &#8211; 2)<br \/>\nAnswer:<br \/>\nThe given vertices are:<br \/>\nK (-1, 1), L (4, 1), M (2, -2), N (-3, -2)<br \/>\nNow,<br \/>\nThe length of KL = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(4 + 1)\u00b2 + (1 &#8211; 1)\u00b2}\\)<br \/>\n= 5<br \/>\nThe length of LM = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(4 &#8211; 2)\u00b2 + (1 + 2)\u00b2}\\)<br \/>\n= 3.6<br \/>\nThe length of MN = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(2 + 3)\u00b2 + (2 &#8211; 2)\u00b2}\\)<br \/>\n= 5<br \/>\nThe length of NK = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3- 1)\u00b2 + (1 + 2)\u00b2}\\)<br \/>\n= 3.6<br \/>\nSo,<br \/>\nThe perimeter of the given vertices = 5 + 5 + 3.6 + 3.6<br \/>\n= 17.2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the perimeter of the given vertices is: 17.2<\/p>\n<p>Question 6.<br \/>\nQ(- 4, &#8211; 1), R(1, 4), S(4, 1), T(- 1, &#8211; 4)<br \/>\nAnswer:<br \/>\nThe given vertices are;<br \/>\nQ (-4, -1), R (1, 4), S (4, 1), T (-1, -4)<br \/>\nNow,<br \/>\nThe length of QR = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(4 + 1)\u00b2 + (4 + 1)\u00b2}\\)<br \/>\n= 7.07<br \/>\nThe length of RS = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(4 &#8211; 1)\u00b2 + (4 &#8211; 1)\u00b2}\\)<br \/>\n= 4.2<br \/>\nThe length of ST = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(4 + 1)\u00b2 + (1 + 4)\u00b2}\\)<br \/>\n= 7.07<br \/>\nThe length of TQ = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4- 1)\u00b2 + (4 &#8211; 1)\u00b2}\\)<br \/>\n= 4.2<br \/>\nSo,<br \/>\nThe perimeter of the given vertices = 7.07 + 7.07 + 4.2 + 4.2<br \/>\n= 22.54<br \/>\nHence, from the above,<br \/>\nWe can conclude that the perimeter of the given vertices is: 22.54<\/p>\n<p>Find the area of the polygon with the given vertices.<\/p>\n<p>Question 7.<br \/>\nG(2, 2), H(3, &#8211; 1), J(- 2, &#8211; 1)<br \/>\nAnswer:<br \/>\nThe given vertices are:<br \/>\nG (2, 2), H (3, -1), I (-2, -1)<br \/>\nNow,<br \/>\nThe length of GH = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(2 &#8211; 3)\u00b2 + (2 + 1)\u00b2}\\)<br \/>\n= 3.16<br \/>\nThe length of HI = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(1 &#8211; 1)\u00b2 + (3 + 2)\u00b2}\\)<br \/>\n= 5<br \/>\nThe length of IG = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(2 + 2)\u00b2 + (2 + 1)\u00b2}\\)<br \/>\n= 5<br \/>\nSo,<br \/>\nThe area of the given vertices = \\(\\frac{1}{2}\\) \u00d7 Base \u00d7 Height<br \/>\n= \\(\\frac{1}{2}\\) \u00d7 5 \u00d7 5<br \/>\n= 12.5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the given vertices is: 12.5<\/p>\n<p>Question 8.<br \/>\nN(- 1, 1), P(2, 1), Q(2, &#8211; 2), R(- 1, &#8211; 2)<br \/>\nAnswer:<br \/>\nThe given vertices are:<br \/>\nN (-1, 1), P (2, 1), Q (2, -2), R (-1, -2)<br \/>\nNow,<br \/>\nThe length of NP = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(2 + 1)\u00b2 + (1 &#8211; 1)\u00b2}\\)<br \/>\n= 3<br \/>\nThe length of PQ = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(2 &#8211; 2)\u00b2 + (1 + 2)\u00b2}\\)<br \/>\n= 3<br \/>\nThe length of QR = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(2 + 1)\u00b2 + (2 &#8211; 2)\u00b2}\\)<br \/>\n= 3<br \/>\nThe length of RN = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(1- 1)\u00b2 + (1 + 2)\u00b2}\\)<br \/>\n= 3<br \/>\nSo,<br \/>\nFrom the lengths of all of the sides,<br \/>\nWe can say that the vertices belong to a square<br \/>\nSo,<br \/>\nThe area of a square = Side\u00b2<br \/>\n= 3\u00b2 = 9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the given vertices is: 9<\/p>\n<p>Question 9.<br \/>\nF(- 2, 3), G(1, 3), H(1, &#8211; 1), J(- 2, &#8211; 1)<br \/>\nAnswer:<br \/>\nThe given vertices are:<br \/>\nF (-2, 3), G (1, 3), H (1, -1), J (-2, -1)<br \/>\nNow,<br \/>\nThe length of FG = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(2 + 1)\u00b2 + (3 &#8211; 3)\u00b2}\\)<br \/>\n= 3<br \/>\nThe length of GH = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(1 &#8211; 1)\u00b2 + (1 + 3)\u00b2}\\)<br \/>\n= 4<br \/>\nThe length of HJ = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(2 + 1)\u00b2 + (1 &#8211; 1)\u00b2}\\)<br \/>\n= 3<br \/>\nThe length of JF = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(2- 2)\u00b2 + (1 + 3)\u00b2}\\)<br \/>\n= 4<br \/>\nSo,<br \/>\nFrom the lengths of all of the sides,<br \/>\nWe can say that the vertices belong to a rectangle since the lengths of the opposite sides are the same<br \/>\nSo,<br \/>\nThe area of a rectangle = Length \u00d7 Width<br \/>\n= 3 \u00d7 4 = 12<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the given vertices is: 12<\/p>\n<p>Question 10.<br \/>\nK(- 3, 3), L(3, 3), M(3, &#8211; 1), N(- 3, &#8211; 1)<br \/>\nAnswer:<br \/>\nThe given vertices are:<br \/>\nK (-3, 3), L (3, 3), M (3, -1), N (-3, -1)<br \/>\nNow,<br \/>\nThe length of KL = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(3 + 3)\u00b2 + (3 &#8211; 3)\u00b2}\\)<br \/>\n= 6<br \/>\nThe length of LM = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(3 &#8211; 3)\u00b2 + (1 + 3)\u00b2}\\)<br \/>\n= 4<br \/>\nThe length of MN = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(3 + 3)\u00b2 + (1 &#8211; 1)\u00b2}\\)<br \/>\n= 6<br \/>\nThe length of NK = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3- 3)\u00b2 + (1 + 3)\u00b2}\\)<br \/>\n= 4<br \/>\nSo,<br \/>\nFrom the lengths of all of the sides,<br \/>\nWe can say that the vertices belong to a rectangle<br \/>\nSo,<br \/>\nThe area of a rectangle = Length \u00d7 Width<br \/>\n= 6 \u00d7 4 = 24<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the given vertices is: 24<\/p>\n<p>Question 11.<br \/>\nYou are building a patio in your school&#8217;s courtyard. In the diagram at the left, the coordinates represent the four vertices of the patio. Each unit in the coordinate plane represents 1 foot. Find the area of the patio.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35815\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-108.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 108\" width=\"249\" height=\"205\" \/><br \/>\nAnswer:<br \/>\nFrom the given graph,<br \/>\nThe coordinates of a patio is:<br \/>\nM (2, 2), N (6, 2), P (6, -3), R (2, -3)<br \/>\nNow,<br \/>\nThe length of MN = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(6 &#8211; 2)\u00b2 + (2 &#8211; 2)\u00b2}\\)<br \/>\n= 4<br \/>\nThe length of NP = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(6 &#8211; 6)\u00b2 + (3 + 2)\u00b2}\\)<br \/>\n= 5<br \/>\nThe length of PR = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(6 &#8211; 2)\u00b2 + (3 &#8211; 3)\u00b2}\\)<br \/>\n= 4<br \/>\nThe length of RM = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(2- 2)\u00b2 + (3 + 2)\u00b2}\\)<br \/>\n= 5<br \/>\nSo,<br \/>\nFrom the lengths of all of the sides,<br \/>\nWe can say that the vertices belong to a rectangle<br \/>\nSo,<br \/>\nThe area of a rectangle = Length \u00d7 Width<br \/>\n= 5 \u00d7 4 = 20<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the patio is: 20<\/p>\n<h3><a id=\"Exercise_1.4_Perimeter_and_Area_in_the_Coordinate_Plane\"><\/a>Exercise 1.4 Perimeter and Area in the Coordinate Plane<\/h3>\n<p>Question 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nThe perimeter of a square with side length s is P = _________ .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47988\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-1.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 1\" width=\"528\" height=\"37\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-1.png 528w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-1-300x21.png 300w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nWhat formulas can you use to find the area of a triangle in a coordinate plane?<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe formula you can use to find the area of a triangle in a coordinate plane is:<br \/>\nArea of a triangle (A) = \\(\\frac{1}{2}\\) \u00d7 Base \u00d7 Height<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3 &#8211; 6, classify the polygon by the number of sides. Tell whether it is convex or concave.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35814\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-109.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 109\" width=\"96\" height=\"58\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47989\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-3.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 3\" width=\"580\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-3.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-3-300x29.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35813\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-110.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 110\" width=\"131\" height=\"59\" \/><br \/>\nAnswer:<br \/>\nThe given polygon is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35813\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-110.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 110\" width=\"131\" height=\"59\" \/><br \/>\nFrom the given polygon,<br \/>\nWe can observe that<br \/>\nThe number of sides is: 3<br \/>\nWe know that,<br \/>\nThe figure is concave if all the interior angles are greater than 180\u00b0<br \/>\nThe figure is convex if all the interior angles are less than 180\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given polygon is a triangle and it is a concave polygon as it has interior angles greater than 180\u00b0<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35812\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-111.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 111\" width=\"79\" height=\"74\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47990\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-5.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 5\" width=\"570\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-5.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-5-300x29.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35811\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-112.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 112\" width=\"53\" height=\"80\" \/><br \/>\nAnswer:<br \/>\nThe given polygon is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35811\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-112.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 112\" width=\"53\" height=\"80\" \/><br \/>\nFrom the given polygon,<br \/>\nWe can observe that<br \/>\nThe number of sides is: 6<br \/>\nWe know that,<br \/>\nThe figure is concave if all the interior angles are greater than 180\u00b0<br \/>\nThe figure is convex if all the interior angles are less than 180\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given polygon is a hexagon and it is a concave polygon as it has interior angles greater than 180\u00b0<\/p>\n<p>In Exercises 7 &#8211; 12. find the perimeter of the polygon with the given vertices.<\/p>\n<p>Question 7.<br \/>\nG(2, 4), H(2, &#8211; 3), J(- 2, &#8211; 3), K(- 2, 4)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47991\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-7.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 7\" width=\"459\" height=\"475\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-7.png 459w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-7-290x300.png 290w\" sizes=\"(max-width: 459px) 100vw, 459px\" \/><\/p>\n<p>Question 8.<br \/>\nQ(- 3, 2), R(1, 2), s(1, &#8211; 2), T(- 3, &#8211; 2)<br \/>\nAnswer:<br \/>\nThe given vertices of a polygon are:<br \/>\nQ (-3, 2), R (1, 2), S (1, -2), T (-3, -2)<br \/>\nNow,<br \/>\nThe length of QR = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(1 + 3)\u00b2 + (2 &#8211; 2)\u00b2}\\)<br \/>\n= 4<br \/>\nThe length of RS = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(1 &#8211; 1)\u00b2 + (2 + 2)\u00b2}\\)<br \/>\n= 4<br \/>\nThe length of ST = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(2 &#8211; 2)\u00b2 + (1 + 3)\u00b2}\\)<br \/>\n= 4<br \/>\nThe length of TQ = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3- 3)\u00b2 + (2 + 2)\u00b2}\\)<br \/>\n= 4<br \/>\nSo,<br \/>\nFrom the lengths of all of the sides,<br \/>\nWe can say that the vertices belong to a square<br \/>\nSo,<br \/>\nThe perimeter of a square = 4 \u00d7 Side<br \/>\n= 4 \u00d7 4<br \/>\n= 16<br \/>\nHence, from the above,<br \/>\nWe can conclude that the perimeter of the given polygon is: 16<\/p>\n<p>Question 9.<br \/>\nU(- 2, 4), V(3, 4), W(3, &#8211; 4)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47992\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-9.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 9\" width=\"435\" height=\"648\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-9.png 435w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-9-201x300.png 201w\" sizes=\"(max-width: 435px) 100vw, 435px\" \/><\/p>\n<p>Question 10.<br \/>\nX(- 1, 3), Y(3, 0), Z(- 1, &#8211; 2)<br \/>\nAnswer:<br \/>\nThe given vertices of a polygon are:<br \/>\nX (-1, 3), Y (3, 0), Z (-1, -2)<br \/>\nNow,<br \/>\nThe length of XY = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(3 + 1)\u00b2 + (3 &#8211; 0)\u00b2}\\)<br \/>\n= 5<br \/>\nThe length of YZ = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(3 + 1)\u00b2 + (0 + 2)\u00b2}\\)<br \/>\n= 4.47<br \/>\nThe length of ZX = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(1 &#8211; 1)\u00b2 + (3 + 2)\u00b2}\\)<br \/>\n= 5<br \/>\nSo,<br \/>\nThe perimeter of the given polygon = 5 + 5 + 4.7<br \/>\n= 14.47<br \/>\nHence, from the above,<br \/>\nWE can conclude that the perimeter of the given polygon is: 14.47<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35810\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-113.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 113\" width=\"189\" height=\"175\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47993\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-11.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 11\" width=\"553\" height=\"529\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-11.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-11-300x287.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35809\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-114.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 114\" width=\"192\" height=\"176\" \/><br \/>\nAnswer:<br \/>\nFrom the given coordinate plane,<br \/>\nThe given vertices of the hexagon are:<br \/>\nA (0, 4), B (2, 0), C (2, -2), D (0, -2), E (-2, 2), F (-2, 4)<br \/>\nNow,<br \/>\nNow,<br \/>\nThe length of AB = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(2 &#8211; 0)\u00b2 + (4 &#8211; 0)\u00b2}\\)<br \/>\n= 4.47<br \/>\nThe length of BC = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(2 &#8211; 2)\u00b2 + (0 + 2)\u00b2}\\)<br \/>\n= 2<br \/>\nThe length of CD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n=\\(\\sqrt{(2 &#8211; 0)\u00b2 + (2 &#8211; 2)\u00b2}\\)<br \/>\n= 2<br \/>\nThe length of DE = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(0 + 2)\u00b2 + (2 + 2)\u00b2}\\)<br \/>\n= 4.47<br \/>\nThe length of EF = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(2 &#8211; 2)\u00b2 + (4 &#8211; 2)\u00b2}\\)<br \/>\n= 2<br \/>\nThe length of FA = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(0 + 2)\u00b2 + (4 &#8211; 4)\u00b2}\\)<br \/>\n= 2<br \/>\nSo,<br \/>\nThe perimeter of the hexagon = AB + BC + CD + DE + EF + FA<br \/>\n= 4.47 + 2 + 2 + 4.47 + 2 + 2<br \/>\n= 16.94<br \/>\nHence, from the above,<br \/>\nWe can conclude that the perimeter of the given hexagon is: 16.94<\/p>\n<p>In Exercises 13 &#8211; 16. find the area of the polygon with the given vertices.<\/p>\n<p>Question 13.<br \/>\nE(3, 1), F(3, &#8211; 2), G(- 2, &#8211; 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47994\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-13.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 13\" width=\"465\" height=\"459\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-13.png 465w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-13-300x296.png 300w\" sizes=\"(max-width: 465px) 100vw, 465px\" \/><\/p>\n<p>Question 14.<br \/>\nJ(- 3, 4), K(4, 4), L(3, &#8211; 3)<br \/>\nAnswer:<br \/>\nThe given vertices are:<br \/>\nJ (-3, 4), K (4, 4), L (3, -3)<br \/>\nNow,<br \/>\nThe length of JK = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4 + 3)\u00b2 + (4 &#8211; 4)\u00b2}\\)<br \/>\n= 7<br \/>\nThe length of KL = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4 &#8211; 3)\u00b2 + (4 + 3)\u00b2}\\)<br \/>\n= 7.07<br \/>\nThe length of LJ = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3 + 3)\u00b2 + (3 + 4)\u00b2}\\)<br \/>\n= 9.21<br \/>\nSo,<br \/>\nThe area of the given vertices = \\(\\frac{1}{2}]\/latex] \u00d7 JK \u00d7KL<br \/>\n= [latex\/]frac{1}{2}\\) \u00d7 7 \u00d7 7.07<br \/>\n= 24.74<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the given vertices is: 24.74<\/p>\n<p>Question 15.<br \/>\nW(0, 0), X(0, 3), Y(- 3, 3), Z(- 3, 0)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47995\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-15.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 15\" width=\"458\" height=\"399\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-15.png 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-15-300x261.png 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><\/p>\n<p>Question 16.<br \/>\nN(- 2, 1), P(3, 1), Q(3, &#8211; 1), R(- 2, 1)<br \/>\nAnswer:<br \/>\nThe given vertices are:<br \/>\nN (-2, 1), P (3, 1), Q (3, -1), R (-2, 1)<br \/>\nNow,<br \/>\nThe length of NP = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3 + 2)\u00b2 + (1 &#8211; 1)\u00b2}\\)<br \/>\n= 5<br \/>\nThe length of PQ = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3 &#8211; 3)\u00b2 + (1 + 1)\u00b2}\\)<br \/>\n= 2<br \/>\nThe length of QR = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3 + 2)\u00b2 + (1 + 1)\u00b2}\\)<br \/>\n= 5.38<br \/>\nThe length of RN = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(2 &#8211; 2)\u00b2 + (1 &#8211; 1)\u00b2}\\)<br \/>\n= 0<br \/>\nSo,<br \/>\nThe area of the given vertices = 5 \u00d7 2 \u00d7 5.38<br \/>\n= 28.97<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the given vertices is: 28.97<\/p>\n<p>In Exercises 17 &#8211; 24, use the diagram.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-35808\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-115.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 115\" width=\"266\" height=\"268\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-115.png 266w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-115-150x150.png 150w\" sizes=\"(max-width: 266px) 100vw, 266px\" \/><\/p>\n<p>Question 17.<br \/>\nFind the perimeter of \u25b3CDE.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47996\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-17.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 17\" width=\"439\" height=\"379\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-17.png 439w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-17-300x259.png 300w\" sizes=\"(max-width: 439px) 100vw, 439px\" \/><\/p>\n<p>Question 18.<br \/>\nFind the perimeter of the rectangle BCEF.<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nThe coordinates of the rectangle BCEF are:<br \/>\nB (0, 3) C (4, -1), E (2, -3), F (-2, 1)<br \/>\nNow,<br \/>\nThe length of BC = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4 &#8211; 0)\u00b2 + (3 + 1)\u00b2}\\)<br \/>\n= 5.65<br \/>\nThe length of CE = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4 &#8211; 2)\u00b2 + (3 &#8211; 1)\u00b2}\\)<br \/>\n= 2.82<br \/>\nThe length of EF = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(1 + 3)\u00b2 + (2 + 2)\u00b2}\\)<br \/>\n= 5.65<br \/>\nThe length of FB = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(0 + 2)\u00b2 + (3 &#8211; 1)\u00b2}\\)<br \/>\n= 2.82<br \/>\nSo,<br \/>\nThe perimeter of the rectangle BCEF = BC + CE + EF + FB<br \/>\n= 5.65 + 2.82 + 5.65 + 2.82<br \/>\n= 16.94<br \/>\nHence, from the above,<br \/>\nWe can conclude that the perimeter of the rectangle BCEF is: 16.94<\/p>\n<p>Question 19.<br \/>\nFind the perimeter of \u25b3ABF.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47997\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-19.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 19\" width=\"448\" height=\"497\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-19.png 448w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-19-270x300.png 270w\" sizes=\"(max-width: 448px) 100vw, 448px\" \/><\/p>\n<p>Question 20.<br \/>\nFind the perimeter of quadrilateral ABCD.<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nThe given vertices of the quadrilateral ABCD are:<br \/>\nA (-5, 4), B (0, 3), C (4, -1), D (4, -5)<br \/>\nNow,<br \/>\nThe length of AB = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(0 + 5)\u00b2 + (4 &#8211; 3)\u00b2}\\)<br \/>\n= 5.09<br \/>\nThe length of BC = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4 &#8211; 0)\u00b2 + (1 + 3)\u00b2}\\)<br \/>\n= 5.65<br \/>\nThe length of CD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4 &#8211; 4)\u00b2 + (5 &#8211; 1)\u00b2}\\)<br \/>\n= 4<br \/>\nThe length of DA = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4 + 5)\u00b2 + (4 + 5)\u00b2}\\)<br \/>\n= 12.72<br \/>\nSo,<br \/>\nThe perimeter of quadrilateral ABCD = AB + BC + CD + DA<br \/>\n= 5.09 + 5.65 + 4 + 12.72<br \/>\n= 31.37<br \/>\nHence, from the above,<br \/>\nWe can conclude that the perimeter of quadrilateral ABCD is: 31.37<\/p>\n<p>Question 21.<br \/>\nFind the area of \u25b3CDE.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47998\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-21.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 21\" width=\"507\" height=\"299\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-21.png 507w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-21-300x177.png 300w\" sizes=\"(max-width: 507px) 100vw, 507px\" \/><\/p>\n<p>Question 22.<br \/>\nFind the area of rectangle BCEF<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nThe coordinates of the rectangle BCEF are:<br \/>\nB (0, 3) C (4, -1), E (2, -3), F (-2, 1)<br \/>\nNow,<br \/>\nThe length of BC = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4 &#8211; 0)\u00b2 + (3 + 1)\u00b2}\\)<br \/>\n= 5.65<br \/>\nThe length of CE = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4 &#8211; 2)\u00b2 + (3 &#8211; 1)\u00b2}\\)<br \/>\n= 2.82<br \/>\nThe length of EF = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(1 + 3)\u00b2 + (2 + 2)\u00b2}\\)<br \/>\n= 5.65<br \/>\nThe length of FB = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(0 + 2)\u00b2 + (3 &#8211; 1)\u00b2}\\)<br \/>\n= 2.82<br \/>\nSo,<br \/>\nThe area of the rectangle BCEF = Length \u00d7 Width<br \/>\n= 2.82 \u00d7 5.65<br \/>\n= 15.93<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the rectangle BCEF is: 15.93<\/p>\n<p>Question 23.<br \/>\nFind the area of \u25b3ABF<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47999\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-23.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 23\" width=\"424\" height=\"551\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-23.png 424w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-23-231x300.png 231w\" sizes=\"(max-width: 424px) 100vw, 424px\" \/><\/p>\n<p>Question 24.<br \/>\nFind the area of quadrilateral ABCD.<br \/>\nAnswer:<br \/>\nThe given vertices of the quadrilateral ABCD are:<br \/>\nA (-5, 4), B (0, 3), C (4, -1), D (4, -5)<br \/>\nNow,<br \/>\nThe length of AB = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(0 + 5)\u00b2 + (4 &#8211; 3)\u00b2}\\)<br \/>\n= 5.09<br \/>\nThe length of BC = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4 &#8211; 0)\u00b2 + (1 + 3)\u00b2}\\)<br \/>\n= 5.65<br \/>\nThe length of CD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4 &#8211; 4)\u00b2 + (5 &#8211; 1)\u00b2}\\)<br \/>\n= 4<br \/>\nThe length of DA = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4 + 5)\u00b2 + (4 + 5)\u00b2}\\)<br \/>\n= 12.72<br \/>\nThe length of AC = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4 + 5)\u00b2 + (4 + 1)\u00b2}\\)<br \/>\n= 10.29<br \/>\nThe length of BD = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4 &#8211; 0)\u00b2 + (3 + 5)\u00b2}\\)<br \/>\n= 8.94<br \/>\nSo,<br \/>\nThe area of the quadrilateral ABCD = \\(\\frac{1}{2}\\) \u00d7AC \u00d7 BD<br \/>\n= \\(\\frac{1}{2}\\) \u00d7 10.29 \u00d7 8.94<br \/>\n= 45.99<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area f the quadrilateral ABCD is: 45.99<\/p>\n<p><strong>ERROR ANALYSIS<\/strong><br \/>\nIn Exercises 25 and 26, describe and correct the error in finding the perimeter or area of the polygon.<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35807\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-116.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 116\" width=\"262\" height=\"246\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48000\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-25.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 25\" width=\"363\" height=\"205\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-25.png 363w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-25-300x169.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35806\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-117.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 117\" width=\"324\" height=\"354\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-117.png 324w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-117-275x300.png 275w\" sizes=\"(max-width: 324px) 100vw, 324px\" \/><br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nThe coordinates of the vertices of \u0394ABC are:<br \/>\nA (4, 3), B (5, 1), C (1, 1)<br \/>\nNow,<br \/>\nThe length of AB = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(5 &#8211; 4)\u00b2 + (3 &#8211; 1)\u00b2}\\)<br \/>\n= 2.23<br \/>\nThe length of BC = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(5 &#8211; 1)\u00b2 + (1 &#8211; 1)\u00b2}\\)<br \/>\n= 4<br \/>\nThe length of CA = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4 &#8211; 1)\u00b2 + (3 &#8211; 1)\u00b2}\\)<br \/>\n= 3.60<br \/>\nSo,<br \/>\nThe area of \u0394ABC = \\(\\frac{1}{2}\\) \u00d7AB \u00d7 BC<br \/>\n= \\(\\frac{1}{2}\\) \u00d7 2.23 \u00d7 4<br \/>\n= 4.46<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of \u0394ABC is: 4.46 sq. units<\/p>\n<p>In Exercises 27 and 28, use the diagram.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-35805\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-118.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 118\" width=\"170\" height=\"170\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-118.png 170w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-118-150x150.png 150w\" sizes=\"(max-width: 170px) 100vw, 170px\" \/><\/p>\n<p>Question 27.<br \/>\nDetermine which point is the remaining vertex of a triangle with an area of 4 square units.<br \/>\nA. R(2, 0)<br \/>\nB. S(- 2, &#8211; 1)<br \/>\nC. T(- 1, 0)<br \/>\nD. U(2, &#8211; 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48001\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-27.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 27\" width=\"583\" height=\"416\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-27.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-27-300x214.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 28.<br \/>\nDetermine which points are the remaining vertices of a rectangle with a perimeter of 14 units.<br \/>\nA. A(2, &#8211; 2) and B(2, &#8211; 1)<br \/>\nB. C(- 2, &#8211; 2) and D(- 2, 2)<br \/>\nC. E(- 2, &#8211; 2) and F(2, &#8211; 2)<br \/>\nD. G(2, 0) and H(2, 0)<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nThe given vertices are:<br \/>\nP (-2, 1), Q (2, 1)<br \/>\nWe know that,<br \/>\nThe perimeter is defined as the sum of all the sides of a given polygon<br \/>\nNow,<br \/>\nLet,<br \/>\nA (x, y), and B(p, q) are the remaining 2 points of a rectangle<br \/>\nNow,<br \/>\nThe length of PQ = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{2 + 2)\u00b2 + (1 &#8211; 1)\u00b2}\\)<br \/>\n= 4<br \/>\nThe length of QA = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(x &#8211; 2)\u00b2 + (y &#8211; 1)\u00b2}\\)<br \/>\nThe length of AB = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(x &#8211; p)\u00b2 + (y &#8211; q)\u00b2}\\)<br \/>\nThe length of BP = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(p + 2)\u00b2 + (q &#8211; 1)\u00b2}\\)<br \/>\nSo,<br \/>\nThe perimeter of the rectangle = PQ + QA + AB + BP<br \/>\n= 4 + \\(\\sqrt{(x &#8211; 2)\u00b2 + (y &#8211; 1)\u00b2}\\) + \\(\\sqrt{(x &#8211; p)\u00b2 + (y &#8211; q)\u00b2}\\) + \\(\\sqrt{(p + 2)\u00b2 + (q &#8211; 1)\u00b2}\\)<br \/>\nIt is given that,<br \/>\nThe perimeter of the rectangle = 14<br \/>\nSo,<br \/>\n4 + \\(\\sqrt{(x &#8211; 2)\u00b2 + (y &#8211; 1)\u00b2}\\) + \\(\\sqrt{(x &#8211; p)\u00b2 + (y &#8211; q)\u00b2}\\) + \\(\\sqrt{(p + 2)\u00b2 + (q &#8211; 1)\u00b2}\\) = 14<br \/>\n\\(\\sqrt{(x &#8211; 2)\u00b2 + (y &#8211; 1)\u00b2}\\) + \\(\\sqrt{(x &#8211; p)\u00b2 + (y &#8211; q)\u00b2}\\) + \\(\\sqrt{(p + 2)\u00b2 + (q &#8211; 1)\u00b2}\\) = 14 &#8211; 4<br \/>\n\\(\\sqrt{(x &#8211; 2)\u00b2 + (y &#8211; 1)\u00b2}\\) + \\(\\sqrt{(x &#8211; p)\u00b2 + (y &#8211; q)\u00b2}\\) + \\(\\sqrt{(p + 2)\u00b2 + (q &#8211; 1)\u00b2}\\) = 10<br \/>\nNow, from the given options,<br \/>\na.<br \/>\nThe given remaining vertices are:<br \/>\nA (2, -2), B (2, -1)<br \/>\nCompare the above vertices with<br \/>\nA (x, y), and B (p, q)<br \/>\nSo,<br \/>\n\\(\\sqrt{(2- 2)\u00b2 + (-2 &#8211; 1)\u00b2}\\) + \\(\\sqrt{(2 &#8211; 2)\u00b2 + (-2 + 1)\u00b2}\\) + \\(\\sqrt{(2 + 2)\u00b2 + (-1 &#8211; 1)\u00b2}\\) = 10<br \/>\n3 + 1 + 4.47 = 10<br \/>\n8.47 \u2260 10<br \/>\nb.<br \/>\nThe given remaining vertices are:<br \/>\nC (-2, -2), and D (-2, 2)<br \/>\nCompare the above vertices with<br \/>\nA (x, y), and B (p, q)<br \/>\nSo,<br \/>\n\\(\\sqrt{(-2 &#8211; 2)\u00b2 + (-2 &#8211; 1)\u00b2}\\) + \\(\\sqrt{(2 &#8211; 2)\u00b2 + (-2 &#8211; 2)\u00b2}\\) + \\(\\sqrt{(-2 + 2)\u00b2 + (2 &#8211; 1)\u00b2}\\) = 10<br \/>\n5 + 4 +1 = 10<br \/>\n10 = 10<br \/>\nHence, from the above,<br \/>\nWe can conclude that the remaining two vertices which gives the perimeter of 14 units are:<br \/>\nC (-2, -2), and D (-2, 2)<\/p>\n<p>Question 29.<br \/>\n<strong>USING STRUCTURE<\/strong><br \/>\nUse the diagram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35804\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-119.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 119\" width=\"189\" height=\"186\" \/><br \/>\na. Find the areas of square EFGH and square EJKL. What happens to the area when the perimeter of square EFGH is doubled?<br \/>\nb. Is this true for every square? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48002\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-29.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 29\" width=\"598\" height=\"354\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-29.png 598w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-29-300x178.png 300w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou are growing zucchini plants in your garden. In the figure. the entire garden is rectangle QRST. Each unit in the coordinate plane represents 1 foot.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35803\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-120.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 120\" width=\"257\" height=\"331\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-120.png 257w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-120-233x300.png 233w\" sizes=\"(max-width: 257px) 100vw, 257px\" \/><br \/>\na. Find the area of the garden.<br \/>\nAnswer:<br \/>\nIt is given that the rectangle QRST represents the garden<br \/>\nSo,<br \/>\nFrom the figure,<br \/>\nThe coordinates of the garden are:<br \/>\nQ (1, 13), R (7, 13), S (7, 1), and T (1, 1)<br \/>\nNow,<br \/>\nThe length of QR = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{13 &#8211; 13)\u00b2 + (7 &#8211; 1)\u00b2}\\)<br \/>\n= 6<br \/>\nThe length of RS = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{13 &#8211; 1)\u00b2 + (7 &#8211; 7)\u00b2}\\)<br \/>\n= 12<br \/>\nThe length of ST = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{1 &#8211; 1)\u00b2 + (7 &#8211; 1)\u00b2}\\)<br \/>\n= 6<br \/>\nThe length of TQ = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{13 &#8211; 1)\u00b2 + (1 &#8211; 1)\u00b2}\\)<br \/>\n= 12<br \/>\nSo,<br \/>\nThe area of the garden = (Length of the garden) \u00d7 (Width of the garden)<br \/>\n= 12 \u00d7 6<br \/>\n= 72 square feet<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the garden is: 72 square feet<\/p>\n<p>b. Zucchini plants require 9 square feet around each plant. How many zucchini plants can you plant?<br \/>\nAnswer:<br \/>\nFrom part (a),<br \/>\nThe area of the entire garden is: 72 square feet<br \/>\nIt is given that zucchini plants require 9 square feet around each plant<br \/>\nSo,<br \/>\nThe number of zucchini plants you can plant = \\(\\frac{The area of the entire garden}{The area required for each zucchini plant}\\)<br \/>\n= \\(\\frac{72}{9}\\)<br \/>\n= 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of zucchini plants you can plant is: 8 plants<\/p>\n<p>c. You decide to use square TUVW to grow lettuce. you can plant lour heads of lettuce per square loot.\u00a0 How many of each vegetable can you plant? Explain.<br \/>\nAnswer:<br \/>\nFrom the figure,<br \/>\nThe coordinates of the vertices of the rectangle TUVW are:<br \/>\nT (1, 1), U (1, 4), V (4, 4), W (4, 1)<br \/>\nNow,<br \/>\nThe length of TU = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{1 &#8211; 1)\u00b2 + (4 &#8211; 1)\u00b2}\\)<br \/>\n= 3<br \/>\nThe length of UV = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{4 &#8211; 4)\u00b2 + (4 &#8211; 1)\u00b2}\\)<br \/>\n= 3<br \/>\nThe length of VW = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{4 &#8211; 4)\u00b2 + (4 &#8211; 1)\u00b2}\\)<br \/>\n= 3<br \/>\nThe length of WT = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{4 &#8211; 1)\u00b2 + (1 &#8211; 1)\u00b2}\\)<br \/>\n= 3<br \/>\nSo,<br \/>\nThe area of square TUVW = Side\u00b2<br \/>\n= 3\u00b2 = 9 square feet<br \/>\nIt is given that,<br \/>\n1 square foot = 4 heads of lettuce<br \/>\nSo,<br \/>\n9 square feet = 9 \u00d7 4 = 36 heads of lettuce<br \/>\nHence, from the above,<br \/>\nWe can conclude that you can plant 36 vegetables of each type<\/p>\n<p>Question 31.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou are going for a hike in the woods. You hike to a waterfall that is 4 miles east of where you left your car. You then hike to a lookout point that is 2 miles north of your car. From the lookout point. you return to our ear.<\/p>\n<p>a. Map out your route in a coordinate plane with our car at the origin. Let each unit in the coordinate plane represent 1 mile. Assume you travel along straight paths.<br \/>\nb. How far do you travel during the entire hike?<br \/>\nc. When you leave the waterfall, you decide to hike to an old wishing well before going to the lookout point. The wishing well is 3 miles north and 2 miles west of the lookout point. How far do you travel during the entire hike?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48003\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-31.1.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 31.1\" width=\"565\" height=\"414\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-31.1.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-31.1-300x220.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48004\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-31.2.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 31.2\" width=\"557\" height=\"642\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-31.2.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-31.2-260x300.png 260w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nWithout performing any calculations, determine whether the triangle or the rectangle has a greater area. Which one has a greater perimeter? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35802\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-121.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 121\" width=\"172\" height=\"171\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-121.png 172w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-121-150x150.png 150w\" sizes=\"(max-width: 172px) 100vw, 172px\" \/><br \/>\nAnswer:<br \/>\nFrom the given graph,<br \/>\nWe can observe that the size of the rectangle is greater than the size of the triangle<br \/>\nSo,<br \/>\nWe can say that<br \/>\nThe area of the rectangle is greater than the area of the triangle<br \/>\nThe perimeter of the rectangle is greater than the perimeter of the triangle<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe area and the perimeter of the rectangle is greater than the area and the perimeter of the triangle<\/p>\n<p>Question 33.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nThe lines y<sub>1<\/sub> = 2x &#8211; 6, y<sub>2<\/sub> = &#8211; 3x + 4, and y<sub>3<\/sub> = &#8211; \\(\\frac{1}{2}\\) + 4 are the sides of a right triangle.<br \/>\na. Use slopes to determine which sides are perpendicular.<br \/>\nb. Find the vertices of the triangle.<br \/>\nc. Find the perimeter and area of the triangle.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48005\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-33.1.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 33.1\" width=\"593\" height=\"633\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-33.1.png 593w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-33.1-281x300.png 281w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48006\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-33.2.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 33.2\" width=\"592\" height=\"556\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-33.2.png 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-33.2-300x282.png 300w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nYour bedroom has an area of 350 square feet. You are remodeling to include an attached bathroom that has an area of 150 square feet. Draw a diagram of the remodeled bedroom and bathroom in a coordinate plane.<br \/>\nAnswer:<br \/>\nIt is given that your bedroom has an area of 350 square feet. You are remodeling to include an attached bathroom that has an area of 150 square feet.<br \/>\nSo,<br \/>\nThe dimensions of the bedroom that has an area of 350 square feet are:<br \/>\nLength: 20 feet and Width: 17.5 feet (Remember that any of the factor products of 350 will be the dimensions of the bedroom)<br \/>\nSo,<br \/>\nThe dimensions of the bedroom that has an area of 350 square feet in the coordinate plane are:<br \/>\n(0, 0), (0, 17.5), (20, 17.5), and (20, 0)<br \/>\nNow,<br \/>\nThe dimensions of an attached bathroom that has an area of 150 square feet are:<br \/>\nLength: 10 feet and Width: 15 feet (Remember that any of the factor products of 350 will be the dimensions of the bedroom)<br \/>\nSo,<br \/>\nThe dimensions of the attached bathroom that has an area of 150 square feet in the coordinate plane are:<br \/>\n(0, 0), (0, 5), (10, 15), (5, 0)<br \/>\nHence,<br \/>\nThe representation of the attached bedroom and the bathroom in a coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-75360\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-45.png\" alt=\"\" width=\"794\" height=\"586\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-45.png 794w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-45-300x221.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-45-768x567.png 768w\" sizes=\"(max-width: 794px) 100vw, 794px\" \/><\/p>\n<p>Question 35.<br \/>\n<strong>PROBLEM-SOLVING<\/strong><br \/>\nUse the diagram<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35801\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-122.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 122\" width=\"168\" height=\"167\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-122.png 168w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-122-150x150.png 150w\" sizes=\"(max-width: 168px) 100vw, 168px\" \/><br \/>\na. Find the perimeter and area of the square.<br \/>\nb. Connect the midpoints of the sides of the given square to make a quadrilateral. Is this quadrilateral a square? Explain our reasoning.<br \/>\nc. Find the perimeter and area of the quadrilateral you made in part (b). Compare this area to the area you found in part (a).<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48007\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-35.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 35\" width=\"582\" height=\"650\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-35.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-35-269x300.png 269w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims that a rectangle with the same perimeter as \u25b3QRS will have the same area as the triangle. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35800\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-123.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 123\" width=\"169\" height=\"171\" \/><br \/>\nAnswer:<br \/>\nNo, your friend is not correct<\/p>\n<p>Explanation:<br \/>\nIt is given that your friend claims that a rectangle with the same perimeter as \u25b3QRS will have the same area as the triangle.<br \/>\nBut,<br \/>\nWe know that,<br \/>\nThe size of the rectangle is greater than the size of the triangle<br \/>\nSo,<br \/>\nThe area of the rectangle will be greater than the area of the triangle even though the perimeter of the rectangle and the triangle are the same<br \/>\nHence, from the above,<br \/>\nWe can conclude that your friend is not correct<\/p>\n<p>Question 37.<br \/>\n<strong>REASONING<\/strong><br \/>\nTriangle ABC has a perimeter of 12 units. The vertices of the triangle are A(x, 2), B(2, &#8211; 2), and C(- 1, 2). Find the value of x.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48008\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-37.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 37\" width=\"461\" height=\"693\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-37.png 461w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-37-200x300.png 200w\" sizes=\"(max-width: 461px) 100vw, 461px\" \/><\/p>\n<p>Maintaining Mathematical Proficiency<\/p>\n<p>Solve the equation.<\/p>\n<p>Question 38.<br \/>\n3x &#8211; 7 = 2<br \/>\nAnswer:<br \/>\nThe given equatio is:<br \/>\n3x &#8211; 7 = 2<br \/>\nSo,<br \/>\n3x = 2 + 7<br \/>\n3x = 9<br \/>\nx = \\(\\frac{9}{3}\\)<br \/>\nx = 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x to the given equation is: 3<\/p>\n<p>Question 39.<br \/>\n5x + 9 = 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48009\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-39.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 39\" width=\"164\" height=\"99\" \/><\/p>\n<p>Question 40.<br \/>\nx + 4 = x &#8211; 12<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\nx + 4 = x &#8211; 12<br \/>\nx &#8211; x + 4 = -12<br \/>\n4 = -12<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given equation has no solution<\/p>\n<p>Question 41.<br \/>\n4x- 9 = 3x + 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48010\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-41.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 41\" width=\"189\" height=\"97\" \/><\/p>\n<p>Question 42.<br \/>\n11 &#8211; 2x = 5x &#8211; 3<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n11 &#8211; 2x = 5x &#8211; 3<br \/>\n11 + 3 = 5x + 2x<br \/>\n7x = 14<br \/>\nx = \\(\\frac{14}{7}\\)<br \/>\nx = 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x to the given equation is: 2<\/p>\n<p>Question 43.<br \/>\n\\(\\frac{x+1}{2}\\) = 4x &#8211; 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48011\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.4-a-43.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.4 a 43\" width=\"203\" height=\"184\" \/><\/p>\n<p>Question 44.<br \/>\nUse a compass and straightedge to construct a copy of the line segment.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35799\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-124.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 124\" width=\"299\" height=\"37\" \/><br \/>\nAnswer:<br \/>\nThe steps used to construct a line segment are:<br \/>\nStep 1:<br \/>\nYou are given\u00a0line segment\u00a0AB to\u00a0copy.<br \/>\nStep 2:<br \/>\nDraw a line segment that is longer than line segment AB. Label one of its endpoints C.<br \/>\nStep 3:<br \/>\nOpen your compass so that the anchor is on one endpoint of line segment AB and the pencil point is on the other endpoint.<\/p>\n<h3><a id=\"1.5_Measuring_and_Constructing_Angles\"><\/a>1.5 Measuring and Constructing Angles<\/h3>\n<p><strong>Essential Question<\/strong><\/p>\n<p>How can you measure and classify an angle?<br \/>\nAnswer:<br \/>\nAn angle is formed when two rays have the same endpoint or vertex.<br \/>\nAn &#8220;Angle&#8221; will be measured by using a protractor<br \/>\nClassification of angles:<br \/>\nAn angle can be classified according to the size of the<br \/>\nopening between its rays.<br \/>\nAn acute angle measures greater than 0\u00b0 and less<br \/>\nthan 90\u00b0.<br \/>\nA right-angle forms a square corner and measures 90\u00b0.<br \/>\nAn obtuse angle measures greater than 90\u00b0 and less than 180\u00b0<\/p>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Measuring and Classifying Angles<\/p>\n<p>Work with a partner: Find the degree measure of each of the following angles. Classify each angle as acute, right, or obtuse.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35798\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-125.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 125\" width=\"440\" height=\"253\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-125.png 440w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-125-300x173.png 300w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><br \/>\na. \u2220AOB<br \/>\nb. \u2220AOC<br \/>\nc. \u2220BOC<br \/>\nd. \u2220BOE<br \/>\ne. \u2220COE<br \/>\nf. \u2220COD<br \/>\ng. \u2220BOD<br \/>\nh. \u2220AOE<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35798\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-125.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 125\" width=\"440\" height=\"253\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-125.png 440w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-125-300x173.png 300w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><br \/>\na. \u2220AOB<br \/>\nFrom the above figure,<br \/>\n\u2220AOB = 35\u00b0<br \/>\nWe know that,<br \/>\nThe angle that is greater than 0\u00b0 and less than 90\u00b0 is an &#8220;Acute angle&#8221;<br \/>\nHence,<br \/>\n\u2220AOB is an acute angle<\/p>\n<p>b. \u2220AOC<br \/>\nFrom the above figure,<br \/>\n\u2220AOC = 65\u00b0<br \/>\nWe know that,<br \/>\nThe angle that is greater than 0\u00b0 and less than 90\u00b0 is an &#8220;Acute angle&#8221;<br \/>\nHence,<br \/>\n\u2220AOC is an acute angle<\/p>\n<p>c. \u2220BOC<br \/>\nFrom the above figure,<br \/>\n\u2220BOC = |65\u00b0 &#8211; 35\u00b0| = 30\u00b0<br \/>\nWe know that,<br \/>\nThe angle that is greater than 0\u00b0 and less than 90\u00b0 is an &#8220;Acute angle&#8221;<br \/>\nHence,<br \/>\n\u2220BOC is an acute angle<\/p>\n<p>d. \u2220BOE<br \/>\nFrom the above figure,<br \/>\n\u2220BOE = |145\u00b0 &#8211; 35\u00b0| = 110\u00b0<br \/>\nWe know that,<br \/>\nThe angle that is greater than 90\u00b0 and less than 180\u00b0 is an &#8220;Obtuse angle&#8221;<br \/>\nHence,<br \/>\n\u2220BOE is an acute angle<\/p>\n<p>e. \u2220COE<br \/>\nFrom the above figure,<br \/>\n\u2220COE = |145\u00b0 &#8211; 65\u00b0| = 80\u00b0<br \/>\nWe know that,<br \/>\nThe angle that is greater than 0\u00b0 and less than 90\u00b0 is an &#8220;Acute angle&#8221;<br \/>\nHence,<br \/>\n\u2220COE is an acute angle<\/p>\n<p>f. \u2220COD<br \/>\nFrom the above figure,<br \/>\n\u2220COD =|70\u00b0 &#8211;\u00a0 65\u00b0| = 5\u00b0<br \/>\nWe know that,<br \/>\nThe angle that is greater than 0\u00b0 and less than 90\u00b0 is an &#8220;Acute angle&#8221;<br \/>\nHence,<br \/>\n\u2220COD is an acute angle<\/p>\n<p>g. \u2220BOD<br \/>\nFrom the above figure,<br \/>\n\u2220BOD = |70\u00b0 &#8211;\u00a0 35\u00b0| = 35\u00b0<br \/>\nWe know that,<br \/>\nThe angle that is greater than 0\u00b0 and less than 90\u00b0 is an &#8220;Acute angle&#8221;<br \/>\nHence,<br \/>\n\u2220BOD is an acute angle<\/p>\n<p>h. \u2220AOE<br \/>\nFrom the above figure,<br \/>\n\u2220AOE = 145\u00b0<br \/>\nWe know that,<br \/>\nThe angle that is greater than 90\u00b0 and less than 180\u00b0 is an &#8220;Obtuse angle&#8221;<br \/>\nHence,<br \/>\n\u2220AOE is an obtuse angle<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Drawing a Regular Polygon<\/p>\n<p>Work with a partner.<\/p>\n<p>a. Use a ruler and protractor to draw the triangular pattern shown at the right.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35797\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-126.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 126\" width=\"195\" height=\"121\" \/><br \/>\nAnswer:<br \/>\nThe representation of the triangular pattern by using a ruler and a protractor is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-75960\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-46.png\" alt=\"\" width=\"213\" height=\"151\" \/><\/p>\n<p>b. Cut out the pattern and use it to draw three regular hexagons<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35796\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-127.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 127\" width=\"444\" height=\"132\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-127.png 444w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-127-300x89.png 300w\" sizes=\"(max-width: 444px) 100vw, 444px\" \/><\/p>\n<p>C. The sum of the angle measures of a polygon with n sides is equal to 180(n &#8211; 2)\u00b0. Do the angle measures at your hexagons agree with this rule? Explain.<br \/>\n<strong>ATTENDING TO PRECISION<\/strong><br \/>\nTo be proficient in math, you need to calculate and measure accurately and efficiently.<br \/>\nAnswer:<br \/>\nIt is given that the sum of the angle measures of a polygon with n sides is equal to 180 (n &#8211; 2)\u00b0<br \/>\nThis rule will be applicable for all the angle measures of all polygons<br \/>\nHence,<br \/>\nWe can conclude that the above rule will be applicable for the angle measures of the hexagon<\/p>\n<p>d. Partition your hexagons into smaller polygons. as shown below. For each hexagon. find the sum of the angle measures of the smaller polygons Does each sum equal the sum of the angle measures of a hexagon? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35795\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-128.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 128\" width=\"397\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-128.png 397w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-128-300x70.png 300w\" sizes=\"(max-width: 397px) 100vw, 397px\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nIf a polygon is divided into n partitions, then the angle measures of that polygon will also be divided into n partitions<br \/>\nSo,<br \/>\nThe sum of the angle measures of hexagon = 180(n &#8211; 2)\u00b0<br \/>\n= 180 ( 6 &#8211; 2 )\u00b0<br \/>\n= 720\u00b0<br \/>\nSo,<br \/>\nIn the first figure, the polygon is divided into 2 partitions<br \/>\nSo,<br \/>\nThe sum of the angle measures of each partition = 720 \/ 2<br \/>\n= 360\u00b0<br \/>\nIn the second figure, the polygon is divided into 3 partitions<br \/>\nSo,<br \/>\nThe sum of the angle measures of each partition = 720 \/ 3<br \/>\n= 240\u00b0<br \/>\nIn the third figure, the polygon is divided into 6 partitions<br \/>\nSo,<br \/>\nThe sum of the angle measures of each partition = 720 \/ 6<br \/>\n= 120\u00b0<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 3.<br \/>\nHow can you measure and classify an angle?<br \/>\nAnswer:<br \/>\nAn angle is formed when two rays have the same endpoint or vertex.<br \/>\nAn &#8220;Angle&#8221; will be measured by using a protractor<br \/>\nClassification of angles:<br \/>\nAn angle can be classified according to the size of the<br \/>\nopening between its rays.<br \/>\nAn acute angle measures greater than 0\u00b0 and less<br \/>\nthan 90\u00b0.<br \/>\nA right-angle forms a square corner and measures 90\u00b0.<br \/>\nAn obtuse angle measures greater than 90\u00b0 and less than 180\u00b0<\/p>\n<h3><a id=\"Lesson_1.5_Measuring_and_Constructing_Angles\"><\/a>Lesson 1.5 Measuring and Constructing Angles<\/h3>\n<p>Monitoring Progress<\/p>\n<p>Write three names for the angle.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35794\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-129.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 129\" width=\"177\" height=\"79\" \/><br \/>\nAnswer:<br \/>\nAn &#8220;Angle&#8221; is formed when two rays have the same endpoint or vertex.<br \/>\nSo,<br \/>\nHere, the angle is Q<br \/>\nHence,<br \/>\nThe three names for the given angle are: \u2220Q, \u2220PQR, and \u2220RQP<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35793\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-130.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 130\" width=\"119\" height=\"85\" \/><br \/>\nAnswer:<br \/>\nAn &#8220;Angle&#8221; is formed when two rays have the same endpoint or vertex.<br \/>\nSo,<br \/>\nHere, the angle is Y<br \/>\nHence,<br \/>\nThe three names for the given angle are: \u22201, \u2220XYZ, and \u2220ZYX<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35792\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-131.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 131\" width=\"133\" height=\"119\" \/><br \/>\nAnswer:<br \/>\nAn &#8220;Angle&#8221; is formed when two rays have the same endpoint or vertex.<br \/>\nSo,<br \/>\nHere, the angle is E<br \/>\nHence,<br \/>\nThe three names for the given angle are: \u22202, \u2220FED, and \u2220DEF<\/p>\n<p>Use the diagram in Example 2 to find the angle measure. Then classify the angle.<\/p>\n<p>Question 4.<br \/>\n\u2220JHM<br \/>\nAnswer:<br \/>\nFrom the above figure,<br \/>\n\u2220JHM =|145\u00b0 &#8211;\u00a0 0\u00b0| = 145\u00b0<br \/>\nWe know that,<br \/>\nThe angle that is greater than 90\u00b0 and less than 180\u00b0 is an &#8220;Obtuse angle&#8221;<br \/>\nHence,<br \/>\n\u2220JHM is an obtuse angle<\/p>\n<p>Question 5.<br \/>\n\u2220MHK<br \/>\nAnswer:<br \/>\nFrom the above figure,<br \/>\n\u2220MHK =|145\u00b0 &#8211;\u00a0 55\u00b0| = 110\u00b0<br \/>\nWe know that,<br \/>\nThe angle that is greater than 90\u00b0 and less than 180\u00b0 is an &#8220;Obtuse angle&#8221;<br \/>\nHence,<br \/>\n\u2220MHK is an obtuse angle<\/p>\n<p>Question 6.<br \/>\n\u2220MHL<br \/>\nAnswer:<br \/>\nFrom the above figure,<br \/>\n\u2220MHL =|145\u00b0 &#8211;\u00a0 90\u00b0| = 55\u00b0<br \/>\nWe know that,<br \/>\nThe angle that is greater than 0\u00b0 and less than 90\u00b0 is an &#8220;Acute angle&#8221;<br \/>\nHence,<br \/>\n\u2220MHL is an acute angle<\/p>\n<p>Question 7.<br \/>\nWithout measuring, is \u2220DAB \u2245 \u2220FEH in Example 3? Explain your reasoning. Use a protractor to verify your answer.<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can observe that,<br \/>\n\u2220DAB \u2245 90\u00b0<br \/>\n\u2220FEH &gt; 90\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that \u2220DAB is not congruent to \u2220FEH<\/p>\n<p>Find the indicated angle measures.<\/p>\n<p>Question 8.<br \/>\nGiven that \u2220KLM is a straight angle. find in \u2220KLN and, m\u2220NLM.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35791\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-132.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 132\" width=\"257\" height=\"126\" \/><br \/>\nAnswer:<br \/>\nAngle Addition Postulate:<br \/>\nIf point B lies in the interior of angle AOC, then. the postulate describes that putting two angles side by side with their vertices together creates a new angle whose measure equals the sum of the measures of the two original angles<br \/>\nIt is given that \u2220KLM is a straight angle<br \/>\nSo,<br \/>\n\u2220KLM = 180\u00b0<br \/>\nSo,<br \/>\n180\u00b0 = (10x &#8211; 5)\u00b0 + (4x + 3)\u00b0<br \/>\n180\u00b0 = (14x -2)\u00b0<br \/>\n180 + 2 = 14x<br \/>\n14x = 182<br \/>\nx = \\(\\frac{182}{14}\\)<br \/>\nx = 13\u00b0<br \/>\nSo,<br \/>\n\u2220KLN = (10x &#8211; 5)\u00b0<br \/>\n= 10 (13) &#8211; 5<br \/>\n= 130 &#8211; 5<br \/>\n= 125\u00b0<br \/>\n\u2220NLM = (4x + 3)\u00b0<br \/>\n= 4 (13) + 3<br \/>\n= 52 + 3<br \/>\n= 55\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220KLN and \u2220NLM are 125\u00b0 and 55\u00b0 respectively<\/p>\n<p>Question 9.<br \/>\nGiven that \u2220EFG is a right angle. find, m\u2220EFH and m\u2220HFG.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35790\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-133.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 133\" width=\"143\" height=\"152\" \/><br \/>\nAnswer:<br \/>\nAngle Addition Postulate:<br \/>\nIf point B lies in the interior of angle AOC, then. the postulate describes that putting two angles side by side with their vertices together creates a new angle whose measure equals the sum of the measures of the two original angles<br \/>\nIt is given that \u2220EFG is a right angle<br \/>\nSo,<br \/>\n\u2220EFG = 90\u00b0<br \/>\nSo,<br \/>\n90\u00b0 = (2x + 2)\u00b0 + (x + 1)\u00b0<br \/>\n90\u00b0 = (3x + 3)\u00b0<br \/>\n90 &#8211; 3 = 3x<br \/>\n3x = 87<br \/>\nx = \\(\\frac{87}{3}\\)<br \/>\nx = 29\u00b0<br \/>\nSo,<br \/>\n\u2220EFH = (2x + 2)\u00b0<br \/>\n= 2 (29) + 2<br \/>\n= 58 + 2<br \/>\n= 60\u00b0<br \/>\n\u2220HFG = (x + 1)\u00b0<br \/>\n= 29 + 1<br \/>\n= 30\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220EFH and \u2220HFG are 60\u00b0 and 30\u00b0 respectively<\/p>\n<p>Question 10.<br \/>\nAngle MNP is a straight angle, and \\(\\vec{N}\\)Q bisects \u2220MNP. Draw \u2220MNP and \\(\\vec{N}\\)Q. Use arcs to mark the congruent angles in your diagram. Find the angle measures of these congruent angles.<br \/>\nAnswer:<br \/>\nIt is given that angle MNP is a straight angle, and \\(\\vec{N}\\)Q bisects \u2220MNP. Draw \u2220MNP and \\(\\vec{N}\\)Q.<br \/>\nSo,<br \/>\nThe representation of the above statement is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-76433\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-47.png\" alt=\"\" width=\"284\" height=\"136\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that the angle measure of each congruent angle is: 55.3\u00b0<\/p>\n<h3><a id=\"Exercise_1.5_Measuring_and_Constructing_Angles\"><\/a>Exercise 1.5 Measuring and Constructing Angles<\/h3>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nTwo angles are __________ angles when they have the same measure.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48012\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-1.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 1\" width=\"503\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-1.png 503w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-1-300x36.png 300w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WHICH ONE DOES DOESN\u2019T BELONG?<\/strong><br \/>\nWhich angle name does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35789\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-134.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 134\" width=\"285\" height=\"131\" \/><br \/>\n\u2220BCA<br \/>\n\u2220BAC<br \/>\n\u22201<br \/>\n\u2220CAB<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nAn angle can be defined as the figure formed by two rays meeting at a common endpoint<br \/>\nSo,<br \/>\nFrom the given figure,<br \/>\nA, B, and C are the given angles<br \/>\nSo,<br \/>\nIn \u2220BCA, C is the angle<br \/>\nIn \u2220BAC, A is the angle<br \/>\nIn \u22201, A is the angle<br \/>\nIn \u2220CAB, A is the angle<br \/>\nHence, from the above,<br \/>\nWe can conclude that \u2220BCA doesn&#8217;t belong with the other three<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3 &#8211; 6. write three names for the angle.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35788\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-135.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 135\" width=\"128\" height=\"92\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48013\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-3.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 3\" width=\"514\" height=\"31\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-3.png 514w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-3-300x18.png 300w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35787\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-136.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 136\" width=\"127\" height=\"156\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nAn angle can be defined as the figure formed by two rays meeting at a common endpoint<br \/>\nHence,<br \/>\nThe names for the given angle are: \u2220G, \u2220FGH, and \u2220HGF<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35786\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-137.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 137\" width=\"184\" height=\"101\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48014\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-5.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 5\" width=\"582\" height=\"28\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-5.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-5-300x14.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35785\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-138.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 138\" width=\"169\" height=\"105\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nAn angle can be defined as the figure formed by two rays meeting at a common endpoint<br \/>\nHence,<br \/>\nThe names for the given angle are: \u22208, \u2220R, \u2220QRS, and \u2220SRQ<\/p>\n<p>In Exercises 7 and 8, name three different angles in the diagram.<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35784\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-139.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 139\" width=\"156\" height=\"125\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48015\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-7.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 7\" width=\"539\" height=\"31\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-7.png 539w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-7-300x17.png 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35783\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-140.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 140\" width=\"162\" height=\"146\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nAn angle can be defined as the figure formed by two rays meeting at a common endpoint<br \/>\nHence,<br \/>\nThe three different angles are: \u2220GJF, \u2220CJF, and \u2220CJG<\/p>\n<p>In Exercises 9 &#8211; 12 find the angle measure. Then classify the angle.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-35782\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-141.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 141\" width=\"300\" height=\"157\" \/><\/p>\n<p>Question 9.<br \/>\nm\u2220AOC<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48016\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-9.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 9\" width=\"579\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-9.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-9-300x48.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 10.<br \/>\nm\u2220BOD<br \/>\nAnswer:<br \/>\nFrom the above figure,<br \/>\n\u2220BOD = |0\u00b0 &#8211;\u00a0 65\u00b0| = 65\u00b0<br \/>\nWe know that,<br \/>\nThe angle that is greater than 0\u00b0 and less than 90\u00b0 is an &#8220;Acute angle&#8221;<br \/>\nHence,<br \/>\n\u2220BOD is an acute angle<\/p>\n<p>Question 11.<br \/>\nm\u2220COD<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48017\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-11.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 11\" width=\"561\" height=\"97\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-11.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-11-300x52.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 12.<br \/>\nm\u2220EOD<br \/>\nAnswer:<br \/>\nFrom the above figure,<br \/>\n\u2220EOD = |40\u00b0 &#8211;\u00a0 65\u00b0| = 25\u00b0<br \/>\nWe know that,<br \/>\nThe angle that is greater than 0\u00b0 and less than 90\u00b0 is an &#8220;Acute angle&#8221;<br \/>\nHence,<br \/>\n\u2220EOD is an acute angle<\/p>\n<p><strong>ERROR ANALYSIS<\/strong><br \/>\nIn Exercises 13 and 14. describe and correct the error in finding the angle measure. Use the diagram from Exercises 9 &#8211; 12.<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35781\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-142.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 142\" width=\"204\" height=\"84\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48018\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-13.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 13\" width=\"593\" height=\"84\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-13.png 593w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-13-300x42.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35780\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-143.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 143\" width=\"186\" height=\"76\" \/><br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\n\u2220D is at 40\u00b0 and \u2220E is at 65\u00b0<br \/>\nSo,<br \/>\n\u2220DOE = |40\u00b0 &#8211;\u00a0 65\u00b0| = 25\u00b0<br \/>\nHence,<br \/>\n\u2220DOE = 25\u00b0<\/p>\n<p><strong>CONSTRUCTION<\/strong><br \/>\nIn Exercises 15 and 16. use a compass and straightedge to copy the angle.<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35779\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-144.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 144\" width=\"138\" height=\"108\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48019\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-15.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 15\" width=\"589\" height=\"214\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-15.png 589w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-15-300x109.png 300w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35778\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-145.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 145\" width=\"139\" height=\"89\" \/><br \/>\nAnswer:<br \/>\nThe steps to copy the angle are:<br \/>\nStep 1:<br \/>\nLabel the vertex of the original angle as A. Draw a segment and label a point D on the segment.<br \/>\nStep 2:<br \/>\nDraw an arc with the center at A. Label the two intersecting points as B and C.<br \/>\nStep 3:<br \/>\nUsing the same radius, draw an arc with center D. Label the intersecting point as E.<br \/>\nStep 4:<br \/>\nDraw an arc with radius BC and center E. Label the intersection F.<br \/>\nStep 5:<br \/>\nDraw \\(\\overline{D F}\\)<\/p>\n<p>In Exercises 17 &#8211; 20, in m\u2220AED = 34\u00b0 and m\u2220EAD = 112\u00b0.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-35777\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-146.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 146\" width=\"369\" height=\"160\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-146.png 369w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-146-300x130.png 300w\" sizes=\"(max-width: 369px) 100vw, 369px\" \/><\/p>\n<p>Question 17.<br \/>\nIdentify the angles congruent to \u2220IED.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48020\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-17.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 17\" width=\"546\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-17.png 546w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-17-300x31.png 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p>Question 18.<br \/>\nIdentify the angles congruent to \u2220EAD.<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nThe angles congruent to \u2220EAD are:<br \/>\n\u2220DBC, \u2220ADB, and \u2220DAE<\/p>\n<p>Question 19.<br \/>\nFind m\u2220BDC.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48021\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-19.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 19\" width=\"229\" height=\"100\" \/><\/p>\n<p>Question 20.<br \/>\nFind m\u2220ADB.<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\n\u2220EAD = 112\u00b0<br \/>\nHence,<br \/>\nBy the property of Congruence,<br \/>\n\u2220EAD \u2261 \u2220ADB<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220ADB = 112\u00b0<\/p>\n<p>In Exercises 21 &#8211; 24, find the indicated angle measure.<\/p>\n<p>Question 21.<br \/>\nFind m\u2220ABC.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35776\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-147.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 147\" width=\"135\" height=\"119\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48022\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-21.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 21\" width=\"329\" height=\"100\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-21.png 329w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-21-300x91.png 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><\/p>\n<p>Question 22.<br \/>\nFind m\u2220LMN.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35775\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-148.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 148\" width=\"192\" height=\"111\" \/><br \/>\nAnswer:<br \/>\nBy using the Angle Addition postulate,<br \/>\n\u2220LMN = \u2220LMP + \u2220PMN<br \/>\n\u2220LMN = 85\u00b0 + 23\u00b0<br \/>\n\u2220LMN = 108\u00b0<\/p>\n<p>Question 23.<br \/>\nm\u2220RST = 114\u00b0. Find m\u2220RSV.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35774\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-149.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 149\" width=\"213\" height=\"132\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48023\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-23.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 23\" width=\"312\" height=\"98\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-23.png 312w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-23-300x94.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><\/p>\n<p>Question 24.<br \/>\n\u2220GHK is a straight angle. Find m\u2220LHK.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35773\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-150.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 150\" width=\"186\" height=\"114\" \/><br \/>\nAnswer:<br \/>\nBy using the Angle Addition Postulate,<br \/>\n\u2220GHK = \u2220GHL + \u2220LHK<br \/>\nIt is given that \u2220GHK is a straight line<br \/>\nSo,<br \/>\n\u2220GHK = 180\u00b0<br \/>\nSo,<br \/>\n180\u00b0 = 79\u00b0 + \u2220LHK<br \/>\n\u2220LHK = 180\u00b0 &#8211; 79\u00b0<br \/>\n\u2220LHK = 101\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220LHK = 101\u00b0<\/p>\n<p>In Exercises 25 &#8211; 30. find the indicated angle measures.<\/p>\n<p>Question 25.<br \/>\nm\u2220ABC = 95\u00b0. Find m\u2220ABD and m\u2220DBC.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35772\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-151.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 151\" width=\"131\" height=\"128\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48024\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-25.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 25\" width=\"444\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-25.png 444w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-25-300x161.png 300w\" sizes=\"(max-width: 444px) 100vw, 444px\" \/><\/p>\n<p>Question 26.<br \/>\nm\u2220XYZ = 117\u00b0. Find m\u2220XYW and m\u2220WYZ<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35771\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-152.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 152\" width=\"213\" height=\"135\" \/><br \/>\nAnswer:<br \/>\nBy using the Angle Addition Postulate,<br \/>\n\u2220XYZ = \u2220XYW + \u2220WYZ<br \/>\nIt is given that \u2220XYZ = 117\u00b0<br \/>\nSo,<br \/>\n117\u00b0 = (6x + 44)\u00b0 + (-10x + 65)\u00b0<br \/>\n117\u00b0 = (-4x + 109)\u00b0<br \/>\n-4x = 117 &#8211; 109<br \/>\n-4x = 8<br \/>\nx = \\(\\frac{-8}{4}\\)<br \/>\nx = -2<br \/>\nHence,<br \/>\n\u2220XYW = (6x + 44)\u00b0<br \/>\n= 6 (-2) + 44<br \/>\n= 44 &#8211; 12<br \/>\n= 32\u00b0<br \/>\n\u2220WYZ = (-10x + 65)\u00b0<br \/>\n= -10 (-2) + 65<br \/>\n= 20 + 65<br \/>\n= 85\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220XYW = 32\u00b0 and \u2220WYZ = 85\u00b0<\/p>\n<p>Question 27.<br \/>\n\u2220LMN is a straight angle. Find m\u2220LMP and m\u2220NMP<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35770\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-153.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 153\" width=\"289\" height=\"115\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48025\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-27.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 27\" width=\"495\" height=\"241\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-27.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-27-300x146.png 300w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><\/p>\n<p>Question 28.<br \/>\n\u2220ABC is a straight angle. Find m\u2220ABX and m\u2220CBX.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35769\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-154.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 154\" width=\"279\" height=\"111\" \/><br \/>\nAnswer:<br \/>\nFrom the Angle Addition Postulate,<br \/>\n\u2220ABC = \u2220ABX + \u2220CBX<br \/>\nIt is given that \u2220ABC is a straight angle<br \/>\nSo,<br \/>\n\u2220ABC = 180\u00b0<br \/>\nSo,<br \/>\n180\u00b0 = (14x + 70)\u00b0 + (20x + 8)\u00b0<br \/>\n180\u00b0 = 34x + 78<br \/>\n180 &#8211; 78 = 34x<br \/>\n34x = 102\u00b0<br \/>\nx = \\(\\frac{102}{34}\\)<br \/>\nx = 3\u00b0<br \/>\nSo,<br \/>\n\u2220ABX = (14x + 70)\u00b0<br \/>\n= 14 (3) + 70<br \/>\n= 42 + 70<br \/>\n= 112\u00b0<br \/>\n\u2220CBX = (20x + 8)\u00b0<br \/>\n= 20 (3) + 8<br \/>\n= 60 + 8<br \/>\n= 68\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220ABX =\u00a0 112\u00b0 and \u2220CBX = 68\u00b0<\/p>\n<p>Question 29.<br \/>\nFind m\u2220RSQ and M\u2220TSQ.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35768\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-155.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 155\" width=\"125\" height=\"132\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48026\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-29.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 29\" width=\"461\" height=\"238\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-29.png 461w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-29-300x155.png 300w\" sizes=\"(max-width: 461px) 100vw, 461px\" \/><\/p>\n<p>Question 30.<br \/>\nFind m\u2220DEH and m\u2220FEH.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35767\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-156.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 156\" width=\"124\" height=\"121\" \/><br \/>\nAnswer:<br \/>\nFrom the Angle Addition Postulate,<br \/>\n\u2220DEF = \u2220DEH + \u2220FEH<br \/>\nFrom the figure,<br \/>\nWe can observe that \u2220DEF is a right angle<br \/>\nSo,<br \/>\n\u2220DEF = 90\u00b0<br \/>\nSo,<br \/>\n90\u00b0 = 13x\u00b0 + (10x + 21)\u00b0<br \/>\n90\u00b0 = 23x + 21<br \/>\n90 &#8211; 21 = 23x<br \/>\n23x = 69\u00b0<br \/>\nx = \\(\\frac{69}{23}\\)<br \/>\nx = 3\u00b0<br \/>\nSo,<br \/>\n\u2220DEH = 13x\u00b0<br \/>\n= 13 (3)<br \/>\n= 39\u00b0<br \/>\n\u2220FEH = (10x + 21)\u00b0<br \/>\n= 10 (3) + 21<br \/>\n= 30 + 21<br \/>\n= 51\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220DEH =\u00a0 39\u00b0 and \u2220FEH = 51\u00b0<\/p>\n<p><strong>CONSTRUCTION<\/strong><br \/>\nIn Exercises 31 and 32. copy the angle. Then construct the angle bisector with a compass and straightedge.<br \/>\nQuestion 31.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35766\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-157.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 157\" width=\"135\" height=\"122\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48027\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-31.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 31\" width=\"585\" height=\"311\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-31.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-31-300x159.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 32.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35765\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-158.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 158\" width=\"138\" height=\"64\" \/><br \/>\nAnswer:<br \/>\nThe steps for the construction of the angle bisector and copying of the angle is:<br \/>\nStep 1:<br \/>\nLabel the vertex of the angle as A. Place the compass at A.<br \/>\nStep 2:<br \/>\nDraw an arc that intersects both sides of the angle. Label the intersections B and C.<br \/>\nStep 3:<br \/>\nPlace the compass at C and draw an arc, then place the compass point at B. Using the same radius, draw another arc. Label the intersection D.<br \/>\nStep 4:<br \/>\nUse a straightedge to draw a ray through A and D.<br \/>\nStep 5:<br \/>\n\\(\\overline{A D}\\) bisects \u2220A<\/p>\n<p>In Exercises 33 &#8211; 36, \\(\\vec{Q}\\)S bisects \u2220PQR. Use the diagram and the given angle measure to find the indicated angle measures.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35764\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-159.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 159\" width=\"156\" height=\"109\" \/><\/p>\n<p>Question 33.<br \/>\nm\u2220PQS = 63\u00b0. Find m\u2220RQS and m\u2220PQR.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48028\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-33.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 33\" width=\"503\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-33.png 503w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-33-300x40.png 300w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><\/p>\n<p>Question 34.<br \/>\nm\u2220RQS = 71\u00b0. Find m\u2220PQS and m\u2220PQR.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nAn &#8220;Angle Bisector&#8221; makes the two angles congruent i.e., equal<br \/>\nSo,<br \/>\nFrom the above figure,<br \/>\nWe can say that,<br \/>\n\u2220PQS = \u2220RQS<br \/>\nNow,<br \/>\nBy using the Angle Addition Postulate,<br \/>\n\u2220PQR = \u2220PQS + \u2220RQS<br \/>\nIt is given that,<br \/>\n\u2220RQS = 71\u00b0<br \/>\nSo,<br \/>\n\u2220PQS = 71\u00b0<br \/>\nSo,<br \/>\n\u2220PQR = 71 + 71 = 142\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220PQS = 71\u00b0 and \u2220PQR = 142\u00b0<\/p>\n<p>Question 35.<br \/>\nm\u2220PQR = 124\u00b0. Find m\u2220PQS and m\u2220RQS.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48029\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-35.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 35\" width=\"382\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-35.png 382w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-35-300x67.png 300w\" sizes=\"(max-width: 382px) 100vw, 382px\" \/><\/p>\n<p>Question 36.<br \/>\nm\u2220PQR = 119\u00b0. Find m\u2220PQS and m\u2220RQS.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nAn &#8220;Angle Bisector&#8221; makes the two angles congruent i.e., equal<br \/>\nSo,<br \/>\nFrom the above figure,<br \/>\nWe can say that,<br \/>\n\u2220PQS = \u2220RQS<br \/>\nNow,<br \/>\nBy using the Angle Addition Postulate,<br \/>\n\u2220PQR = \u2220PQS + \u2220RQS<br \/>\nIt is given that,<br \/>\n\u2220PQR = 119\u00b0<br \/>\nSo,<br \/>\n119\u00b0 = 2 (\u2220PQS)<br \/>\n\u2220PQS = 59.5\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220PQS = 59.5\u00b0 and \u2220RQS = 59.5\u00b0<\/p>\n<p>In Exercises 37 &#8211; 40, \\(\\overrightarrow{B D}\\) bisects \u2220ABC. Find m\u2220ABD, m\u2220CBD, and m\u2220ABC.<\/p>\n<p>Question 37.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35763\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-160.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 160\" width=\"110\" height=\"120\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48030\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-37.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 37\" width=\"444\" height=\"272\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-37.png 444w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-37-300x184.png 300w\" sizes=\"(max-width: 444px) 100vw, 444px\" \/><\/p>\n<p>Question 38.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35762\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-161.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 161\" width=\"131\" height=\"97\" \/><br \/>\nAnswer:<br \/>\nIt is given that \\(\\overrightarrow{B D}\\) bisects \u2220ABC<br \/>\nSo,<br \/>\nBy using the bisector property,<br \/>\n\u2220ABD = \u2220DBC<br \/>\nSo,<br \/>\n(3x + 6)\u00b0 = (7x &#8211; 18)\u00b0<br \/>\n3x &#8211; 7x = -18 &#8211; 6<br \/>\n-4x = -24<br \/>\n4x = 24<br \/>\nx = \\(\\frac{24}{4}\\)<br \/>\nx = 6\u00b0<br \/>\nSo,<br \/>\n\u2220ABD = (3x + 6)\u00b0<br \/>\n= 3 (6) + 6<br \/>\n= 18 + 6<br \/>\n= 24\u00b0<br \/>\n\u2220DBC = (7x &#8211; 18)\u00b0<br \/>\n= 7 (6) &#8211; 18<br \/>\n= 42 &#8211; 18<br \/>\n= 24\u00b0<br \/>\n\u2220ABC = \u2220ABD + \u2220DBC<br \/>\n= 24 + 24 = 48\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220ABC = 48\u00b0, \u2220ABD = 24\u00b0, and \u2220CBD = 24\u00b0<\/p>\n<p>Question 39.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35761\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-162.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 162\" width=\"164\" height=\"114\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48031\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-39.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 39\" width=\"491\" height=\"275\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-39.png 491w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-39-300x168.png 300w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><\/p>\n<p>Question 4o.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35760\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-163.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 163\" width=\"162\" height=\"110\" \/><br \/>\nAnswer:<br \/>\nIt is given that \\(\\overrightarrow{B D}\\) bisects \u2220ABC<br \/>\nSo,<br \/>\nBy using the bisector property,<br \/>\n\u2220ABD = \u2220DBC<br \/>\nSo,<br \/>\n(8x + 35)\u00b0 = (11x + 23)\u00b0<br \/>\n8x &#8211; 11x = 23\u00a0 35<br \/>\n-3x = -12<br \/>\n3x = 12<br \/>\nx = \\(\\frac{12}{3}\\)<br \/>\nx = 4\u00b0<br \/>\nSo,<br \/>\n\u2220ABD = (8x + 35)\u00b0<br \/>\n= 8 (4) + 35<br \/>\n= 32 + 35<br \/>\n= 67\u00b0<br \/>\n\u2220DBC = (11x + 23)\u00b0<br \/>\n= 11 (4) + 23<br \/>\n= 44 + 23<br \/>\n= 67\u00b0<br \/>\n\u2220ABC = \u2220ABD + \u2220DBC<br \/>\n= 67 + 67 = 134\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220ABC = 134\u00b0, \u2220ABD = 67\u00b0, and \u2220CBD = 67\u00b0<\/p>\n<p>Question 41.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how to find m\u2220ABD when you are given m\u2220ABC and m\u2220CBD.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35759\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-164.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 164\" width=\"182\" height=\"92\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48032\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-41.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 41\" width=\"592\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-41.png 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-41-300x43.png 300w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nThe map shows the intersections of three roads. Malcolm Way intersects Sydney Street at an angle of 162\u00b0. Park Road intersects Sydney Street at an an\u00cce of 87\u00b0. Find the angle at which Malcom Way intersects Park Road.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35758\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-165.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 165\" width=\"353\" height=\"149\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-165.png 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-165-300x127.png 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nAnswer:<br \/>\nIt is given that Malcolm Way intersects Sydney Street at an angle of 162\u00b0. Park Road intersects Sydney Street at an an\u00cce of 87\u00b0.<br \/>\nFrom the figure,<br \/>\nWe can observe that<br \/>\nThe angle between Malcolm Way and Sydney street = The angle between Sydney street and Park Road + The angle between Malcolm way and Park road<br \/>\nSo,<br \/>\n162\u00b0 = 87\u00b0 + The angle between Malcolm way and Park Road<br \/>\nThe angle between Malcolm Way and Park Road = 162 &#8211; 87<br \/>\nThe angle between Malcolm Way and Park Road = 75\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the angle at which Malcolm Way intersects Park Road is: 75\u00b0<\/p>\n<p>Question 43.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nIn the sculpture shown in the photograph. the measure of \u2220LMN is 76\u00b0 and the measure of \u2220PMN is 36\u00b0. What is the measure of \u2220LMP?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35757\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-166.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 166\" width=\"292\" height=\"222\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48033\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-43.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 43\" width=\"339\" height=\"96\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-43.png 339w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-43-300x85.png 300w\" sizes=\"(max-width: 339px) 100vw, 339px\" \/><\/p>\n<p><strong>USING STRUCTURE<\/strong><br \/>\nIn Exercise 44 &#8211; 46. use the diagram of the roof truss.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35756\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-167.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 167\" width=\"442\" height=\"185\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-167.png 442w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-167-300x126.png 300w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><\/p>\n<p>Question 44.<br \/>\nIn the roof truss, \\(\\vec{B}\\)G bisects \u2220ABC and \u2220DEF. m\u2220ABC = 112\u00b0. and \u2220ABC \u2245 \u2220DEF Find the measure of each angle.<br \/>\na. m\u2220DEF<br \/>\nAnswer:<br \/>\nIt is given that<br \/>\n\\(\\vec{B}\\)G bisects \u2220ABC and \u2220DEF<br \/>\nIt is also given that<br \/>\n\u2220ABC = \u2220DEF<br \/>\n\u2220ABC = 112\u00b0<br \/>\nHence,<br \/>\n\u2220DEF = 112\u00b0<\/p>\n<p>b. m\u2220ABG<br \/>\nAnswer:<br \/>\nIt is given that \\(\\vec{B}\\)G bisects \u2220ABC and \u2220DEF<br \/>\nSo,<br \/>\nFor \u2220ABC,<br \/>\nBy congruence property,<br \/>\n\u2220ABG = \u2220CBG<br \/>\nHence,<br \/>\n\u2220ABG = \u2220ABC \/ 2<br \/>\n= 112 \/ 2<br \/>\n= 56\u00b0<\/p>\n<p>c. m\u2220CBG<br \/>\nAnswer:<br \/>\nIt is given that \\(\\vec{B}\\)G bisects \u2220ABC and \u2220DEF<br \/>\nSo,<br \/>\nFor \u2220ABC,<br \/>\nBy congruence property,<br \/>\n\u2220ABG = \u2220CBG<br \/>\nHence,<br \/>\n\u2220CBG = \u2220ABC \/ 2<br \/>\n= 112 \/ 2<br \/>\n= 56\u00b0<\/p>\n<p>d. m\u2220DEG<br \/>\nAnswer:<br \/>\nIt is given that \\(\\vec{B}\\)G bisects \u2220ABC and \u2220DEF<br \/>\nSo,<br \/>\nFor \u2220DEF,<br \/>\nBy congruence property,<br \/>\n\u2220DEG = \u2220EGF<br \/>\nHence,<br \/>\n\u2220DEG = \u2220DEF \/ 2<br \/>\n= 112 \/ 2<br \/>\n= 56\u00b0<\/p>\n<p>Question 45.<br \/>\nIn the roof truss, \u2220DGF is a straight angle, and \\(\\vec{G}\\)B bisects \u2220DGF Find m\u2220DGE and m\u2220FGE.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48034\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-45.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 45\" width=\"504\" height=\"97\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-45.png 504w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-45-300x58.png 300w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><\/p>\n<p>Question 46.<br \/>\nName an example of each of the four types of angles according to their measures in the diagram.<br \/>\nAnswer:<br \/>\nThere are 4 types of angles. They are:<br \/>\na. Acute angle:<br \/>\nThe angle that is greater than 0\u00b0 and less than 90\u00b0 is an &#8220;Acute angle&#8221;<br \/>\nb. Obtuse angle:<br \/>\nThe angle that is greater than 90\u00b0 and less than 180\u00b0 is an &#8220;Obtuse angle&#8221;<br \/>\nc. Straight angle:<br \/>\nThe angle 180\u00b0 is called a &#8220;Straight angle&#8221;<br \/>\nd. Right angle:<br \/>\nThe angle 90\u00b0 is called a &#8220;Right angle&#8221;<\/p>\n<p><strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\n47. In \u2220ABC. \\(\\vec{B}\\)X is in the interior 0f the angle. m\u2220ABX is 12 more than 4 times m\u2220CBX. and in m\u2220ABC = 92\u00b0.<br \/>\na. Draw a diagram to represent the situation.<br \/>\nb. Write and solve an equation to find m\u2220ABX and, m\u2220CBX.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48035\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-47.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 47\" width=\"463\" height=\"429\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-47.png 463w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-47-300x278.png 300w\" sizes=\"(max-width: 463px) 100vw, 463px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nThe angle between the minute hand and the hour hand of a clock is 90\u00b0 What time is it? Justify your answer.<br \/>\nAnswer:<br \/>\nFrom the clock,<br \/>\nWe can observe that the angle between the minute hand and the hour hand of a clock is 90\u00b0 when the time will be 3:00 and 9:00<\/p>\n<p>Question 49.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nClassify the angles that result from bisecting each type of angle.<br \/>\na. acute angle<br \/>\nb. right angle<br \/>\nc. obtuse angle<br \/>\nd. straight angle<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48036\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-49.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 49\" width=\"578\" height=\"273\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-49.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-49-300x142.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 50.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nClassify the angles that result from drawing a ray in the interior of each type of angle. Include all possibilities and explain your reasoning.<br \/>\na. acute angle<br \/>\nb. right angle<br \/>\nc. obtuse angle<br \/>\nd. straight angle<br \/>\nAnswer:<br \/>\nThe classification of angles that result from drawing a ray in the interior of each type of angle is:<br \/>\na. Acute angle:<br \/>\nThe angle that is greater than 0\u00b0 and less than 90\u00b0 is an &#8220;Acute angle&#8221;<br \/>\nb. Obtuse angle:<br \/>\nThe angle that is greater than 90\u00b0 and less than 180\u00b0 is an &#8220;Obtuse angle&#8221;<br \/>\nc. Straight angle:<br \/>\nThe angle 180\u00b0 is called a &#8220;Straight angle&#8221;<br \/>\nd. Right angle:<br \/>\nThe angle 90\u00b0 is called a &#8220;Right angle&#8221;<\/p>\n<p>Question 51.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nThe ray from the origin through (4, 0) forms one side of an angle. Use the numbers below as x- and y-coordinates to create each type of angle in a coordinate plane.<br \/>\n&#8211; 2 &#8211; 1 0 1 2<br \/>\na. acute angle<br \/>\nb. right angle<br \/>\nc. obtuse angle<br \/>\nd. straight angle<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48037\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-51.1.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 51.1\" width=\"436\" height=\"524\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-51.1.png 436w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-51.1-250x300.png 250w\" sizes=\"(max-width: 436px) 100vw, 436px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48038\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-51.2.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 51.2\" width=\"485\" height=\"456\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-51.2.png 485w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-51.2-300x282.png 300w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><\/p>\n<p>Question 52.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims it is possible for a straight angle to Consist of two obtuse angles. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\nNo, your friend is not correct<br \/>\nWe know that,<br \/>\nA straight angle consists of 2 Right angles or a Right angle and an obtuse angle<br \/>\nSo,<br \/>\nThe claim of your friend which is a straight angle consists of two obtuse angles is not correct<br \/>\nHence, from the above,<br \/>\nWe can conclude that the claim of your friend is not correct<\/p>\n<p>Question 53.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nTwo acute angles are added together. What type(s) of angle(s) do they form? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48039\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-53.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 53\" width=\"573\" height=\"89\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-53.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-53-300x47.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 54.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nUse the diagram<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35755\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-168.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 168\" width=\"252\" height=\"151\" \/><br \/>\na. Is it possible for \u2220XYZ to be a straight angle? Explain your reasoning.<br \/>\nAnswer:<br \/>\nFrom the figure,<br \/>\n\u2220XYZ is a flat line i.e., there is no angle<br \/>\nSo,<br \/>\n\u2220XYZ = 0\u00b0 or 180\u00b0<br \/>\nWe know that,<br \/>\nThe line that has an angle of 0\u00b0 or 180\u00b0 is called a &#8220;Straight line&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220XYZ is a straight angle<\/p>\n<p>b. What can you change in the diagram so that \u2220XYZ is a straight angle?<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\n\u2220XYZ is already a straight angle<br \/>\nSo,<br \/>\nThere is no change to make \u2220XYZ a straight line<\/p>\n<p>Question 55.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain the process of bisecting an angle in your own words. Compare it to bisecting a segment.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48040\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-55.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 55\" width=\"601\" height=\"194\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-55.png 601w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-55-300x97.png 300w\" sizes=\"(max-width: 601px) 100vw, 601px\" \/><\/p>\n<p>Question 56.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\n\\(\\vec{S}\\)Q bisects \u2220RST, \\(\\vec{S}\\)P bisects \u2220RSQ. and \\(\\vec{S}\\)V bisects \u2220RSP. The measure of \u2220VSP is 17\u00b0. Find in m\u2220TSQ. Explain.<br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nA bubble level is a tool used<br \/>\nto determine whether a surface is horizontal. like the top of a picture frame. If the bubble is not exactly in the middle when the level is placed on the surface. then the surface is not horizontal. What is the most realistic type of angle Formed by the level and a horizontal line when the bubble is not in the middle? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35754\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-1-Basics-of-Geometry-169.png\" alt=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry 169\" width=\"301\" height=\"80\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48041\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-57.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 57\" width=\"539\" height=\"91\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-57.png 539w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-57-300x51.png 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/p>\n<p>Maintaining Mathematical Proficiency<\/p>\n<p>Solve the equation.<\/p>\n<p>Question 58.<br \/>\nx + 67 = 180<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\nx + 67 = 180<br \/>\nSo,<br \/>\nx = 180 &#8211; 67<br \/>\nx = 113<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 113<\/p>\n<p>Question 59.<br \/>\nx + 58 = 90<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48043\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-61.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 61\" width=\"173\" height=\"58\" \/><\/p>\n<p>Question 60.<br \/>\n16 + x = 90<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n16 + x = 90<br \/>\nSo,<br \/>\nx = 90 &#8211; 16<br \/>\nx = 74<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 74<\/p>\n<p>Question 61.<br \/>\n109 + x = 180<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n109 + x = 180<br \/>\nSo,<br \/>\nx = 180 &#8211; 109<br \/>\nx = 71<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 71<\/p>\n<p>Question 62.<br \/>\n(6x + 7) + (13x + 21) = 180<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n(6x + 7) + (13x + 21) = 180<br \/>\nSo,<br \/>\n19x + 28 = 180<br \/>\n19x = 180 &#8211; 28<br \/>\n19x = 152<br \/>\nx = \\(\\frac{152}{9}\\)<br \/>\nx = 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 8<\/p>\n<p>Question 63.<br \/>\n(3x + 15) + (4x &#8211; 9) = 90<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48044\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-63.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 63\" width=\"246\" height=\"126\" \/><\/p>\n<p>Question 64.<br \/>\n(11x &#8211; 25) + (24x + 10) = 90<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n(11x &#8211; 25) + (24x + 10) = 90<br \/>\nSo,<br \/>\n35x &#8211; 15 = 90<br \/>\n35x = 90 + 15<br \/>\n35x = 105<br \/>\nx = \\(\\frac{105}{35}\\)<br \/>\nx = 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 3<\/p>\n<p>Question 65.<br \/>\n(14x &#8211; 18) + (5x + 8) = 180<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48045\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-1.5-a-65.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 1.5 a 65\" width=\"284\" height=\"134\" \/><\/p>\n<h3><a id=\"1.6_Describing_Pairs_of_Angles\"><\/a>1.6 Describing Pairs of Angles<\/h3>\n<p><strong>Essential Question<\/strong><\/p>\n<p>How can you describe angle pair relationships and use these descriptions to find angle measures?<br \/>\nAnswer:<br \/>\nTwo adjacent angles are a linear pair when their non-common sides are opposite rays. The angles in a linear pair are supplementary angles. common side L1+22=180\u00b0. Two angles are vertical angles when their sides form two pairs of opposite rays<\/p>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Work with a partner: The five-pointed star has a regular pentagon at its center.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35753\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-170.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 170\" width=\"243\" height=\"230\" \/><\/p>\n<p>a. What do you notice about the following angle pairs?<br \/>\nx\u00b0 and y\u00b0<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nx and y share a common line<br \/>\nWe know that,<br \/>\nThe angles that share a common side are called &#8220;Adjacent angles&#8221;<br \/>\nHence,<br \/>\nx\u00b0 and y\u00b0 are called &#8220;Adjacent angles&#8221;<\/p>\n<p>y\u00b0 and z\u00b0<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\ny and z share a common line<br \/>\nWe know that,<br \/>\nThe angles that share a common side are called &#8220;Adjacent angles&#8221;<br \/>\nHence,<br \/>\ny\u00b0 and z\u00b0 are called &#8220;Adjacent angles&#8221;<\/p>\n<p>x\u00b0 and z\u00b0<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nx and z share a common vertex<br \/>\nWe know that,<br \/>\nThe angles that share a common vertex are called &#8220;Vertical angles&#8221;<br \/>\nHence,<br \/>\nx\u00b0 and z\u00b0 are called &#8220;Vertical angles&#8221;<\/p>\n<p>b. Find the values of the indicated variables. Do not use a protractor to measure the angles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35752\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-171.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 171\" width=\"75\" height=\"148\" \/><br \/>\nExplain how you obtained each answer.<br \/>\nAnswer:<br \/>\nwe know that,<br \/>\nAdjacent angles will always be 180\u00b0 or 90\u00b0<br \/>\nVertical angles are equal<br \/>\nSo,<br \/>\nFrom the figure,<br \/>\nWe can observe that<br \/>\nx + 108\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 108\u00b0<br \/>\nx\u00b0 = 72\u00b0<br \/>\nNow,<br \/>\nFrom the figure,<br \/>\nWe can observe that x and y are the vertical angles<br \/>\nSo,<br \/>\ny\u00b0 = 72\u00b0<br \/>\nNow,<br \/>\nFrom the figure,<br \/>\nWe can observe that y and z are the adjacent angles<br \/>\nSo,<br \/>\ny\u00b0 + z\u00b0 = 180\u00b0<br \/>\nz\u00b0 = 180\u00b0 &#8211; 72\u00b0<br \/>\nz\u00b0 = 108\u00b0<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe vertically opposite angles are equal<br \/>\nSo,<br \/>\ny = v<br \/>\nSo,<br \/>\nv\u00b0 = 72\u00b0<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe vertically opposite angles are equal<br \/>\nSo,<br \/>\nw = v<br \/>\nSo,<br \/>\nw\u00b0 = 72\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the angle measures are:<br \/>\nx\u00b0 = 72\u00b0, y\u00b0 = 72\u00b0, z\u00b0 = 108\u00b0, v\u00b0 = 72\u00b0 and w\u00b0 = 72\u00b0<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Finding Angle Measures<\/p>\n<p>Work with a partner: A square is divided by its diagonals into four triangles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35751\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-172.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 172\" width=\"200\" height=\"197\" \/><\/p>\n<p>a. What do you notice about the following angle pairs?<br \/>\na\u00b0 and b\u00b0<br \/>\nAnswer:<br \/>\nFrom the above figure,<br \/>\nWe can observe that a\u00b0 and b\u00b0 are adjacent angles<br \/>\nSo,<br \/>\nWe can say that<br \/>\na\u00b0 + b\u00b0 = 90\u00b0<\/p>\n<p>c\u00b0 and d\u00b0<br \/>\nAnswer:<br \/>\nFrom the above figure,<br \/>\nWe can observe that c\u00b0 and d\u00b0 are adjacent angles<br \/>\nSo,<br \/>\nWe can say that<br \/>\nc\u00b0 + d\u00b0 = 90\u00b0<\/p>\n<p>c\u00b0 and e\u00b0<br \/>\nAnswer:<br \/>\nFrom the above figure,<br \/>\nWe can observe that c\u00a0and e\u00a0are the opposite angles<br \/>\nSo,<br \/>\nWe can say that,<br \/>\nc\u00b0 = e\u00b0<\/p>\n<p>b. Find the values of the indicated variables. Do not use a protractor to measure the angles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35750\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-173.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 173\" width=\"69\" height=\"89\" \/><br \/>\nExplain how you obtained each answer.<br \/>\nAnswer:<br \/>\nThe given figure is: Square<br \/>\nSo,<br \/>\nWe know that,<br \/>\nAll the angles in the square are: 90\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nc\u00b0 = 90\u00b0, d\u00b0 = 90\u00b0, and e\u00b0 = 90\u00b0<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 3.<br \/>\nHow can you describe angle pair relationships and use these descriptions to find angle measures?<br \/>\nAnswer:<br \/>\nTwo adjacent angles are a linear pair when their non-common sides are opposite rays. The angles in a linear pair are supplementary angles. common side L1+22=180\u00b0. Two angles are vertical angles when their sides form two pairs of opposite rays<\/p>\n<p>Question 4.<br \/>\nWhat do you notice about the angle measures of complementary angles, supplementary angles, and vertical angles?<br \/>\n<strong>ATTENDING TO PRECISION<\/strong><br \/>\nTo be proficient in math, you need to communicate precisely with others.<br \/>\nAnswer:<br \/>\nThe &#8220;Complementary angles&#8221; are the angles that the measure of angles is 90\u00b0<br \/>\nThe &#8220;Supplementary angles&#8221; are the angles that the measure of angles is 180\u00b0<br \/>\nThe opposite angles are the angles that have a common side and opposite to each other<\/p>\n<h3><a id=\"Lesson_1.6_Describing_Pairs_of_Angles\"><\/a>Lesson 1.6 Describing Pairs of Angles<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>In Exercises 1 and 2. use the figure.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-35749\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-174.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 174\" width=\"194\" height=\"110\" \/><\/p>\n<p>Question 1.<br \/>\nName a pair of complementary angles, a pair of supplementary angles, and a pair of adjacent angles.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe pair of angles that the sum of the angle measures is 90\u00b0 is called &#8220;Complementary angles&#8221;<br \/>\nThe pair of angles that the sum of the angle measures is 180\u00b0 is called &#8220;Supplementary angles&#8221;<br \/>\nThe angle that is the same in more than 1 angle-pair is called &#8220;Adjacent Angle&#8221;<br \/>\nSo,<br \/>\nFrom the given figure,<br \/>\nThe pair of complementary angles is: \u2220FGK and \u2220LKG<br \/>\nThe pair of supplementary angles is: \u2220HGK and \u2220GKL<br \/>\nThe pair of adjacent angles is: \u2220FGK and \u2220HGK<\/p>\n<p>Question 2.<br \/>\nAre \u2220KGH and \u2220LKG adjacent angles? Are \u2220FGK and \u2220FGH adjacent angles? Explain.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe angle that is the same in more than 1 angle-pair is called &#8220;Adjacent Angle&#8221;<br \/>\nBut,<br \/>\nIn \u2220KGH and \u2220LKG, the angle is not the same<br \/>\nSo,<br \/>\n\u2220KGH and \u2220LKG are not the adjacent angles<br \/>\nIn \u2220FGK and \u2220FGH, the angle is the same<br \/>\nSo,<br \/>\n\u2220FGK and \u2220FGH are adjacent angles<\/p>\n<p>Question 3.<br \/>\n\u22201 is a complement of \u22202. arid m\u22202 = 5\u00b0. Find m\u22201.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe pair of angles that the sum of the angle measures is 90\u00b0 is called &#8220;Complementary angles&#8221;<br \/>\nIt is given that<br \/>\n\u22201 is a complement of \u22202<br \/>\nSo,<br \/>\n\u22201 + \u22202 = 90\u00b0<br \/>\nIt is also given that<br \/>\n\u22202 = 5\u00b0<br \/>\nSo,<br \/>\n\u22201 = 90\u00b0 &#8211; \u22202<br \/>\n\u22201 = 90\u00b0 &#8211; 5\u00b0<br \/>\n\u22201 = 85\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u22201 = 85\u00b0<\/p>\n<p>Question 4.<br \/>\n\u22203 is a supplement of \u22204. and m\u22203 = 148\u00b0. Find m\u22204.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe pair of angles that the sum of the angle measures is 180\u00b0 is called &#8220;Supplementary angles&#8221;<br \/>\nIt is given that<br \/>\n\u22203 is a supplement of \u22204<br \/>\nSo,<br \/>\n\u22203 + \u22204 = 180\u00b0<br \/>\nIt is also given that<br \/>\n\u22203 = 148\u00b0<br \/>\nSo,<br \/>\n\u22204 = 180\u00b0 &#8211; \u22203<br \/>\n\u22204 = 180\u00b0 &#8211; 148\u00b0<br \/>\n\u22204 = 32\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u22204 = 32\u00b0<\/p>\n<p>Question 5.<br \/>\n\u2220LMN and \u2220PQR are complementary angles. Find the measures of the angles when in m\u2220LMN = (4x &#8211; 2)\u00b0 and m\u2220PQR = (9x + 1)\u00b0.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe pair of angles that the sum of the angle measures is 90\u00b0 is called &#8220;Complementary angles&#8221;<br \/>\nIt is given that<br \/>\n\u2220LMN and \u2220PQR are complementary angles<br \/>\nSo,<br \/>\n\u2220LMN + \u2220PQR = 90\u00b0<br \/>\nIt is also given that<br \/>\n\u2220LMN = (4x &#8211; 2)\u00b0 and \u2220PQR = (9x + 1)\u00b0<br \/>\nSo,<br \/>\n(4x &#8211; 2)\u00b0 + (9x + 1)\u00b0 = 90\u00b0<br \/>\n13x &#8211; 1 = 90\u00b0<br \/>\n13x = 90 + 1<br \/>\nx = \\(\\frac{91}{13}\\)<br \/>\nx = 7\u00b0<br \/>\nSo,<br \/>\n\u2220LMN = (4x &#8211; 2)\u00b0<br \/>\n= 4 (7) &#8211; 2<br \/>\n= 28 &#8211; 2<br \/>\n= 26\u00b0<br \/>\n\u2220PQR = (9x + 1)\u00b0<br \/>\n= 9 (7) + 1<br \/>\n= 63 + 1<br \/>\n= 64\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220LMN = 26\u00b0 and \u2220PQR = 64\u00b0<\/p>\n<p>Question 6.<br \/>\nDo any of the numbered angles in the figure form a linear pair? Which angles are vertical angles? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35748\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-175.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 175\" width=\"241\" height=\"202\" \/><br \/>\nAnswer:<br \/>\nFrom the above figure,<br \/>\nWe can observe that 1, 2, 3, 4, 5, and 6 are the angles<br \/>\nWe know that,<br \/>\nA linear pair of angles are formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines<br \/>\nHence,<br \/>\nThe linear pair of angles in the given figure are: \u22201 and \u22202; \u22203 and \u22204; \u22205 and \u22206<br \/>\nThe vertical angles from the given figure are: \u22201 and \u22202; \u22202 and \u22205; \u22203 and \u22206<\/p>\n<p>Question 7.<br \/>\nThe measure of an angle is twice the measure of its complement. Find the measure of each angle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35748\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-175.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 175\" width=\"241\" height=\"202\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nA linear pair of angles are formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines<br \/>\nSo,<br \/>\n\u22201 and \u22202 (or) \u22203 and \u22204 (or) \u22205 and \u22206 are the complementary angles<br \/>\nIt is given that,<br \/>\nThe measure of an angle is twice the measure of its component<br \/>\nLet the angle be x\u00b0<br \/>\nSo,<br \/>\nx + 2x = 90\u00b0<br \/>\n3x = 90\u00b0<br \/>\nx = \\(\\frac{90}{3}\\)<br \/>\nx = 30\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u22201 = \u22203 = \u22205 = 30\u00b0<br \/>\n\u22202 = \u22204 = \u22206 = 60\u00b0<\/p>\n<p>Question 8.<br \/>\nTwo angles form a linear pair. The measure of one angle is 1\\(\\frac{1}{2}\\) times the measure of the other angle. Find the measure of each angle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35748\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-175.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 175\" width=\"241\" height=\"202\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nA linear pair of angles are formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines<br \/>\nSo,<br \/>\n\u22201 and \u22202 (or) \u22203 and \u22204 (or) \u22205 and \u22206 are the supplementary angles<br \/>\nIt is given that,<br \/>\nThe measure of one angle is 1\\(\\frac{1}{2}\\) times the measure of the other angle<br \/>\nLet the angle be x\u00b0<br \/>\nSo,<br \/>\nx + 1\\(\\frac{1}{2}\\)x = 180\u00b0<br \/>\nx + \\(\\frac{3}{2}\\)x = 180\u00b0<br \/>\n\\(\\frac{5x}{2}\\) = 180\u00b0<br \/>\n5x = 180\u00b0 (2)<br \/>\n5x = 360\u00b0<br \/>\nx = \\(\\frac{360}{5}\\)<br \/>\nx = 72\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u22201 = \u22203 = \u22205 = 72\u00b0<br \/>\n\u22202 = \u22204 = \u22206 = 108\u00b0<\/p>\n<h3><a id=\"Exercise_1.6_Describing_Pairs_of_Angles\"><\/a>Exercise 1.6 Describing Pairs of Angles<\/h3>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain what is different between adjacent angles and vertical angles.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48135\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-1.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 1\" width=\"557\" height=\"79\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-1.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-1-300x43.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WHICH ONE DID DOESN\u2019T BELONG?<\/strong><br \/>\nWhich one does hot belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35747\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-176.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 176\" width=\"678\" height=\"97\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-176.png 678w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-176-300x43.png 300w\" sizes=\"(max-width: 678px) 100vw, 678px\" \/><br \/>\nAnswer:<br \/>\nThe angle that is the same in more than 1 angle-pair and has a common side is called \u201cAdjacent Angle\u201d<br \/>\nSo,<br \/>\nFrom the above figure,<br \/>\nWe can observe that only the first figure has an adjacent angle whereas all the three figures don&#8217;t have any adjacent angles<br \/>\nHence, from the above,<br \/>\nWe can conclude that the first figure does not belong with the other three<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3-6, use the figure.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-35746\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-177.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 177\" width=\"268\" height=\"122\" \/><\/p>\n<p>Question 3.<br \/>\nName a pair of adjacent complementary angles.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48136\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-3.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 3\" width=\"590\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-3.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-3-300x30.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p>Question 4.<br \/>\nName a pair of adjacent supplementary angles.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe angles that have the sum of the angle measures 180\u00b0 are called &#8220;Supplementary angles<br \/>\nHence, from the figure,<br \/>\nA pair of adjacent supplementary angles are: \u2220LJN + \u2220LJK<\/p>\n<p>Question 5.<br \/>\nName a pair of nonadjacent complementary angles.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48137\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-5.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 5\" width=\"545\" height=\"64\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-5.png 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-5-300x35.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Question 6.<br \/>\nName a pair of nonadjacent supplementary angles.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe angles that have the sum of the angle measures 180\u00b0 are called &#8220;Supplementary angles<br \/>\nHence, from the figure,<br \/>\nA pair of adjacent supplementary angles are: \u2220LJN + \u2220LJK and \u2220NGP + \u2220HGF<\/p>\n<p>In Exercises 7 &#8211; 10. find the angle measure.<\/p>\n<p>Question 7.<br \/>\n\u22201 is a complement of \u22202, and m\u22201 = 23\u00b0. Find, m\u22202.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48138\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-7.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 7\" width=\"215\" height=\"100\" \/><\/p>\n<p>Question 8.<br \/>\n\u22203 is a complement of \u22204. and m\u22203 = 46\u00b0. Find, m\u22204.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe pair of angles that the sum of the angle measures is 90\u00b0 is called &#8220;Complementary angles&#8221;<br \/>\nIt is given that<br \/>\n\u22203 is a complement of \u22204<br \/>\nSo,<br \/>\n\u22203 + \u22204 = 90\u00b0<br \/>\nIt is also given that<br \/>\n\u22203 = 46\u00b0<br \/>\nSo,<br \/>\n\u22204 = 90\u00b0 &#8211; \u22203<br \/>\n\u22204 = 90\u00b0 &#8211; 46\u00b0<br \/>\n\u22204 = 44\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u22204 = 44\u00b0<\/p>\n<p>Question 9.<br \/>\n\u22205 is a supplement of \u22206. and m\u22205 = 78\u00b0. Find m\u22206.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48139\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-9.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 9\" width=\"225\" height=\"98\" \/><\/p>\n<p>Question 10.<br \/>\n\u22207 is a supplement of \u22208. and m\u22207 = 109\u00b0. Find m\u22208.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe pair of angles that the sum of the angle measures is 180\u00b0 is called \u201cSupplementary angles\u201d<br \/>\nIt is given that<br \/>\n\u22207 is a supplement of \u22208<br \/>\nSo,<br \/>\n\u22207 + \u22208 = 180\u00b0<br \/>\nIt is also given that<br \/>\n\u22207 = 109\u00b0<br \/>\nSo,<br \/>\n\u22208 = 180\u00b0 \u2013 \u22207<br \/>\n\u22208 = 180\u00b0 \u2013 109\u00b0<br \/>\n\u22208 = 71\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u22208 = 71\u00b0<\/p>\n<p>In Exercises 11 &#8211; 14. find the measure of each angle.<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35745\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-178.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 178\" width=\"199\" height=\"100\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48140\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-11.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 11\" width=\"472\" height=\"240\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-11.png 472w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-11-300x153.png 300w\" sizes=\"(max-width: 472px) 100vw, 472px\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35744\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-179.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 179\" width=\"120\" height=\"124\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nBy using the Angle Addition Postulate,<br \/>\n\u2220BAD = \u2220CAB + \u2220CAD<br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\n\u2220BAD = 90\u00b0<br \/>\nSo,<br \/>\n(15x &#8211; 2)\u00b0 + (7x + 4)\u00b0 = 90\u00b0<br \/>\n22x + 2 = 90\u00b0<br \/>\n22x = 88\u00b0<br \/>\nx = \\(\\frac{88}{22}\\)<br \/>\nx = 4\u00b0<br \/>\nSo,<br \/>\n\u2220CAB = (15x &#8211; 2)\u00b0<br \/>\n= 15 (4) &#8211; 2<br \/>\n= 60 &#8211; 2<br \/>\n= 58\u00b0<br \/>\n\u2220CAD = (7x + 4)\u00b0<br \/>\n= 7 (4) + 4<br \/>\n= 28 + 4<br \/>\n= 32\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220CAB = 58\u00b0 and \u2220CAD = 32\u00b0<\/p>\n<p>Question 13.<br \/>\n\u2220UVW and \u2220XYZ arc complementary angles, m\u2220UVW = (x &#8211; 10)\u00b0. and m\u2220XYZ = (4x &#8211; 10)\u00b0.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48141\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-13.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 13\" width=\"449\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-13.png 449w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-13-300x160.png 300w\" sizes=\"(max-width: 449px) 100vw, 449px\" \/><\/p>\n<p>Question 14.<br \/>\n\u2220EFG and \u2220LMN are supplementary angles. m\u2220EFG = (3x + 17)\u00b0, and m\u2220LMN = (\\(\\frac{1}{2} x\\) &#8211; 5)\u00b0<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe pair of angles that the sum of the angle measures is 180\u00b0 is called \u201cSupplementary angles\u201d<br \/>\nIt is given that<br \/>\n\u2220EFG and \u2220LMN are supplementary angles<br \/>\nSo,<br \/>\n\u2220LMN + \u2220EFG = 180\u00b0<br \/>\nIt is also given that<br \/>\n\u2220LMN = (\\(\\frac{1}{2} x\\) &#8211; 5)\u00b0 and \u2220EFG = (3x + 17)\u00b0<br \/>\nSo,<br \/>\n(\\(\\frac{1}{2} x\\) &#8211; 5)\u00b0 + (3x + 17)\u00b0 = 180\u00b0<br \/>\n\\(\\frac{7}{2} x\\) + 12 = 180\u00b0<br \/>\n\\(\\frac{7}{2} x\\) = 180 &#8211; 12<br \/>\n\\(\\frac{7}{2} x\\) = 168\u00b0<br \/>\n7x = 168 (2)<br \/>\n7x = 336<br \/>\nx = \\(\\frac{336}{7}\\)<br \/>\nx = 48\u00b0<br \/>\nSo,<br \/>\n\u2220LMN = (\\(\\frac{1}{2} x\\) &#8211; 5)\u00b0<br \/>\n= \\(\\frac{1}{2} \\) \u00d7 48 &#8211; 5<br \/>\n= 24 \u2013 5<br \/>\n= 19\u00b0<br \/>\n\u2220EFG = (3x + 17)\u00b0<br \/>\n= 3 (48) + 17<br \/>\n= 144 + 17<br \/>\n= 161\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220LMN = 19\u00b0 and \u2220EFG = 161\u00b0<\/p>\n<p>In Exercises 15 &#8211; 18. use the figure.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-35743\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-180.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 180\" width=\"73\" height=\"184\" \/><\/p>\n<p>Question 15.<br \/>\nIdentify the linear pair(s) that include \u22201.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48142\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-15.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 15\" width=\"299\" height=\"34\" \/><\/p>\n<p>Question 16.<br \/>\nIdentify the linear pair(s) that include \u22207.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe angle that is the same in more than 1 angle-pair is called \u201cAdjacent Angle\u201d<br \/>\nHence, from the figure,<br \/>\nWe can conclude that<br \/>\nThe linear pairs that include \u22207 are: \u22206 and \u22207 and \u22207 and \u22208<\/p>\n<p>Question 17.<br \/>\nAre \u22206 and \u22208 vertical angles? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48143\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-17.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 17\" width=\"560\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-17.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-17-300x32.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 18.<br \/>\nAre \u22202 and \u22205 vertical angles? Explain your reasoning.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe angles that have the same vertex are called &#8220;Vertical angles&#8221;<br \/>\nHence, from the figure,<br \/>\nWe can conclude that \u22202 and \u22205 are vertical angles<\/p>\n<p>In Exercises 19 &#8211; 22, find the measure of each angle.<\/p>\n<p>Question 19.<br \/>\nTwo angles form a linear pair. The measure of one angle is twice the measure of the other angle.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48144\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-19.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 19\" width=\"530\" height=\"203\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-19.png 530w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-19-300x115.png 300w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><\/p>\n<p>Question 20.<br \/>\nTwo angles form a linear pair. The measure of one angle is \\(\\frac{1}{3}\\) the measure of the other angle.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nA linear pair of angles are formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines<br \/>\nSo,<br \/>\nThe given angles are the supplementary angles<br \/>\nIt is given that,<br \/>\nThe measure of one angle is \\(\\frac{1}{3}\\)\u00a0times the measure of the other angle<br \/>\nLet the angle be x\u00b0<br \/>\nSo,<br \/>\nx + \\(\\frac{1}{3}\\)x = 180\u00b0<br \/>\n\\(\\frac{4}{3}\\)x\u00a0= 180\u00b0<br \/>\n4x = 180\u00b0 (3)<br \/>\n4x = 540\u00b0<br \/>\nx = \\(\\frac{540}{4}\\)<br \/>\nx = 135\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe measure of one angle is 135\u00b0 and the measure of the other angle is 270\u00b0<\/p>\n<p>Question 21.<br \/>\nThe measure of an angle is nine times the measure of its complement.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48145\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-21.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 21\" width=\"528\" height=\"240\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-21.png 528w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-21-300x136.png 300w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><\/p>\n<p>Question 22.<br \/>\nThe measure of an angle is \\(\\frac{1}{4}\\) the measure of its complement.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nA linear pair of angles are formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines<br \/>\nSo,<br \/>\nThe given angles are the complementary angles<br \/>\nIt is given that,<br \/>\nThe measure of one angle is \\(\\frac{1}{4}\\) times the measure of the other angle<br \/>\nLet the angle be x\u00b0<br \/>\nSo,<br \/>\nx + \\(\\frac{1}{4}\\)x = 90\u00b0<br \/>\n\\(\\frac{5}{4}\\)x = 90\u00b0<br \/>\n5x = 90\u00b0 (4)<br \/>\n5x = 360\u00b0<br \/>\nx = \\(\\frac{360}{5}\\)<br \/>\nx = 72\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe measure of one angle is 72\u00b0 and the measure of the other angle is 144\u00b0<\/p>\n<p><strong>ERROR ANALYSIS<\/strong><br \/>\nIn Exercises 23 and 24, describe and correct the error in identifying pairs of angles in the figure.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-35742\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-181.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 181\" width=\"183\" height=\"71\" \/><\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35741\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-182.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 182\" width=\"280\" height=\"61\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48146\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-23.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 23\" width=\"609\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-23.png 609w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-23-300x30.png 300w\" sizes=\"(max-width: 609px) 100vw, 609px\" \/><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35740\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-183.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 183\" width=\"272\" height=\"51\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nA linear pair of angles are formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines<br \/>\nHence, from the figure,<br \/>\nWe can conclude that \u22201 and \u22203 do not form a linear pair<\/p>\n<p>In Exercises 25 and 26. the picture shows the Alamillo Bridge in Seville, Spain. In the picture, m\u22201 = 58\u00b0 and m\u22202 = 24\u00b0.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35739\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-184.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 184\" width=\"263\" height=\"168\" \/><\/p>\n<p>Question 25.<br \/>\nFind the measure of the supplement of \u22201<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48147\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-25.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 25\" width=\"319\" height=\"137\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-25.png 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-25-300x129.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><\/p>\n<p>Question 26.<br \/>\nFind the measure of the supplement of \u22202.<br \/>\nAnswer:<br \/>\nLet the other angle with \u22202 be x\u00b0<br \/>\nWe know that,<br \/>\nThe sum of the angle measures of supplementary angles is: 180\u00b0<br \/>\nSo,<br \/>\n\u22202 + x\u00b0 = 180\u00b0<br \/>\nFro the above,<br \/>\nIt is given that<br \/>\n\u22202 = 24\u00b0<br \/>\nSo,<br \/>\n24\u00b0 + x\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 24\u00b0<br \/>\nx\u00b0 = 156\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the supplement of \u22202 is: 156\u00b0<\/p>\n<p>Question 27.<br \/>\n<strong>PROBLEM-SOLVING<\/strong><br \/>\nThe arm of a crossing gate moves 42\u00b0 from a vertical position. How many more degrees does the arm have to move so that it is horizontal?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35738\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-185.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 185\" width=\"330\" height=\"180\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-185.png 330w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-185-300x164.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><br \/>\nA. 42\u00b0<br \/>\nB. 138\u00b0<br \/>\nC. 48\u00b0<br \/>\nD. 90\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48148\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-27.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 27\" width=\"613\" height=\"55\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-27.png 613w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-27-300x27.png 300w\" sizes=\"(max-width: 613px) 100vw, 613px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe foul lines of a baseball field intersect at home plate to form a right angle. A batter hits a fair ball such that the path of the baseball forms an angle of 27\u00b0 with the third base foul line. What is the measure of the angle between the first base foul line and the path of the baseball?<br \/>\nAnswer:<br \/>\nIt is given that the foul lines of a baseball field intersect at home plate to form a right angle. A batter hits a fair ball such that the path of the baseball forms an angle of 27\u00b0 with the third base foul line.<br \/>\nSo,<br \/>\nWe can say that<br \/>\nThe angle between the path of the baseball and the third base foul line is complementary i.e., 90\u00b0 with the angle between the path of the baseball and the base of the first foul line<br \/>\nSo,<br \/>\nThe angle between the first base foul line and the path of the baseball = 90\u00b0 &#8211; (The angle between the path of the baseball and the third base foul line)<br \/>\n=90\u00b0 &#8211; 27\u00b0<br \/>\n= 63\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the angle between the first base foul line and the path of the baseball is: 63\u00b0<\/p>\n<p>Question 29.<br \/>\n<strong>CONSTRUCTION<\/strong><br \/>\nConstruct a linear pair where one angle measure is 115\u00b0.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48149\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-29.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 29\" width=\"225\" height=\"107\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>CONSTRUCTION<\/strong><br \/>\nConstruct a pair of adjacent angles that have angle measures of 45\u00b0 and 97\u00b0.<br \/>\nAnswer:<br \/>\nThe representation of the pair of adjacent angles that has the angle measures of 45\u00b0 and 97\u00b0 is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-77829\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-49.png\" alt=\"\" width=\"367\" height=\"145\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-49.png 367w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-49-300x119.png 300w\" sizes=\"(max-width: 367px) 100vw, 367px\" \/><\/p>\n<p>Question 31.<br \/>\n<strong>PROBLEM-SOLVING<\/strong><br \/>\nm\u2220U = 2x\u00b0, and m\u2220V = 4m\u2220U. Which value of x makes \u2220U and \u2220V complements of each other?<br \/>\nA. 25<br \/>\nB. 9<br \/>\nC. 36<br \/>\nD. 18<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48150\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-31.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 31\" width=\"548\" height=\"304\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-31.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-31-300x166.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p><strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nIn Exercises 32 &#8211; 35, write and solve an algebraic equation to find the measure of each angle based on the given description.<\/p>\n<p>Question 32.<br \/>\nThe measure of an angle is 6\u00b0 less than the measure of its complement.<br \/>\nAnswer:<br \/>\nIt is given that the measure of an angle is 6\u00b0 less than the measure of its complement<br \/>\nLet the angle be x\u00b0<br \/>\nS0,<br \/>\nThe complement of the angle is: (90 &#8211; x)\u00b0<br \/>\nSo,<br \/>\n(90 &#8211; x)\u00b0 = x &#8211; 6\u00b0<br \/>\n90 + 6 = x + x<br \/>\n2x = 96\u00b0<br \/>\nx = \\(\\frac{96}{2}\\)<br \/>\nx = 48\u00b0<br \/>\nSo,<br \/>\nThe measures of the two angles are: 48\u00b0, 90\u00b0 &#8211; 48\u00b0 = 42\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the measures of the angles are: 48\u00b0, 42\u00b0<\/p>\n<p>Question 33.<br \/>\nThe measure of an angle is 12\u00b0 more than twice the measure of its complement.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48151\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-33.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 33\" width=\"449\" height=\"314\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-33.png 449w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-33-300x210.png 300w\" sizes=\"(max-width: 449px) 100vw, 449px\" \/><\/p>\n<p>Question 34.<br \/>\nThe measure of one angle is 3\u00b0 more than \\(\\frac{2}{3}\\) the measure of its supplement.<br \/>\nAnswer:<br \/>\nIt is given that the measure of an angle is 3\u00b0 more than \\(\\frac{2}{3}\\) the measure of its supplement<br \/>\nNow,<br \/>\nLet the measure of an angle be x\u00b0<br \/>\nSo,<br \/>\nThe measure of the other angle is (180 &#8211; x)\u00b0<br \/>\nSo,<br \/>\nx\u00b0 = 3\u00b0 + \\(\\frac{2}{3}\\) (180 &#8211; x)\u00b0<br \/>\n3x\u00b0 = 9\u00b0 + 360\u00b0 &#8211; 2x\u00b0<br \/>\n5x\u00b0 = 369\u00b0<br \/>\nx = \\(\\frac{369}{5}\\)<br \/>\nx\u00b0 = 73.4\u00b0<br \/>\nSo,<br \/>\nThe measures of the angles are: 73.4\u00b0 and 180\u00b0 &#8211; 73.4\u00b0 = 106.6\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the measures of the angles are: 73.4v and 106.6\u00b0<\/p>\n<p>Question 35.<br \/>\nTwo angles form a linear pair. The measure of one angle is 15\u00b0 less than \\(\\frac{2}{3}\\) the measure of the other angle.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48152\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-35.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 35\" width=\"460\" height=\"343\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-35.png 460w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-35-300x224.png 300w\" sizes=\"(max-width: 460px) 100vw, 460px\" \/><\/p>\n<p><strong>CRITICAL THINKING<\/strong><br \/>\nIn Exercises 36 &#8211; 41. tell whether the statement is always, sometimes, or never true. Explain your reasoning.<\/p>\n<p>Question 36.<br \/>\nComplementary angles are adjacent.<br \/>\nAnswer:<br \/>\nThe given statement is &#8220;Complementary angles are adjacent&#8221;<br \/>\nWe know that,<br \/>\nThe complementary angles sometimes will be vertical angles or sometimes adjacent angles or sometimes non-adjacent angles<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given statement is sometimes true<\/p>\n<p>Question 37.<br \/>\nAngles in a linear pair are supplements of each other.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48153\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-37.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 37\" width=\"545\" height=\"35\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-37.png 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-37-300x19.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Question 38.<br \/>\nVertical angles are adjacent.<br \/>\nAnswer:<br \/>\nThe given statement is &#8220;Vertical angles are adjacent&#8221;<br \/>\nWe know that,<br \/>\nThe vertical angles are the angles formed by the intersection of two lines whereas adjacent angles share a common side and a common vertex<br \/>\nHence, from the above,<br \/>\nWe can conclude that vertical angles are never adjacent<\/p>\n<p>Question 39.<br \/>\nVertical angles are supplements of each other.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48154\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-39.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 39\" width=\"531\" height=\"31\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-39.png 531w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-39-300x18.png 300w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><\/p>\n<p>Question 40.<br \/>\nIf an angle is acute. then its complement is greater than its supplement.<br \/>\nAnswer:<br \/>\nThe given statement is &#8220;If an angle is acute, then its complement is greater than its supplement&#8221;<br \/>\nwe know that,<br \/>\nThe sum of complementary angles is 90\u00b0 i.e., the measures of the angles are always acute<br \/>\nThe sum of the supplementary angles is 180\u00b0 i.e., the measure of 1 angle is acute and the measure of the other angle is obtuse<br \/>\nHence, from the above,<br \/>\nWe can conclude that if an angle is acute, then its complement will never be greater than its supplement<\/p>\n<p>Question 41.<br \/>\nIf two complementary angles are congruent, then the measure of each angle is 45\u00b0,<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48155\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-41.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 41\" width=\"585\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-41.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-41-300x45.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain why the supplement of an acute angle must be obtuse.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe sum of the measures of the supplementary angles is: 180\u00b0<br \/>\nSo,<br \/>\nIf one angle is acute i.e., the angle less than 90\u00b0, then the other angle must be obtuse to make the sum 180\u00b0<br \/>\nHence,<br \/>\nThe supplement of an acute angle must be obtuse<\/p>\n<p>Question 43.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain why an obtuse angle does not have a complement.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48156\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-43.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 43\" width=\"589\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-43.png 589w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-43-300x32.png 300w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nSketch an intersection of roads. Identify any supplementary, complementary, or vertical angles.<br \/>\nAnswer:<br \/>\nThe representation of the intersection of roads is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-77836\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-50.png\" alt=\"\" width=\"330\" height=\"138\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-50.png 330w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-50-300x125.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><br \/>\nWe know that,<br \/>\nThe angles that have the sum of the angle measures 90\u00b0 are &#8220;Complementary angles&#8221;<br \/>\nThe angles that have the sum of the angle measures 180\u00b0 are &#8220;Supplementary angles&#8221;<br \/>\nThe angles that form with the intersection of 2 lines are &#8220;Vertical angles&#8221;<br \/>\nSo,<br \/>\nFrom the figure,<br \/>\nThe supplementary angles are:<br \/>\n\u22201 and \u22202; \u22202 and \u22203; \u22203 and \u22204; \u22204 and \u22201<br \/>\nThere are no complementary angles<br \/>\nThe vertical angles are:<br \/>\n\u22201 and \u22203; \u22202 and \u22204<\/p>\n<p>Question 45.<br \/>\n<strong>ATTENDING TO PRECISION<\/strong><br \/>\nUse the figure.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35737\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-186.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 186\" width=\"136\" height=\"102\" \/><\/p>\n<p>a. Find m\u2220UWV, m\u2220TWU, and m\u2220TWX.<br \/>\nb. YOU write the measures of \u2220TWU, \u2220TWX, \u2220UWV and \u2220VWX on separate pieces of paper and place the pieces of paper in a box. Then you pick two pieces of paper out of the box at random. What is the probability that the angle measures you choose are supplementary? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48157\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-45.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 45\" width=\"623\" height=\"561\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-45.png 623w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-45-300x270.png 300w\" sizes=\"(max-width: 623px) 100vw, 623px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nTell whether you can conclude that each statement is true based on the figure. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35736\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-187.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 187\" width=\"171\" height=\"151\" \/><br \/>\na. \\(\\overline{C A}\\) \u2245 \\(\\overline{A F}\\)<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can observe that \\(\\overline{C A}\\) has the same length as \\(\\overline{A F}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\overline{C A}\\) \u2245 \\(\\overline{A F}\\)<\/p>\n<p>b. Points C, A, and F are collinear<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe points that are present on the same line are called &#8220;Collinear points&#8221;<br \/>\nFrom the figure,<br \/>\nWe can observe that C, A, and F lie on the same line<br \/>\nHence, from the above,<br \/>\nWe can conclude that C, A, and F are collinear points<\/p>\n<p>c. \u2220CAD \u2245 \u2220EAF.<br \/>\nAnswer:<br \/>\nFrom the figure,<br \/>\nWe can observe that point A is the angle bisector of C and D<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220CAD \u2245 \u2220EAF<\/p>\n<p>d. \\(\\overline{B A}\\) \u2245 \\(\\overline{A E}\\)<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nC is the Bisector&#8221;<br \/>\nA &#8220;Bisector&#8221; divides anything into 2 congruent parts<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\overline{B A}\\) \u2245 \\(\\overline{A E}\\)<\/p>\n<p>e. <img loading=\"lazy\" class=\"alignnone size-full wp-image-35735\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-188.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 188\" width=\"247\" height=\"29\" \/><br \/>\nAnswer:<br \/>\nFrom the figure,<br \/>\nWe can observe that there are 3 lines intersect at point A<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\overline{C F}\\), \\(\\overline{B E}\\), and \\(\\overline{A D}\\) intersect at point A<\/p>\n<p>f. \u2220BAC and \u2220CAD are complementary angles.<br \/>\nAnswer:<br \/>\nFrom the figure,<br \/>\nWe can observe that \u2220A has a complementary angle<br \/>\nHence, from the above,<br \/>\nWe can conclude that \u2220BAC and \u2220CAD are complementary angles<\/p>\n<p>g. \u2220DAE is a right angle.<br \/>\nAnswer:<br \/>\nFrom the figure,<br \/>\nWe can observe that,<br \/>\nD is perpendicular to E and A has a complementary angle<br \/>\nHence, from the above,<br \/>\nWe can conclude that \u2220DAE is a right angle<\/p>\n<p>Question 47.<br \/>\nREASONING<br \/>\n\u2220KJL and \u2220LJM arc complements, and \u2220MJN and \u2220LJM are complements. Can you show that \u2220KJL \u2245 \u2220MJN? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35734\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-189.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 189\" width=\"136\" height=\"123\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48158\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-47.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 47\" width=\"481\" height=\"163\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-47.png 481w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-47-300x102.png 300w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nLight from a flashlight strikes a mirror and is reflected so that the angle of reflection is congruent to the angle of incidence. Your classmate claims that \u2220QPR is congruent to \u2220TPU regardless of the measure of \u2220RPS. Is your classmate correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35733\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-1-Basics-of-Geometry-190.png\" alt=\"Big Ideas Math Answers Geometry Chapter 1 Basics of Geometry 190\" width=\"297\" height=\"181\" \/><br \/>\nAnswer:<br \/>\nYes, your classmate is correct<\/p>\n<p>Explanation:<br \/>\nIt is given that the light from a flashlight strikes a mirror and is reflected so that the angle of reflection is congruent to the angle of incidence. Your classmate claims that \u2220QPR is congruent to \u2220TPU regardless of the measure of \u2220RPS.<br \/>\nWe know that,<br \/>\nThe vertical angle is the intersection of two lines and \\(\\overline{S P}\\) is the angle bisector<br \/>\nSo,<br \/>\n\u2220QPR is congruent to \u2220TPU regardless of the measure of \u2220RPS.<br \/>\nHence, from the above,<br \/>\nWe can conclude that the claim of your friend is correct<\/p>\n<p>Question 49.<br \/>\n<strong>DRAWING CONCLUSIONS<\/strong><br \/>\nUse the figure.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35732\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometr-Chapter-1-Basics-of-Geometryy-191.png\" alt=\"Big Ideas Math Answers Geometr Chapter 1 Basics of Geometryy 191\" width=\"133\" height=\"85\" \/><br \/>\na. Write expressions for the measures of \u2220BAE, \u2220DAE, and \u2220CAB.<br \/>\nb. What do you notice about the measures of vertical angles? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48159\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-49.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 49\" width=\"574\" height=\"271\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-49.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-49-300x142.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 50.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nLet m\u22201 = x\u00b0, m\u22202 = y<sub>1<\/sub>\u00b0, and m\u22203 = y<sub>2<\/sub>\u00b0 \u22202 is the complement of \u22201, and \u22203 is the supplement of \u22201.<\/p>\n<p>a. Write equations for y<sub>1<\/sub> as a function of x and for y<sub>2<\/sub> as a function of x. What is the domain of each function? Explain.<br \/>\nAnswer:<br \/>\nIt is given that<br \/>\nm\u22201 = x\u00b0, m\u22202 = y<sub>1<\/sub>\u00b0, and m\u22203 = y<sub>2<\/sub>\u00b0<br \/>\n\u22202 is the complement of \u22201, and \u22203 is the supplement of \u22201<br \/>\nSo,<br \/>\n\u22201 + \u22202 = 90\u00b0 and \u22203 + \u22201 = 180\u00b0<br \/>\nx\u00b0 + y1\u00b0 = 90\u00b0 and y2\u00b0 + x\u00b0 = 180\u00b0<br \/>\nSo,<br \/>\ny1\u00b0 = 90\u00b0 &#8211; x\u00b0 and y2\u00b0 = 180\u00b0 &#8211; x\u00b0<br \/>\nHence, from the above,<br \/>\nThe domain of y1 can be given as: 0\u00b0 \u2264 x \u2264 90\u00b0<br \/>\nThe domain of y2 can be given as: 0\u00b0 \u2264 x \u2264 180\u00b0<\/p>\n<p>b. Graph each function and describe its range.<br \/>\nAnswer:<br \/>\nFrom part (a),<br \/>\nThe 2 functions are:<br \/>\ny1\u00b0 = 90\u00b0 &#8211; x\u00b0 and y2\u00b0 = 180\u00b0 &#8211; x\u00b0<br \/>\nHence,<br \/>\nThe representations of the 2 functions in the coordinate plane are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-77907\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-51.png\" alt=\"\" width=\"499\" height=\"497\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-51.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-51-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-51-150x150.png 150w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><br \/>\nHence, from the above graph,<br \/>\nThe range of y1 is: 90 \u2264 y \u2264 200<br \/>\nThe range of y2 is: 0 \u2264 y \u2264 200<\/p>\n<p>Question 51.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nThe sum of the measures of two complementary angles is 74\u00b0 greater than the difference of their measures. Find the measure of each angle. Explain how you found the angle measures.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48160\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-51.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 51\" width=\"577\" height=\"329\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-51.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-51-300x171.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><br \/>\nMaintaining MathematicaI Proficiency<\/p>\n<p>Determine whether the statement is always, sometimes, or never true. Explain your reasoning.<\/p>\n<p>Question 52.<br \/>\nAn integer is a whole number.<br \/>\nAnswer:<br \/>\nThe given statement is &#8220;An integer is a whole number&#8221;<br \/>\nWe know that,<br \/>\nAll whole numbers must be integers but all integers are not whole numbers<br \/>\nExample:<br \/>\n&#8211;6 is an integer but not a whole number<br \/>\n3 is a whole number and also an integer<br \/>\nHence, from the above,<br \/>\nWe can conclude that an integer is sometimes a whole number<\/p>\n<p>Question 53.<br \/>\nAn integer is an irrational number.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48161\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-53.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 53\" width=\"585\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-53.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-53-300x45.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 54.<br \/>\nAn irrational number is a real number.<br \/>\nAnswer:<br \/>\nThe given statement is &#8220;An irrational number is a real number&#8221;<br \/>\nWe know that,<br \/>\n&#8220;Real numbers&#8221; are the numbers that can be written in the form of \\(\\frac{p}{q}\\) whereas &#8220;Irrational numbers&#8221; can&#8217;t be written in the form of \\(\\frac{p}{q}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that an irrational number is never a real number<\/p>\n<p>Question 55.<br \/>\nA whole number is negative.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48162\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-55.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 55\" width=\"447\" height=\"31\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-55.png 447w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-55-300x21.png 300w\" sizes=\"(max-width: 447px) 100vw, 447px\" \/><\/p>\n<p>Question 56.<br \/>\nA rational number is an integer.<br \/>\nAnswer:<br \/>\nThe given statement is &#8220;A rational number is an integer&#8221;<br \/>\nWe know that,<br \/>\nRational numbers are the numbers that can be written in the form of \\(\\frac{p}{q}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that a rational number is sometimes an integer<\/p>\n<p>Question 57.<br \/>\nA natural number is an integer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48163\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-57.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 57\" width=\"556\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-57.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-57-300x31.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 58.<br \/>\nA whole number is a rational number.<br \/>\nAnswer:<br \/>\nThe given statement is &#8220;A whole number is a rational number&#8221;<br \/>\nWe know that,<br \/>\nA whole number can be written in the form of \\(\\frac{p}{q}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that a whole number is always a rational number<\/p>\n<p>Question 59.<br \/>\nAn irrational number is negative.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48164\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-59.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 1 Basics of Geometry 1.6 a 59\" width=\"547\" height=\"32\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-59.png 547w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-1-Basics-of-Geometry-1.6-a-59-300x18.png 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><\/p>\n<h3><a id=\"1.4_-_1.6_Performance_Task:_Comfortable_Horse_Stalls\"><\/a>1.4 &#8211; 1.6 Performance Task: Comfortable Horse Stalls<\/h3>\n<p>Mathematical Practices<\/p>\n<p>Question 1.<br \/>\nHow could you explain your answers to Exercise 33 on page 36 to a friend who is unable to hear\u2019?<br \/>\nAnswer:<br \/>\nIn Exercise 33 on page 36,<br \/>\nThe given vertices of the triangle are in the form of the standard linear equation<br \/>\nSo,<br \/>\nCompare the given vertices with the standard linear equation and find the slopes and x and y-intercepts for the coordinates of the vertices of the triangle<\/p>\n<p>Question 2.<br \/>\nWhat tool(s) could you use to verify your answers to Exercises 25 &#8211; 30 on page 44?<br \/>\nAnswer:<br \/>\nTo verify the answers to Exercise 25 &#8211; 30 on page 44,<br \/>\nWe can use &#8220;Angle Addition Postulate&#8221;<\/p>\n<p>Question 3.<br \/>\nYour friend says that the angles in Exercise 28 on page 53 are supplementary angles. Explain why you agree or disagree.<br \/>\nAnswer:<br \/>\nIn Exercise 28 on page 53,<br \/>\nIt is given that a right-angled triangle is formed<br \/>\nWe know that,<br \/>\nThe sum of the complementary angles is: 90\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that you disagree with your friend about supplementary angle<\/p>\n<h3><a id=\"Basics_of_Geometry_Chapter_Review\"><\/a>Basics of Geometry Chapter Review<\/h3>\n<h4>1.1 Points, Lines, and Planes<\/h4>\n<p>Use the diagram.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-35731\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-192.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 192\" width=\"259\" height=\"166\" \/><\/p>\n<p>Question 1.<br \/>\nGive another name for plane M.<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can conclude that<br \/>\nAnother name for plane M is: Plane XNZ or plane g<\/p>\n<p>Question 2.<br \/>\nName a line in the plane.<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can conclude that<br \/>\nThe names of lines in the pane are: Line PY or Line XZ<\/p>\n<p>Question 3.<br \/>\nName a line intersecting the plane.<br \/>\nAnswer:<br \/>\nFrom the above figure,<br \/>\nWe can conclude that<br \/>\nThe line intersecting the plane is: Line PY<\/p>\n<p>Question 4.<br \/>\nName two rays.<br \/>\nAnswer:<br \/>\nFrom the above figure,<br \/>\nWe can conclude that<br \/>\nThe two rays are: Ray g and Ray h<\/p>\n<p>Question 5.<br \/>\nName a pair of opposite rays.<br \/>\nAnswer:<br \/>\nFrom the above figure,<br \/>\nWe can conclude that<br \/>\nThe opposite rays are: Rays g and h<\/p>\n<p>Question 6.<br \/>\nName a point, not in plane M.<br \/>\nAnswer:<br \/>\nFrom the above figure,<br \/>\nWe can conclude that<br \/>\nThe point that is not in plane M is: point p<\/p>\n<h4>1.2 Measuring and Constructing Segments<\/h4>\n<p>Find XZ.<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35730\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-193.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 193\" width=\"176\" height=\"31\" \/><br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nBy using the Segment Addition Postulate,<br \/>\nXZ = XY + YZ<br \/>\nXZ = 17 + 24<br \/>\nXZ = 41<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of XZ is: 41<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35729\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-194.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 194\" width=\"176\" height=\"51\" \/><br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nBy using the Segment Addition Postulate,<br \/>\nAZ = AX + XZ<br \/>\n38 = 27 + XZ<br \/>\nXZ = 38 &#8211; 27<br \/>\nXZ = 11<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of XZ is: 11<\/p>\n<p>Question 9.<br \/>\nPlot A(8, &#8211; 4), B(3, &#8211; 4), C(7, 1), and D(7, &#8211; 3) in a coordinate plane.<br \/>\nThen determine whether \\(\\overline{A B}\\) and \\(\\overline{C D}\\) are congruent.<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nA (8, -4), B (3, -4), C (7, 1), and D (7, -3)<br \/>\nCompare the given points with<br \/>\nA (x1, y1), B (x2, y2), C (x3, y3), and D (x4, y4)<br \/>\nNow,<br \/>\n\\(\\overline{A B}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(8 &#8211; 3)\u00b2 + (4 &#8211; 4)\u00b2}\\)<br \/>\n= 5<br \/>\n\\(\\overline{C D}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(7 &#8211; 7)\u00b2 + (1 + 3)\u00b2}\\)<br \/>\n= 4<br \/>\nHence,<br \/>\nThe representation of the given points in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-78189\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-52.png\" alt=\"\" width=\"483\" height=\"504\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-52.png 483w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-52-288x300.png 288w\" sizes=\"(max-width: 483px) 100vw, 483px\" \/><br \/>\n\\(\\overline{A B}\\) is not congruent to \\(\\overline{C D}\\)<\/p>\n<h4>1.3 Using Midpoint and Distance Formulas<\/h4>\n<p>Find the coordinates of the midpoint M. Then find the distance between points S and T.<\/p>\n<p>Question 10.<br \/>\nS(- 2, 4) and T(3, 9)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nS (-2, 4) and T (3, 9)<br \/>\nWe know that,<br \/>\nThe coordinates of the Midpoint = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nSo,<br \/>\nThe coordinates of the Midpoint = (\\(\\frac{3 &#8211; 2}{2}\\), \\(\\frac{9 + 4}{2}\\))<br \/>\nThe coordinates of the Midpoint = (\\(\\frac{1}{2}\\), \\(\\frac{13}{2}\\) )<br \/>\nHence, from the above,<br \/>\nWe can conclude that the coordinates of the Midpoint are: (\\(\\frac{1}{2}\\), \\(\\frac{13}{2}\\))<\/p>\n<p>Question 11.<br \/>\nS(6, &#8211; 3) and T(7, &#8211; 2)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nS (6, -3) and T (7, -2)<br \/>\nWe know that,<br \/>\nThe coordinates of the Midpoint = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nSo,<br \/>\nThe coordinates of the Midpoint = (\\(\\frac{7 + 6}{2}\\), \\(\\frac{-2 &#8211; 3}{2}\\))<br \/>\nThe coordinates of the Midpoint = (\\(\\frac{13}{2}\\), \\(\\frac{-5}{2}\\))<br \/>\nHence, from the above,<br \/>\nWe can conclude that the coordinates of the Midpoint are: (\\(\\frac{13}{2}\\), \\(\\frac{-5}{2}\\))<\/p>\n<p>Question 12.<br \/>\nThe midpoint of \\(\\overline{J K}\\) is M(6, 3). One endpoint is J(14, 9). Find the coordinates of endpoint K.<br \/>\nAnswer:<br \/>\nThe given points of \\(\\overline{J K}\\) are:<br \/>\nM (6, 3) and J (14, 9)<br \/>\nLet H be (x. y)<br \/>\nWe know that,<br \/>\nThe coordinates of the Midpoint = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nSo,<br \/>\n(6, 3) = (\\(\\frac{x + 14}{2}\\), \\(\\frac{y + 9}{2}\\))<br \/>\n\\(\\frac{x + 14}{2}\\) = 6\u00a0 \u00a0 \u00a0 \u00a0 \\(\\frac{y + 9}{2}\\) = 3<br \/>\nx + 14 = 6 (2)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0y + 9 = 3 (2)<br \/>\nx = 12 &#8211; 14\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0y = 6 &#8211; 9<br \/>\nx = -2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 y = -3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the coordinates of H are: (-2, -3)<\/p>\n<p>Question 13.<br \/>\nPoint M is the midpoint of \\(\\overline{A B}\\) here AM = 3x + 8 and MB = 6x &#8211; 4. Find AB.<br \/>\nAnswer:<br \/>\nIt is given that Point M is the midpoint of \\(\\overline{A B}\\) here AM = 3x + 8 and MB = 6x &#8211; 4.<br \/>\nNow,<br \/>\nBy using the Segment Addition Postulate,<br \/>\nAB = AM + MB<br \/>\nAB = (3x + 8) + (6x &#8211; 4)<br \/>\nAB = 9x &#8211; 4<\/p>\n<h4>1.4 Perimeter and Area in the Coordinate Plane<\/h4>\n<p>Find the perimeter and area of the polygon with the given vertices.<\/p>\n<p>Question 14.<br \/>\nW(5, &#8211; 1), X(5, 6), Y(2, 1) Z(2, 6)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nW (5, -1), X (5, 6), Y (2, 1), Z (2, 6)<br \/>\nNow,<br \/>\n\\(\\overline{W X}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(5 &#8211; 5)\u00b2 + (1 + 6)\u00b2}\\)<br \/>\n= 7<br \/>\n\\(\\overline{X Y}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(5 &#8211; 2)\u00b2 + (6 &#8211; 1)\u00b2}\\)<br \/>\n= 5.8<br \/>\n\\(\\overline{Y Z}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(2 &#8211; 2)\u00b2 + (6 &#8211; 1)\u00b2}\\)<br \/>\n= 5<br \/>\n\\(\\overline{Z W}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(5 &#8211; 2)\u00b2 + (6 + 1)\u00b2}\\)<br \/>\n= 7.6<br \/>\n\\(\\overline{W Y}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(5 &#8211; 2)\u00b2 + (1 + 1)\u00b2}\\)<br \/>\n= 3.6<br \/>\n\\(\\overline{X Z}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(5 &#8211; 2)\u00b2 + (6 &#8211; 6)\u00b2}\\)<br \/>\n= 3<br \/>\nHence,<br \/>\nThe perimeter of the given polygon = WX + XY + YZ + ZW<br \/>\n= 7 + 5.8 + 5 + 7.6<br \/>\n= 25.4<br \/>\nSince all the lengths of the sides are different,<br \/>\nThe area of the given polygon = \\(\\frac{1}{2}\\) (d1) (d2)<br \/>\nWhere,<br \/>\nd1 and d2 are the diagonals<br \/>\nSo,<br \/>\nThe area of the polygon = \\(\\frac{1}{2}\\) (WY) (XZ)<br \/>\n= \\(\\frac{1}{2}\\) (3) (3.6)<br \/>\n= 5.4<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe perimeter of the given polygon is: 25.4<br \/>\nThe area of the given polygon is: 5.4<\/p>\n<p>Question 15.<br \/>\nE(6, &#8211; 2) , F(6, 5), G(- 1, 5)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nE (6, -2), F (6, 5), G (-1, 5)<br \/>\nNow,<br \/>\n\\(\\overline{E F}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(6 &#8211; 6)\u00b2 + (2 + 5)\u00b2}\\)<br \/>\n= 7<br \/>\n\\(\\overline{F G}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(6 + 1)\u00b2 + (5 &#8211; 5)\u00b2}\\)<br \/>\n= 7<br \/>\n\\(\\overline{G E}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(6 + 1)\u00b2 + (5 + 2)\u00b2}\\)<br \/>\n= 9.8<br \/>\nHence,<br \/>\nThe perimeter of the given polygon = EF + FG + GE<br \/>\n= 7 + 7 + 9.8<br \/>\n= 23.8<br \/>\nNow,<br \/>\nThe area of the given polygon = \\(\\frac{1}{2}\\) (Base) (Height)<br \/>\nSo,<br \/>\nThe area of the polygon = \\(\\frac{1}{2}\\) (EF) (FG)<br \/>\n= \\(\\frac{1}{2}\\) (7) (7)<br \/>\n= 24.5<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe perimeter of the given polygon is: 23.8<br \/>\nThe area of the given polygon is: 24.5<\/p>\n<h4>1.5 Measuring and Constructing Angles<\/h4>\n<p>Find m\u2220ABD and m\u2220CBD.<\/p>\n<p>Question 16.<br \/>\nm\u2220ABC = 77\u00b0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35728\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-195.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 195\" width=\"120\" height=\"118\" \/><br \/>\nAnswer:<br \/>\nFrom the above figure,<br \/>\nBy using the Angle Addition Postulate,<br \/>\n\u2220ABC = \u2220ABD + \u2220DBC<br \/>\nIt is given that<br \/>\n\u2220ABC = 77\u00b0<br \/>\nSo,<br \/>\n77\u00b0 = (3x + 22)\u00b0 + (5x &#8211; 17)\u00b0<br \/>\n8x + 5 = 77\u00b0<br \/>\n8x = 77\u00b0 &#8211; 5\u00b0<br \/>\n8x = 72\u00b0<br \/>\nx = \\(\\frac{72}{8}\\)<br \/>\nx = 9\u00b0<br \/>\nSo,<br \/>\n\u2220ABD = (3x + 22)\u00b0<br \/>\n= 3 (9) + 22<br \/>\n= 27 + 22<br \/>\n= 49\u00b0<br \/>\n\u2220CBD = (5x &#8211; 17)\u00b0<br \/>\n= 5 (9) &#8211; 17<br \/>\n= 45 &#8211; 17<br \/>\n= 28\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220ABD = 49\u00b0 and \u2220CBD = 28\u00b0<\/p>\n<p>Question 17.<br \/>\nm\u2220ABC = 111\u00b0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35727\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-196.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 196\" width=\"165\" height=\"115\" \/><br \/>\nAnswer:<br \/>\nFrom the above figure,<br \/>\nBy using the Angle Addition Postulate,<br \/>\n\u2220ABC = \u2220ABD + \u2220DBC<br \/>\nIt is given that<br \/>\n\u2220ABC = 111\u00b0<br \/>\nSo,<br \/>\n111\u00b0 = (-10x + 58)\u00b0 + (6x + 41)\u00b0<br \/>\n-4x + 99 = 111\u00b0<br \/>\n-4x = 111\u00b0 &#8211; 99\u00b0<br \/>\n-4x = 12\u00b0<br \/>\nx = \\(\\frac{-12}{4}\\)<br \/>\nx = -3\u00b0<br \/>\nSo,<br \/>\n\u2220ABD = (-10x + 58)\u00b0<br \/>\n= -10 (-3) + 58<br \/>\n= 30 + 58<br \/>\n= 88\u00b0<br \/>\n\u2220CBD = (6x + 41)\u00b0<br \/>\n= 6 (-3) + 41<br \/>\n= 41 &#8211; 18<br \/>\n= 23\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220ABD = 88\u00b0 and \u2220CBD = 23\u00b0<\/p>\n<p>Question 18.<br \/>\nFind the measure of the angle using a protractor.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35726\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-1-Basics-of-Geometry-197.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 1 Basics of Geometry 197\" width=\"171\" height=\"90\" \/><br \/>\nAnswer:<br \/>\nThe measure of the angle of the given figure using a protractor is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-78203\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-53.png\" alt=\"\" width=\"191\" height=\"107\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that the angle is: 127.3\u00b0<\/p>\n<h4>1.6 Describing Pairs of Angles<\/h4>\n<p>\u22201 and \u22202 are complementary angles. Given m\u22201, find m\u22202.<\/p>\n<p>Question 19.<br \/>\nm\u22201 = 12\u00b0<br \/>\nAnswer:<br \/>\nIt is given that \u22201 and \u22202 are the complementary angles<br \/>\n\u22201 = 12\u00b0<br \/>\nSo,<br \/>\n\u22201 + \u22202 = 90\u00b0<br \/>\nSo,<br \/>\n\u22202 = 90\u00b0 &#8211; 12\u00b0<br \/>\n\u22202 = 78\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u22202 = 78\u00b0<\/p>\n<p>Question 20.<br \/>\nm\u22201 = 83\u00b0<br \/>\nAnswer:<br \/>\nIt is given that \u22201 and \u22202 are the complementary angles<br \/>\n\u22201 = 83\u00b0<br \/>\nSo,<br \/>\n\u22201 + \u22202 = 90\u00b0<br \/>\nSo,<br \/>\n\u22202 = 90\u00b0 &#8211; 83\u00b0<br \/>\n\u22202 = 7\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u22202 = 7\u00b0<\/p>\n<p>\u22203 and \u22204 are supplementary angles. Given m\u22203, find m\u22204.<\/p>\n<p>Question 21.<br \/>\nm\u22203 = 116\u00b0<br \/>\nAnswer:<br \/>\nIt is given that \u22203 and \u22204 are the supplementary angles<br \/>\n\u22203 = 116\u00b0<br \/>\nSo,<br \/>\n\u22203 + \u22204 = 180\u00b0<br \/>\nSo,<br \/>\n\u22204 = 180\u00b0 &#8211; 116\u00b0<br \/>\n\u22204 = 64\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u22204 = 64\u00b0<\/p>\n<p>Question 22.<br \/>\nm\u22203 = 56\u00b0<br \/>\nAnswer:<br \/>\nIt is given that \u22203 and \u22204 are the supplementary angles<br \/>\n\u22203 = 56\u00b0<br \/>\nSo,<br \/>\n\u22203 + \u22204 = 180\u00b0<br \/>\nSo,<br \/>\n\u22204 = 180\u00b0 &#8211; 56\u00b0<br \/>\n\u22204 = 124\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u22204 = 124\u00b0<\/p>\n<h3><a id=\"Basics_of_Geometry_Chapter_Test\"><\/a>Basics of Geometry Chapter Test<\/h3>\n<p>Find the length of \\(\\overline{Q S}\\). Explain how you found your answer.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35725\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-198.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 198\" width=\"235\" height=\"36\" \/><br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nBy using the Segment Addition Postulate,<br \/>\n\\(\\overline{Q S}\\) = \\(\\overline{Q R}\\) + \\(\\overline{R S}\\)<br \/>\n= 12 + 19<br \/>\n= 31<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of \\(\\overline{Q S}\\) is: 31<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35724\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-199.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 199\" width=\"278\" height=\"55\" \/><br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nBy using the Segment Addition Postulate,<br \/>\n\\(\\overline{Q R}\\) = \\(\\overline{Q S}\\) + \\(\\overline{S R}\\)<br \/>\n59 = \\(\\overline{Q S}\\) + 47<br \/>\n\\(\\overline{Q S}\\) = 59 &#8211; 47<br \/>\n\\(\\overline{Q S}\\) = 12<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of \\(\\overline{Q S}\\) is: 12<\/p>\n<p>Find the coordinates of tile midpoint M. Then find the distance between the two points.<\/p>\n<p>Question 3.<br \/>\nA(- 4, &#8211; 8) and B(- 1, 4)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nA (-4, -8), and B (-1, 4)<br \/>\nWe know that,<br \/>\nThe coordinates of the midpoint = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nSo,<br \/>\nThe coordinates of the midpoint = (\\(\\frac{-1 &#8211; 4}{2}\\), \\(\\frac{-8 + 4}{2}\\))<br \/>\nThe coordinates of the midpoint = (\\(\\frac{-5}{2}\\), \\(\\frac{-4}{2}\\))<br \/>\nThe coordinates of the midpoint = (\\(\\frac{-5}{2}\\), \\(\\frac{-2}\\))<br \/>\nHence, from the above,<br \/>\nWe can conclude that the coordinates of the midpoint are: (\\(\\frac{-5}{2}\\), -2)<\/p>\n<p>Question 4.<br \/>\nC(- 1, 7) and D(- 8, &#8211; 3)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nC (-1, 7), and D (-8, -3)<br \/>\nWe know that,<br \/>\nThe coordinates of the midpoint = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nSo,<br \/>\nThe coordinates of the midpoint = (\\(\\frac{-1 &#8211; 8}{2}\\), \\(\\frac{-3 + 7}{2}\\))<br \/>\nThe coordinates of the midpoint = (\\(\\frac{-9}{2}\\), \\(\\frac{4}{2}\\))<br \/>\nThe coordinates of the midpoint = (\\(\\frac{-9}{2}\\), 2)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the coordinates of the midpoint are: (\\(\\frac{-9}{2}\\), 2)<\/p>\n<p>Question 5.<br \/>\nThe midpoint of \\(\\overline{E F}\\) is M(1, &#8211; 1). One endpoint is E(- 3, 2). Find the coordinates of<br \/>\nendpoint F.<br \/>\nAnswer:<br \/>\nThe given points of \\(\\overline{E F}\\) are:<br \/>\nM (1, -1), and E (-3, 2)<br \/>\nLet the other endpoint be F (x, y)<br \/>\nWe know that,<br \/>\nThe coordinates of the midpoint = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\nSo,<br \/>\n(1, -1) = (\\(\\frac{x &#8211; 3}{2}\\), \\(\\frac{y + 2}{2}\\))<br \/>\n\\(\\frac{x &#8211; 3}{2}\\) = 1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\\(\\frac{y + 2}{2}\\) = -1<br \/>\nx &#8211; 3 = 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0y + 2 = -2<br \/>\nx = 5\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 y = -4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the coordinates of the other endpoint are: (5, -4)<\/p>\n<p>Use the diagram to decide whether the statement is true or false.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-35723\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-200.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 200\" width=\"171\" height=\"118\" \/><\/p>\n<p>Question 6.<br \/>\nPoints A, R, and B are collinear.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe points that lie in the same line are called &#8220;Collinear points&#8221;<br \/>\nFrom the figure,<br \/>\nWe can observe that A, R, and B are in the same plane but not in the same line<br \/>\nHence, from the above,<br \/>\nWe can conclude that A, R, and B are not collinear<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35240\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-201.png\" alt=\"Big Ideas Math Geometry Solutions 201\" width=\"153\" height=\"26\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-201.png 153w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-201-150x26.png 150w\" sizes=\"(max-width: 153px) 100vw, 153px\" \/><br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can observe there are two lines in the plane<br \/>\nHence, from the above,<br \/>\nWe can conclude that BW and AT are lines<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35239\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-202.png\" alt=\"Big Ideas Math Geometry Solutions 202\" width=\"197\" height=\"32\" \/><br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can observe that BR and RT are perpendicular lines<br \/>\nHence, from the above,<br \/>\nWe can conclude that BR and RT are opposite rays<\/p>\n<p>Question 9.<br \/>\nPlane D could also be named plane ART.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe points that are coplanar in the given plane can also be named for the name of the plane<br \/>\nHence, from the above,<br \/>\nWe can conclude that plane D can also be named plane ART<\/p>\n<p>Find the perimeter and area of the polygon with the given vertices. Explain how you found your answer.<\/p>\n<p>Question 10.<br \/>\nP(- 3, 4), Q(1, 4), R(- 3, &#8211; 2), S(3, &#8211; 2)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nP(- 3, 4), Q(1, 4), R(- 3, &#8211; 2), S(3, &#8211; 2)<br \/>\nNow,<br \/>\n\\(\\overline{P Q}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(1 + 3)\u00b2 + (4 &#8211; 4)\u00b2}\\)<br \/>\n= 4<br \/>\n\\(\\overline{Q R}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(1 + 3)\u00b2 + (4 + 2)\u00b2}\\)<br \/>\n= 7.2<br \/>\n\\(\\overline{R S}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(2 &#8211; 2)\u00b2 + (3 + 3)\u00b2}\\)<br \/>\n= 6<br \/>\n\\(\\overline{S P}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3 + 3)\u00b2 + (4 + 2)\u00b2}\\)<br \/>\n= 7.2<br \/>\nHence,<br \/>\nThe perimeter of the given polygon = PQ + QR + RS + SP<br \/>\n= 4 + 6 + 7.2 + 7.2<br \/>\n= 24.4<br \/>\nThe area of the given polygon = \\(\\frac{1}{2}\\) (a + b) (h)<br \/>\nWhere,<br \/>\na and b are the sides that are not equal<br \/>\nSo,<br \/>\nThe area of the polygon = \\(\\frac{1}{2}\\) (4 + 6) (7.2)<br \/>\n= \\(\\frac{1}{2}\\) (10) (7.2)<br \/>\n= 36<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe perimeter of the given polygon is: 24.4<br \/>\nThe area of the given polygon is: 36<\/p>\n<p>Question 11.<br \/>\nJ(- 1, 3), K(5, 3), L(2, &#8211; 2)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nJ(- 1, 3), K(5, 3), L(2, &#8211; 2)<br \/>\nNow,<br \/>\n\\(\\overline{J K}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3 &#8211; 3)\u00b2 + (1 + 5)\u00b2}\\)<br \/>\n= 6<br \/>\n\\(\\overline{K L}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3 + 2)\u00b2 + (5 &#8211; 2)\u00b2}\\)<br \/>\n= 5.8<br \/>\n\\(\\overline{L J}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(2 + 1)\u00b2 + (3 + 2)\u00b2}\\)<br \/>\n= 5.8<br \/>\nHence,<br \/>\nThe perimeter of the given polygon = JK + KL + LJ<br \/>\n= 6 + 5.8 + 5.8<br \/>\n= 17.8<br \/>\nNow,<br \/>\nThe area of the given polygon = \\(\\frac{1}{2}\\) (Base) (Height)<br \/>\nSo,<br \/>\nThe area of the polygon = \\(\\frac{1}{2}\\) (JK) (KL)<br \/>\n= \\(\\frac{1}{2}\\) (6) (5.8)<br \/>\n= 17.4<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe perimeter of the given polygon is: 17.8<br \/>\nThe area of the given polygon is: 17.4<\/p>\n<p>Question 12.<br \/>\nIn the diagram. \u2220AFE is a straight angle and \u2220CFE is a right angle. Identify all supplementary and complementary angles. Explain. Then find, m\u2220DFE, m\u2220BFC, and m\u2220BFE.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35720\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-203.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 203\" width=\"237\" height=\"141\" \/><br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nUse the clock at the left.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35719\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-204.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 204\" width=\"187\" height=\"188\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-204.png 187w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-204-150x150.png 150w\" sizes=\"(max-width: 187px) 100vw, 187px\" \/><br \/>\na. What is the measure of the acute angle created when the clock is at 10:00?<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\n12 sectors = 360\u00b0<br \/>\nFrom the above clock,<br \/>\nWe can observe that there are 2 sectors at 10:00<br \/>\nSo,<br \/>\nThe angle created when the clock is at 10:00 = 2 (30)<br \/>\n= 60\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the measure of the acute angle created when the clock is at 10:00 is: 60\u00b0<\/p>\n<p>b. What is the measure of the obtuse angle created when the clock is at 5:00?<br \/>\nAnswer:<br \/>\nFrom the figure,<br \/>\nWe can observe that there are 4 sectors between 12 and\u00a0 at 5:00<br \/>\nSo,<br \/>\nThe acute angle created when the clock is at 5:00 = 4 (30)<br \/>\n= 120\u00b0<br \/>\nSo,<br \/>\nThe obtuse angle created when the clock is at 5:00 = 360 &#8211; 120<br \/>\n= 240\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the obtuse angle created when the clock is at 5:00 is: 240\u00b0<\/p>\n<p>c. Find a time where the hour and minute hands create a straight angle.<br \/>\nAnswer:<br \/>\nwe know that,<br \/>\nA straight angle is an angle that is 180\u00b0<br \/>\nNow,<br \/>\nFrom the figure,<br \/>\nWe can observe that the hour and minute hands create a straight angle is: 6:00, 2:45<br \/>\nHence, from the above,<br \/>\nWe can conclude that the time where the hour and minute hands create a straight angle is: 6:00 and 2:45<\/p>\n<p>Question 14.<br \/>\nSketch a figure that contains a plane and two lines that intersect the plane at one point.<br \/>\nAnswer:<br \/>\nThe representation of a plane and two planes intersection at a point is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-68999\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-3.png\" sizes=\"(max-width: 482px) 100vw, 482px\" srcset=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-3.png 482w, https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-3-300x151.png 300w\" alt=\"\" width=\"482\" height=\"243\" \/><\/p>\n<p>Question 15.<br \/>\nYour parents decide they would like to install a rectangular swimming pool in the backyard. There is a 15-foot by the 20-foot rectangular area available. Your parents request a 3-foot edge around each side of the pool. Draw a diagram of this situation in a coordinate plane. What is the perimeter and area of the largest swimming pool that will fit?<br \/>\nAnswer:<br \/>\nIt is given that your parents decide they would like to install a rectangular swimming pool in the backyard. There is a 15-foot by the 20-foot rectangular area available. Your parents request a 3-foot edge around each side of the pool.<br \/>\nSince the 3 ft edge is on both sides of the pool, each dimension of the pool is 6 ft shorter than the corresponding dimension of the space.<br \/>\nSo,<br \/>\nThe pool will be<br \/>\n15 ft -6 ft = 9 ft in one direction and 20 ft -6 ft = 14 ft in the other direction.<br \/>\nWe know that,<br \/>\nThe perimeter of the pool is the sum of its side lengths:<br \/>\nSo,<br \/>\nP = 9 ft + 14 ft + 9 ft + 14 ft = 2(9 ft +14 ft)<br \/>\n= 2(23 ft)<br \/>\n= 46 ft<br \/>\nNow,<br \/>\nThe area of the pool = 14 (9)<br \/>\n= 126 ft\u00b2<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe perimeter of the pool is: 46 ft<br \/>\nThe area of the pool is 126 ft\u00b2<br \/>\nThe representation of the pool in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-78546\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-54.png\" alt=\"\" width=\"621\" height=\"460\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-54.png 621w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-1-54-300x222.png 300w\" sizes=\"(max-width: 621px) 100vw, 621px\" \/><\/p>\n<p>Question 16.<br \/>\nThe picture shows the arrangement of balls in a game of boccie. The object of the game is to throw your ball closest to the small. while ball, which is called the Pallino. The green ball is the midpoint between the red ball and the Pallino. The distance between the green hail and the red ball is 10 inches. The distance between the yellow ball and the Pallino is 8 inches. Which bail is closer to the Pallino. the green ball or the yellow ball? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35718\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-205.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 205\" width=\"183\" height=\"244\" \/><br \/>\nAnswer:<br \/>\nIt is given that the picture shows the arrangement of balls in a game of boccie. The object of the game is to throw your ball closest to the small. while ball, which is called the Pallino. The green ball is the midpoint between the red ball and the Pallino. The distance between the green hail and the red ball is 10 inches. The distance between the yellow ball and the Pallino is 8 inches.<br \/>\nNow,<br \/>\nWhen we compare the distances between the Pallino and the green ball and between the yellow ball and the Pallino,<br \/>\nWe can observe that the distance between the yellow ball and Pallino is less<br \/>\nHence, from the above,<br \/>\nWe can conclude that the yellow ball is closer to the Pallino<\/p>\n<h3><a id=\"Basics_of_Geometry_Cumulative_Assessment\"><\/a>Basics of Geometry Cumulative Assessment<\/h3>\n<p>Question 1.<br \/>\nUse the diagram to determine which segments, if any, are congruent. List all congruent segments.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35717\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-206.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 206\" width=\"232\" height=\"224\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe &#8220;Congruency&#8221; means having the same size and the same length<br \/>\nBut, from the above coordinate plane,<br \/>\nWe can observe that there are no congruent lines<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are no congruent line segments in the coordinate plane<\/p>\n<p>Question 2.<br \/>\nOrder the terms so that each consecutive term builds off the previous term.<br \/>\nplane\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0segment\u00a0 \u00a0 \u00a0 line\u00a0 \u00a0 \u00a0point\u00a0 \u00a0 ray<br \/>\nAnswer:<br \/>\nThe given terms are:<br \/>\na. Plane b. Segment c. Line d. Point e. Ray<br \/>\nHence,<br \/>\nThe order of the given terms are:<br \/>\nPoint, Line, Ray, Segment, and Plane<\/p>\n<p>Question 3.<br \/>\nThe endpoints of a line segment are (- 6, 13) and (11, 5). Which choice shows the correct midpoint and distance between these two points?<br \/>\n(A) \\(\\left(\\frac{5}{2}, 4\\right)\\); 18.8 units<br \/>\n(B) \\(\\left(\\frac{5}{2}, 9\\right)\\); 18.8 units<br \/>\n(C) \\(\\left(\\frac{5}{2}, 4\\right)\\); 9.4 units<br \/>\n(D) \\(\\left(\\frac{5}{2}, 9\\right)\\); 9.4 units<br \/>\nAnswer:<br \/>\nThe given endpoints of a line segment are: (-6, 13) and (11, 5)<br \/>\nWe know that,<br \/>\nThe coordinates of the midpoint = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\n= (\\(\\frac{11 &#8211; 6}{2}\\), \\(\\frac{13 + 5}{2}\\))<br \/>\n= (\\(\\frac{5}{2}\\), \\(\\frac{18}{2}\\))<br \/>\n= (\\(\\frac{5}{2}\\), 9)<br \/>\nWe know that,<br \/>\nThe distance between the coordinates = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(11 + 6)\u00b2 + (13 &#8211; 5)\u00b2}\\)<br \/>\n= 18.78 \u2248 18.8<br \/>\nHence, from the above,<br \/>\nWe can conclude that option (B) shows the correct midpoint and distance<\/p>\n<p>Question 4.<br \/>\nFind the perimeter and area of the figure shown<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35716\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-207.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 207\" width=\"212\" height=\"207\" \/><br \/>\nAnswer:<br \/>\nFrom the coordinate plane,<br \/>\nThe points are:<br \/>\nQ (-4, 3), R (2, 3), S (3, 3), and T (-3, 3)<br \/>\nNow,<br \/>\n\\(\\overline{Q R}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3 &#8211; 3)\u00b2 + (4 + 2)\u00b2}\\)<br \/>\n= 6<br \/>\n\\(\\overline{R S}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3 &#8211; 2)\u00b2 + (3 &#8211; 3)\u00b2}\\)<br \/>\n= 1<br \/>\n\\(\\overline{S T}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3 + 3)\u00b2 + (3 &#8211; 3)\u00b2}\\)<br \/>\n= 6<br \/>\n\\(\\overline{T Q}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4 &#8211; 3)\u00b2 + (3 &#8211; 3)\u00b2}\\)<br \/>\n= 1<br \/>\nHence,<br \/>\nThe perimeter of the given polygon = QR + RS + ST + TQ<br \/>\n= 6 + 1 + 6 + 1<br \/>\n= 14<br \/>\nThe area of the given polygon = Length \u00d7 Width<br \/>\nSo,<br \/>\nThe area of the polygon = 6 (1)<br \/>\n= 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe perimeter of the given polygon is: 14<br \/>\nThe area of the given polygon is: 6<\/p>\n<p>Question 5.<br \/>\nPlot the points W(- 1, 1), X(5, 1), Y(5, &#8211; 2), and Z(- 1, &#8211; 2) in a coordinate plane. What type of polygon do the points form? Your friend claims that you could use this figure to represent a basketball court with an area of 4050 square feet and a perimeter of 270 feet. Do you support your friend&#8217;s claim? Explain.<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nW (-1, 1), X (5, 1), Y (5, -2), and Z (-1, -2)<br \/>\nNow,<br \/>\n\\(\\overline{W X}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(1 &#8211; 1)\u00b2 + (5 + 1)\u00b2}\\)<br \/>\n= 6<br \/>\n\\(\\overline{X Y}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(1 + 2)\u00b2 + (5 &#8211; 5)\u00b2}\\)<br \/>\n= 3<br \/>\n\\(\\overline{Y Z}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(5 + 1)\u00b2 + (2 &#8211; 2)\u00b2}\\)<br \/>\n= 6<br \/>\n\\(\\overline{Z W}\\) = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(1 &#8211; 1)\u00b2 + (2 + 1)\u00b2}\\)<br \/>\n= 3<br \/>\nHence,<br \/>\nThe perimeter of the given polygon = WX + XY + YZ + ZW<br \/>\n= 6 + 3 + 6 + 3<br \/>\n= 18<br \/>\nBut,<br \/>\nIt is given that the actual perimeter is: 270 ft<br \/>\nSo,<br \/>\nThe scale = 270 \/ 18 = 15<br \/>\nNow,<br \/>\nThe area of the given polygon = Length \u00d7 Width<br \/>\nSo,<br \/>\nThe area of the polygon = 6 (3)<br \/>\n= 18<br \/>\nThe area of the basketball = 15 (15) (18)<br \/>\n= 4050 ft\u00b2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the claim of your friend is correct<br \/>\nQuestion 6.<br \/>\nUse the steps in the construction to explain how you know that \\(\\vec{A}\\)G is the angle bisector<br \/>\nof \u2220CAB.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35715\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-208.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 208\" width=\"721\" height=\"171\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-208.png 721w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-208-300x71.png 300w\" sizes=\"(max-width: 721px) 100vw, 721px\" \/><br \/>\nAnswer:<br \/>\nStep 1:<br \/>\nDraw an angle \u2220CAB. Measure the length of AC and draw an arc by using the compass by taking the length more than half of the length of AC<br \/>\nStep 2:<br \/>\nFrom the arc, by using a compass, draw 2 arcs by taking more than half of the length of the arc on both sides of the arc<br \/>\nStep 3:<br \/>\nUse a straightedge to measure the length from the arcs to angle A and that line is called &#8220;Angle Bisector&#8221;<\/p>\n<p>Question 7.<br \/>\nThe picture shows an aerial view of a city. Use the streets highlighted in red to identify all congruent angles. Assume all streets are straight angles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35714\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-209.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 209\" width=\"346\" height=\"259\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-209.png 346w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-209-300x225.png 300w\" sizes=\"(max-width: 346px) 100vw, 346px\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe &#8220;Congruent angles&#8221; are the angles that have the same angle measure<br \/>\nHence, from the above figure,<br \/>\nThe congruent angles are: \u2220E and \u2220M; \u2220O and \u2220R<\/p>\n<p>Question 8.<br \/>\nThree roads come to an intersection point that the People in your town call Five Corners. as shown in the figure.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35713\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-210.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 1 Basics of Geometry 210\" width=\"500\" height=\"174\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-210.png 500w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-1-Basics-of-Geometry-210-300x104.png 300w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><br \/>\na. Identify all vertical ang\u00cces.<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nThe vertical angles are \u2220LJK, \u2220MJP, \u2220MJN<\/p>\n<p>b. Identify all linear pairs.<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nThe linear pairs are: \u2220LJK, \u2220MJP, \u2220MJN<\/p>\n<p>C. you are traveling east on Buffalo Road and decide to turn left onto Carter Hill.<br \/>\nName the angle of the turn you made.<br \/>\n\u2220KJL\u00a0 \u00a0 \u00a0\u2220KJM\u00a0 \u00a0 \u00a0\u2220KJN\u00a0 \u00a0 \u00a0 \u2220KJP\u00a0 \u00a0 \u00a0 \u00a0\u2220LJM<br \/>\n\u2220LJN\u00a0 \u00a0 \u00a0\u2220LJP\u00a0 \u00a0 \u00a0 \u2220MJN\u00a0 \u00a0 \u00a0\u2220MJP\u00a0 \u00a0 \u00a0\u2220NJP<br \/>\nAnswer:<br \/>\nFrom the above figure,<br \/>\nThe angle made by you when you are traveling east n BuffaloRoad and decide to turn left onto Carter hill is: \u2220KJL<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Looking across the web for a friendly site that caters to all your needs regarding the Big Ideas Math Geometry Concepts? Don&#8217;t worry we are with you in this and we will provide you the Complete Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry. All the Solutions covered in the BIM Geometry Ch &#8230; <a title=\"Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-geometry-answers-chapter-1\/\" aria-label=\"More on Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":89443,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[4],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-1-1.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/33461"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=33461"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/33461\/revisions"}],"predecessor-version":[{"id":90296,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/33461\/revisions\/90296"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89443"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=33461"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=33461"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=33461"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}