{"id":37021,"date":"2022-04-02T13:02:21","date_gmt":"2022-04-02T07:32:21","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=37021"},"modified":"2022-04-07T11:11:45","modified_gmt":"2022-04-07T05:41:45","slug":"big-ideas-math-geometry-answers-chapter-3","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-geometry-answers-chapter-3\/","title":{"rendered":"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines"},"content":{"rendered":"<p>Seeking help regarding the concepts of Big Ideas Geometry Answer Key Ch 3 Parallel and Perpendicular Lines? If so, don&#8217;t bother as you will get a complete idea through our BIM Geometry Chapter 3 Parallel and Perpendicular Lines Answer Key. Make the most out of these preparation resources and stand out from the rest of the crowd. All the Questions prevailing here in <a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-geometry-answers\/\">Big Ideas Math Geometry Answers<\/a> Chapter 3 adhere and meets the Common Core Curriculum Standards. You will find Solutions to all the BIM Book Geometry Ch 3 Parallel and Perpendicular Concepts aligned as per the BIM Textbooks.<\/p>\n<h2>Big Ideas Math Book Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines<\/h2>\n<p>Solving the concepts from the Big Ideas Math Book Geometry Ch 3 Parallel and Perpendicular Lines Answers on a regular basis boosts the problem-solving ability in you. Embedded mathematical practices, exercises provided make it easy for you to understand the concepts quite quickly. Begin your preparation right away and clear the exams with utmost confidence. Simply click on the below available and learn the respective topics in no time.<\/p>\n<ul>\n<li><a href=\"#Parallel_and_Perpendicular_Lines_Maintaining_Mathematical_Proficiency\">Parallel and Perpendicular Lines Maintaining Mathematical Proficiency &#8211; Page 123\u00a0<\/a><\/li>\n<li><a href=\"#Parallel_and_Perpendicular_Lines_Mathematical_Practices\">Parallel and Perpendicular Lines Mathematical Practices &#8211; Page 124<\/a><\/li>\n<li><a href=\"#3.1_Pairs_of_Lines_and_Angles\">3.1 Pairs of Lines and Angles &#8211; Page(125-130)<\/a><\/li>\n<li><a href=\"#Lesson_3.1_Pairs_of_Lines_and_Angles\">Lesson 3.1 Pairs of Lines and Angles &#8211; Page(126-128)<\/a><\/li>\n<li><a href=\"#Exercise_3.1_Pairs_of_Lines_and_Angles\">Exercise 3.1 Pairs of Lines and Angles &#8211; Page(129-130)<\/a><\/li>\n<li><a href=\"#3.2_Parallel_Lines_and_Transversals\">3.2 Parallel Lines and Transversals &#8211; Page(131-136)<\/a><\/li>\n<li><a href=\"#Lesson_3.2_Parallel_Lines_and_Transversals\">Lesson 3.2 Parallel Lines and Transversals &#8211; Page(132-134)<\/a><\/li>\n<li><a href=\"#Exercise_3.2_Parallel_Lines_and_Transversals\">Exercise 3.2 Parallel Lines and Transversals &#8211; Page(135-136)<\/a><\/li>\n<li><a href=\"#3.3_Proofs_with_Parallel_Lines\">3.3 Proofs with Parallel Lines &#8211; Page(137-144)<\/a><\/li>\n<li><a href=\"#Lesson_3.3_Proofs_with_Parallel_Lines\">Lesson 3.3 Proofs with Parallel Lines &#8211; Page(138-141)<\/a><\/li>\n<li><a href=\"#Exercise_3.3_Proofs_with_Parallel_Lines\">Exercise 3.3 Proofs with Parallel Lines &#8211; Page(142-144)<\/a><\/li>\n<li><a href=\"#3.1_-_3.3_Study_Skills:_Analyzing_Your_Errors\">3.1 &#8211; 3.3 Study Skills: Analyzing Your Errors &#8211; Page 145<\/a><\/li>\n<li><a href=\"#3.1_-_3.3_Quiz\">3.1 &#8211; 3.3 Quiz &#8211; Page 146<\/a><\/li>\n<li><a href=\"#3.4_Proofs_with_Perpendicular_Lines\">3.4 Proofs with Perpendicular Lines &#8211; Page(147-154)<\/a><\/li>\n<li><a href=\"#Lesson_3.4_Proofs_with_Perpendicular_Lines\">Lesson 3.4 Proofs with Perpendicular Lines &#8211; Page(148-151)<\/a><\/li>\n<li><a href=\"#Exercise_3.4_Proofs_with_Perpendicular_Lines\">Exercise 3.4 Proofs with Perpendicular Lines &#8211; Page(152-154)<\/a><\/li>\n<li><a href=\"#3.5_Equations_of_Parallel_and_Perpendicular_Lines\">3.5 Equations of Parallel and Perpendicular Lines &#8211; Page(155-162)<\/a><\/li>\n<li><a href=\"#Lesson_3.5_Equations_of_Parallel_and_Perpendicular_Lines\">Lesson 3.5 Equations of Parallel and Perpendicular Lines &#8211; Page(156-159)<\/a><\/li>\n<li><a href=\"#Exercise_3.5_Equations_of_Parallel_and_Perpendicular_Lines\">Exercise 3.5 Equations of Parallel and Perpendicular Lines &#8211; Page(160-162)<\/a><\/li>\n<li><a href=\"#3.4_-_3.5_Performance_Task:_Navajo_Rugs\">3.4 &#8211; 3.5 Performance Task: Navajo Rugs &#8211; Page 163<\/a><\/li>\n<li><a href=\"#Parallel_and_Perpendicular_Lines_Chapter_Review\">Parallel and Perpendicular Lines Chapter Review &#8211; Page(164-166)<\/a><\/li>\n<li><a href=\"#Parallel_and_Perpendicular_Lines_Test\">Parallel and Perpendicular Lines Test &#8211; Page 167<\/a><\/li>\n<li><a href=\"#Parallel_and_Perpendicular_Lines_Cumulative_Assessment\">Parallel and Perpendicular Lines Cumulative Assessment &#8211; Page(168-169)<\/a><\/li>\n<\/ul>\n<h3><a id=\"Parallel_and_Perpendicular_Lines_Maintaining_Mathematical_Proficiency\"><\/a>Parallel and Perpendicular Lines Maintaining Mathematical Proficiency<\/h3>\n<p>Find the slope of the line.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37024\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 1\" width=\"179\" height=\"169\" \/><br \/>\nAnswer:<br \/>\nFrom the given coordinate plane,<br \/>\nLet the given points are:<br \/>\nA (-1, 2), and B (3, -1)<br \/>\nCompare the given points with<br \/>\nA (x1, y1), B (x2, y2)<br \/>\nWe know that,<br \/>\nSlope of the line (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\nSlope of the line (m) = \\(\\frac{-1 &#8211; 2}{3 + 1}\\)<br \/>\n= \\(\\frac{-3}{4}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the slope of the given line is: \\(\\frac{-3}{4}\\)<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37023\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-2.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 2\" width=\"175\" height=\"175\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-2.png 175w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-2-150x150.png 150w\" sizes=\"(max-width: 175px) 100vw, 175px\" \/><br \/>\nAnswer:<br \/>\nFrom the given coordinate plane,<br \/>\nLet the given points are:<br \/>\nA (-2, 2), and B (-3, -1)<br \/>\nCompare the given points with<br \/>\nA (x1, y1), B (x2, y2)<br \/>\nWe know that,<br \/>\nSlope of the line (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\nSlope of the line (m) = \\(\\frac{-1 &#8211; 2}{-3 + 2}\\)<br \/>\n= \\(\\frac{-3}{-1}\\)<br \/>\n= 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the slope of the given line is: 3<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37022\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3\" width=\"175\" height=\"174\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.png 175w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3-150x150.png 150w\" sizes=\"(max-width: 175px) 100vw, 175px\" \/><br \/>\nAnswer:<br \/>\nFrom the given coordinate plane,<br \/>\nLet the given points are:<br \/>\nA (-3, -2), and B (1, -2)<br \/>\nCompare the given points with<br \/>\nA (x1, y1), B (x2, y2)<br \/>\nWe know that,<br \/>\nSlope of the line (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\nSlope of the line (m) = \\(\\frac{-2 + 2}{3 + 1}\\)<br \/>\n= \\(\\frac{0}{4}\\)<br \/>\n= 0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the slope of the given line is: 0<\/p>\n<p>Write an equation of the line that passes through the given point and has the given slope.<\/p>\n<p>Question 4.<br \/>\n(6, 1); m = &#8211; 3<br \/>\nAnswer:<br \/>\nThe given point is: (6, 1)<br \/>\nThe slope of the given line is: m = -3<br \/>\nWe know that,<br \/>\nThe equation of a line is:<br \/>\ny = mx + b<br \/>\nWhere,<br \/>\nm is the slope<br \/>\nb is the y-intercept<br \/>\nSo,<br \/>\ny = -3x + b &#8212;&#8212;&#8211;(1)<br \/>\nTo find the value of b,<br \/>\nSubstitute the given point in eq. (1)<br \/>\nSo,<br \/>\n1 = -3 (6) + b<br \/>\n1 = -18 + b<br \/>\n1 + 18 = b<br \/>\nb = 19<br \/>\nHence,<br \/>\nThe equation of the line along with y-intercept is:<br \/>\ny = -3x + 19<\/p>\n<p>Question 5.<br \/>\n(-3, 8); m = &#8211; 2<br \/>\nAnswer:<br \/>\nThe given point is: (-3, 8)<br \/>\nThe slope of the given line is: m = -2<br \/>\nWe know that,<br \/>\nThe equation of a line is:<br \/>\ny = mx + b<br \/>\nWhere,<br \/>\nm is the slope<br \/>\nb is the y-intercept<br \/>\nSo,<br \/>\ny = -2x + b &#8212;&#8212;&#8211;(1)<br \/>\nTo find the value of b,<br \/>\nSubstitute the given point in eq. (1)<br \/>\nSo,<br \/>\n8 = -2 (-3) + b<br \/>\n8 = 6 + b<br \/>\n8 &#8211; 6 = b<br \/>\nb = 2<br \/>\nHence,<br \/>\nThe equation of the line along with y-intercept is:<br \/>\ny = -2x + 2<\/p>\n<p>Question 6.<br \/>\n(- 1, 5); m = 4<br \/>\nAnswer:<br \/>\nThe given point is: (-1, 5)<br \/>\nThe slope of the given line is: m = 4<br \/>\nWe know that,<br \/>\nThe equation of a line is:<br \/>\ny = mx + b<br \/>\nWhere,<br \/>\nm is the slope<br \/>\nb is the y-intercept<br \/>\nSo,<br \/>\ny = 4x + b &#8212;&#8212;&#8211;(1)<br \/>\nTo find the value of b,<br \/>\nSubstitute the given point in eq. (1)<br \/>\nSo,<br \/>\n5 = 4 (-1) + b<br \/>\n5 = -4 + b<br \/>\n5 + 4 = b<br \/>\nb = 9<br \/>\nHence,<br \/>\nThe equation of the line along with y-intercept is:<br \/>\ny = 4x + 9<\/p>\n<p>Question 7.<br \/>\n(2, &#8211; 4); m = \\(\\frac{1}{2}\\)<br \/>\nAnswer:<br \/>\nThe given point is: (2, -4)<br \/>\nThe slope of the given line is: m = \\(\\frac{1}{2}\\)<br \/>\nWe know that,<br \/>\nThe equation of a line is:<br \/>\ny = mx + b<br \/>\nWhere,<br \/>\nm is the slope<br \/>\nb is the y-intercept<br \/>\nSo,<br \/>\ny = \\(\\frac{1}{2}\\)x + b &#8212;&#8212;&#8211;(1)<br \/>\nTo find the value of b,<br \/>\nSubstitute the given point in eq. (1)<br \/>\nSo,<br \/>\n-4 = \\(\\frac{1}{2}\\) (2) + b<br \/>\n-4 = 1 + b<br \/>\n-4 &#8211; 1 = b<br \/>\nb = -5<br \/>\nHence,<br \/>\nThe equation of the line along with y-intercept is:<br \/>\ny = \\(\\frac{1}{2}\\)x &#8211; 5<\/p>\n<p>Question 8.<br \/>\n(- 8, &#8211; 5); m = &#8211;\\(\\frac{1}{4}\\)<br \/>\nAnswer:<br \/>\nThe given point is: (-8, -5)<br \/>\nThe slope of the given line is: m = &#8211;\\(\\frac{1}{4}\\)<br \/>\nWe know that,<br \/>\nThe equation of a line is:<br \/>\ny = mx + b<br \/>\nWhere,<br \/>\nm is the slope<br \/>\nb is the y-intercept<br \/>\nSo,<br \/>\ny = &#8211;\\(\\frac{1}{4}\\)x + b &#8212;&#8212;&#8211;(1)<br \/>\nTo find the value of b,<br \/>\nSubstitute the given point in eq. (1)<br \/>\nSo,<br \/>\n-5 = &#8211;\\(\\frac{1}{4}\\) (-8) + b<br \/>\n-5 = 2 + b<br \/>\n-5 &#8211; 2 = b<br \/>\nb = -7<br \/>\nHence,<br \/>\nThe equation of the line along with y-intercept is:<br \/>\ny = &#8211;\\(\\frac{1}{4}\\)x &#8211; 7<\/p>\n<p>Question 9.<br \/>\n(0, 9); m = \\(\\frac{2}{3}\\)<br \/>\nAnswer:<br \/>\nThe given point is: (0, 9)<br \/>\nThe slope of the given line is: m = \\(\\frac{2}{3}\\)<br \/>\nWe know that,<br \/>\nThe equation of a line is:<br \/>\ny = mx + b<br \/>\nWhere,<br \/>\nm is the slope<br \/>\nb is the y-intercept<br \/>\nSo,<br \/>\ny = \\(\\frac{2}{3}\\)x + b &#8212;&#8212;&#8211;(1)<br \/>\nTo find the value of b,<br \/>\nSubstitute the given point in eq. (1)<br \/>\nSo,<br \/>\n9 = \\(\\frac{2}{3}\\) (0) + b<br \/>\n9 = 0 + b<br \/>\n9 &#8211; 0 = b<br \/>\nb = 9<br \/>\nHence,<br \/>\nThe equation of the line along with y-intercept is:<br \/>\ny = \\(\\frac{2}{3}\\)x + 9<\/p>\n<p>Question 10.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nWhy does a horizontal line have a slope of 0, but a vertical line has an undefined slope?<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nSlope of the line (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nWe know that,<br \/>\nFor a horizontal line,<br \/>\nThe coordinates of y are the same. i.e.,<br \/>\ny1 = y2 = y3\u00a0 &#8230;&#8230;&#8230;<br \/>\nFor a vertical line,<br \/>\nThe coordinates of x are the same. i.e.,<br \/>\nx1 = x2 = x3 &#8230;&#8230;.<br \/>\nSo,<br \/>\nThe slope of the horizontal line (m) = \\(\\frac{y2 &#8211; y2}{x2 &#8211; x1}\\)<br \/>\nWe know that,<br \/>\nAny fraction that contains 0 in the numerator has its value equal to 0<br \/>\nSo,<br \/>\nThe slope of horizontal line (m) = 0<br \/>\nThe slope of vertical line (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nWe know that,<br \/>\nAny fraction that contains 0 in the denominator has its value undefined<br \/>\nSo,<br \/>\nThe slope of the vertical line (m) = Undefined<\/p>\n<h3><a id=\"Parallel_and_Perpendicular_Lines_Mathematical_Practices\"><\/a>Parallel and Perpendicular Lines Mathematical Practices<\/h3>\n<p>Use a graphing calculator to graph the pair of lines. Use a square viewing window. Classify the lines as parallel, perpendicular, coincident, or non-perpendicular intersecting lines. Justify your answer.<\/p>\n<p>Question 1.<br \/>\nx + 2y = 2<br \/>\n2x &#8211; y = 4<br \/>\nAnswer:<br \/>\nThe given pair of lines are:<br \/>\nx + 2y = 2<br \/>\n2x &#8211; y = 4<br \/>\nHence,<br \/>\nThe representation of the given pair of lines in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-79087\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3.png\" alt=\"\" width=\"495\" height=\"515\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-288x300.png 288w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><br \/>\nWe know that,<br \/>\nFor a pair of lines to be perpendicular, the product of the slopes i.e., the product of the slope of the first line and the slope of the second line will be equal to -1<br \/>\nSo,<br \/>\nBy comparing the given pair of lines with<br \/>\ny = mx + b<br \/>\nWe get<br \/>\nThe slope of first line (m1) = &#8211;\\(\\frac{1}{2}\\)<br \/>\nThe slope of second line (m2) = 2<br \/>\nSo,<br \/>\nm1 \u00d7m2 = &#8211;\\(\\frac{1}{2}\\) \u00d7 2<br \/>\n= -1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given pair of lines are perpendicular lines<\/p>\n<p>Question 2.<br \/>\nx + 2y = 2<br \/>\n2x + 4y = 4<br \/>\nAnswer:<br \/>\nThe give pair of lines are:<br \/>\nx + 2y = 2<br \/>\n2x + 4y = 4<br \/>\nHence,<br \/>\nThe representation of the given pair of lines in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-79088\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-1.png\" alt=\"\" width=\"497\" height=\"524\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-1.png 497w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-1-285x300.png 285w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><br \/>\nWe know that,<br \/>\nFor a pair of lines to be coincident, the pair of lines have the same slope and the same y-intercept<br \/>\nSo,<br \/>\nBy comparing the given pair of lines with<br \/>\ny = mx + b<br \/>\nWe get<br \/>\nm1 = &#8211;\\(\\frac{1}{2}\\), b1 = 1<br \/>\nm2 = &#8211;\\(\\frac{1}{2}\\), b2 = 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given pair of lines are coincident lines<\/p>\n<p>Question 3.<br \/>\nx + 2y = 2<br \/>\nx + 2y = &#8211; 2<br \/>\nAnswer:<br \/>\nThe given pair of lines are:<br \/>\nx + 2y = 2<br \/>\nx + 2y = -2<br \/>\nHence,<br \/>\nThe representation of the given pair of lines in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-79089\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-2.png\" alt=\"\" width=\"489\" height=\"521\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-2.png 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-2-282x300.png 282w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><br \/>\nWe know that,<br \/>\nFor a pair of lines to be parallel, the pair of lines have the same slope but different y-intercepts<br \/>\nSo,<br \/>\nBy comparing the given pair of lines with<br \/>\ny = mx + b<br \/>\nWe get<br \/>\nm1 = &#8211;\\(\\frac{1}{2}\\), b1 = 1<br \/>\nm2 = \\(\\frac{1}{2}\\), b2 = -1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given pair of lines are parallel lines<\/p>\n<p>Question 4.<br \/>\nx &#8211; 2y = 2<br \/>\nx &#8211; y = &#8211; 4<br \/>\nAnswer:<br \/>\nThe given pair of lines are:<br \/>\nx &#8211; 2y = 2<br \/>\nx &#8211; y = -4<br \/>\nHence,<br \/>\nThe representation of the given pair of lines in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-79090\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-3.png\" alt=\"\" width=\"527\" height=\"519\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-3.png 527w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-3-300x295.png 300w\" sizes=\"(max-width: 527px) 100vw, 527px\" \/><\/p>\n<p>We know that,<br \/>\nFor a pair of lines to be non-perpendicular, the product of the slopes i.e., the product of the slope of the first line and the slope of the second line will not be equal to -1<br \/>\nSo,<br \/>\nBy comparing the given pair of lines with<br \/>\ny = mx + b<br \/>\nWe get<br \/>\nThe slope of first line (m1) = \\(\\frac{1}{2}\\)<br \/>\nThe slope of second line (m2) = 1<br \/>\nSo,<br \/>\nm1 \u00d7m2\u00a0 = \\(\\frac{1}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given pair of lines are non-perpendicular lines<\/p>\n<h3><a id=\"3.1_Pairs_of_Lines_and_Angles\"><\/a>3.1 Pairs of Lines and Angles<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Points of intersection<\/p>\n<p>work with a partner: Write the number of points of intersection of each pair of coplanar lines.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37067\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-4.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 4\" width=\"559\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-4.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-4-300x65.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><br \/>\nAnswer:<br \/>\nThe given coplanar lines are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37067\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-4.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 4\" width=\"559\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-4.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-4-300x65.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><br \/>\na. The points of intersection of parallel lines:<br \/>\nWe know that,<br \/>\nThe &#8220;Parallel lines&#8221; have the same slope but have different y-intercepts<br \/>\nSo,<br \/>\nWe can say that any parallel line do not intersect at any point<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of points of intersection of parallel lines is: 0<\/p>\n<p>a. The points of intersection of intersecting lines:<br \/>\nWe know that,<br \/>\nThe &#8220;Intersecting lines&#8221; have a common point to intersect<br \/>\nSo,<br \/>\nWe can say that any intersecting line do intersect at 1 point<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of points of intersection of intersecting lines is: 1<\/p>\n<p>c. The points of intersection of coincident lines:<br \/>\nWe know that,<br \/>\nThe &#8220;Coincident lines&#8221; may be intersecting or parallel<br \/>\nSo,<br \/>\nWe can say that any coincident line do not intersect at any point or intersect at 1 point<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of points of intersection of coincident lines is: 0 or 1<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Classifying Pairs of Lines<\/p>\n<p>Work with a partner: The figure shows a right rectangular prism. All its angles are right angles. Classify each of the following pairs of lines as parallel, intersecting, coincident, or skew. Justify your answers. (Two lines are skew lines when they do not intersect and are not coplanar.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 5\" width=\"212\" height=\"154\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37065\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-6.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 6\" width=\"578\" height=\"196\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-6.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-6-300x102.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><br \/>\nAnswer:<br \/>\nThe given rectangular prism is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 5\" width=\"212\" height=\"154\" \/><br \/>\nWe know that,<br \/>\nThe &#8220;Parallel lines&#8221; are the lines that do not intersect with each other and present in the same plane<br \/>\nThe &#8220;Intersecting lines&#8221; are the lines that intersect with each other and in the same plane<br \/>\nThe &#8220;Coincident lines&#8221; are the lines that lie on one another and in the same plane<br \/>\nThe &#8220;Skew lines&#8221; are the lines that do not present in the same plane and do not intersect<br \/>\nHence,<br \/>\nThe completed table of the nature of the given pair of lines is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-79094\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3.jpg\" alt=\"\" width=\"593\" height=\"199\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3.jpg 593w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-300x101.jpg 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><\/p>\n<p><strong>Exploration 3<\/strong><\/p>\n<p>Identifying Pairs of Angles<\/p>\n<p>Work with a partner: In the figure, two parallel lines are intersected by a third line called a transversal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37064\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-7.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 7\" width=\"164\" height=\"158\" \/><br \/>\na. Identify all the pairs of vertical angles. Explain your reasoning.<br \/>\n<strong>CONSTRUCTING VIABLE ARGUMENTS<\/strong><br \/>\nTo be proficient in math, you need to understand and use stated assumptions, definitions, and previously established results.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe angles that are opposite to each other when two lines cross are called &#8220;Vertical angles&#8221;<br \/>\nHence, from the given figure,<br \/>\nWe can conclude that the vertical angles are:<br \/>\n\u22201 and \u22203; \u22202 and \u22204; \u22205 and \u22207; \u22206 and \u22208<\/p>\n<p>b. Identify all the linear pairs of angles. Explain your reasoning.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nA &#8220;Linear pair&#8221; is a pair of adjacent angles formed when two lines intersect<br \/>\nHence, from the given figure,<br \/>\nWe can conclude that the linear pair of angles is:<br \/>\n\u22201 and \u22202; \u22204 and \u22203; \u22205 and \u22206; \u22208 and \u22207<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 4.<br \/>\nWhat does it mean when two lines are parallel, intersecting, coincident, or skew?<br \/>\nAnswer:<br \/>\nThe two lines are &#8220;Parallel&#8221; when they do not intersect each other and are coplanar<br \/>\nThe two lines are &#8220;Intersecting&#8221; when they intersect each other and are coplanar<br \/>\nThe two lines are &#8220;Coincident&#8221; when they lie on each other and are coplanar<br \/>\nThe two lines are &#8220;Skew&#8221; when they do not intersect each other and are not coplanar<\/p>\n<p>Question 5.<br \/>\nIn Exploration 2. find more pairs of lines that are different from those given. Classify the pairs of lines as parallel, intersecting, coincident, or skew. Justify your answers.<br \/>\nAnswer:<br \/>\nThe given rectangular prism of Exploration 2 is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 5\" width=\"212\" height=\"154\" \/><br \/>\nThe pair of lines that are different from the given pair of lines in Exploration 2 are:<br \/>\na. \\(\\overline{C D}\\) and \\(\\overline{A E}\\)<br \/>\nb. \\(\\overline{D H}\\) and \\(\\overline{F G}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\na. \\(\\overline{C D}\\) and \\(\\overline{A E}\\) are &#8220;Skew lines&#8221; because they are not intersecting and are non coplanar<br \/>\nb. \\(\\overline{D H}\\) and \\(\\overline{F G}\\) are &#8220;Skew lines&#8221; because they are not intersecting and are non coplanar<\/p>\n<h3><a id=\"Lesson_3.1_Pairs_of_Lines_and_Angles\"><\/a>Lesson 3.1 Pairs of Lines and Angles<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nLook at the diagram in Example 1. Name the line(s) through point F that appear skew to <img loading=\"lazy\" class=\"alignnone size-full wp-image-37063\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-8.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 8\" width=\"35\" height=\"24\" \/>.<br \/>\nAnswer:<br \/>\nFrom Example 1,<br \/>\nWe can observe that<br \/>\nThe line that passes through point F that appear skew to \\(\\overline{E H}\\) is: \\(\\overline{F C}\\)<\/p>\n<p>Question 2.<br \/>\nIn Example 2, can you use the Perpendicular Postulate to show that <img loading=\"lazy\" class=\"alignnone size-full wp-image-37062\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-9.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 9\" width=\"39\" height=\"29\" \/> is not perpendicular to <img loading=\"lazy\" class=\"alignnone size-full wp-image-37061\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-10.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 10\" width=\"34\" height=\"26\" \/>? Explain why or why not.<br \/>\nAnswer:<br \/>\nPerpendicular Postulate:<br \/>\nAccording to this Postulate,<br \/>\nIf there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line<br \/>\nNow,<br \/>\nIn Example 2,<br \/>\nWe can observe that \\(\\overline{A C}\\) is not perpendicular to \\(\\overline{B F}\\) because according to the perpendicular Postulate, \\(\\overline{A C}\\) will be a straight line but it is not a straight line when we observe Example 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that we can use &#8220;Perpendicular Postulate&#8221; to show that \\(\\overline{A C}\\) is not perpendicular to \\(\\overline{B F}\\)<\/p>\n<p>Classify the pair of numbered angles.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-11.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 11\" width=\"134\" height=\"70\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-11.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 11\" width=\"134\" height=\"70\" \/><br \/>\nWe know that,<br \/>\nThe angles that have the same corner are called &#8220;Adjacent angles&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that \u22201 and \u22205 are the adjacent angles<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37059\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-12.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 12\" width=\"138\" height=\"81\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37059\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-12.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 12\" width=\"138\" height=\"81\" \/><br \/>\nWe know that,<br \/>\nThe angles that have the opposite corners are called &#8220;Vertical angles&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that \u22202 and \u22207 are the &#8220;Vertical angles&#8221;<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37058\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-13.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 13\" width=\"150\" height=\"69\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37058\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-13.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 13\" width=\"150\" height=\"69\" \/><br \/>\nWe know that,<br \/>\nThe angles that have the opposite corners are called &#8220;Vertical angles&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that \u22204 and \u22205 are the &#8220;Vertical angles&#8221;<\/p>\n<h3><a id=\"Exercise_3.1_Pairs_of_Lines_and_Angles\"><\/a>Exercise 3.1 Pairs of Lines and Angles<\/h3>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nTwo lines that do not intersect and are also not parallel are ________ lines.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48326\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-1.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 1\" width=\"507\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-1.png 507w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-1-300x34.png 300w\" sizes=\"(max-width: 507px) 100vw, 507px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WHICH ONE did DOESN\u2019T BELONG?<\/strong><br \/>\nWhich angle pair does not belong with the other three? Explain our reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37057\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-14.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 14\" width=\"263\" height=\"120\" \/><br \/>\n\u22202 and \u22203<br \/>\n\u22204 and \u22205<br \/>\n\u22201 and \u22208<br \/>\n\u22202 and\u22207<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37057\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-14.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 14\" width=\"263\" height=\"120\" \/><br \/>\nWe know that,<br \/>\nThe angles that have the common side are called &#8220;Adjacent angles&#8221;<br \/>\nThe angles that are opposite to each other when 2 lines cross are called &#8220;Vertical angles&#8221;<br \/>\nSo,<br \/>\n\u22202 and \u22203 are vertical angles<br \/>\n\u22204 and \u22205 are adjacent angles<br \/>\n\u22201 and \u22208 are vertical angles<br \/>\n\u22202 and \u22207 are vertical angles<br \/>\nHence, from the above,<br \/>\nWe can conclude that \u22204 and \u22205 angle-pair do not belong with the other three<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3 &#8211; 6, think of each segment in the diagram as part of a line. All the angles are right angles. Which line(s) or plane(s) contain point B and appear to fit the description?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37056\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-15.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 15\" width=\"230\" height=\"177\" \/><br \/>\nQuestion 3.<br \/>\nline(s) parallel to <img loading=\"lazy\" class=\"alignnone size-full wp-image-37055\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-16.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 16\" width=\"37\" height=\"27\" \/>.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48327\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-3.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 3\" width=\"466\" height=\"39\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-3.png 466w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-3-300x25.png 300w\" sizes=\"(max-width: 466px) 100vw, 466px\" \/><\/p>\n<p>Question 4.<br \/>\nline(s) PerPendicular to <img loading=\"lazy\" class=\"alignnone size-full wp-image-37054\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-17.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 17\" width=\"37\" height=\"26\" \/>.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe lines that are a straight angle with the given line and are coplanar is called &#8220;Perpendicular lines&#8221;<br \/>\nSo,<br \/>\nFrom the given figure,<br \/>\nWe can conclude that the line that is perpendicular to \\(\\overline{C D}\\) is: \\(\\overline{A D}\\) and \\(\\overline{C B}\\)<\/p>\n<p>Question 5.<br \/>\nline(s) skew to <img loading=\"lazy\" class=\"alignnone size-full wp-image-37053\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-18.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 18\" width=\"39\" height=\"26\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48328\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-5.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 5\" width=\"503\" height=\"39\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-5.png 503w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-5-300x23.png 300w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><\/p>\n<p>Question 6.<br \/>\nplane(s) parallel to plane CDH<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can observe that the plane parallel to plane CDH is: Plane BAE<\/p>\n<p>In Exercises 7-10, Use the diagram.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-37052\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-19.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 19\" width=\"274\" height=\"129\" \/><\/p>\n<p>Question 7.<br \/>\nName a pair of parallel lines.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48329\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-7.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 7\" width=\"283\" height=\"36\" \/><\/p>\n<p>Question 8.<br \/>\nName a pair of perpendicular lines.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe lines that have an angle of 90\u00b0 with each other are called &#8220;Perpendicular lines&#8221;<br \/>\nHence,<br \/>\nFrom the figure,<br \/>\nWe can conclude that \\(\\overline{N P}\\) and \\(\\overline{P O}\\) are perpendicular lines<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37051\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-20.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 20\" width=\"149\" height=\"30\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48330\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-9.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 9\" width=\"227\" height=\"37\" \/><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37050\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-21.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 21\" width=\"150\" height=\"27\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe lines that have an angle of 90\u00b0 with each other are called &#8220;Perpendicular lines&#8221;<br \/>\nHence,<br \/>\nFrom the figure,<br \/>\nWe can conclude that \\(\\overline{P R}\\) and \\(\\overline{P O}\\) are not perpendicular lines<\/p>\n<p>In Exercises 11-14, identify all pairs of angles of the given type.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-37049\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-22.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 22\" width=\"169\" height=\"113\" \/><br \/>\nQuestion 11.<br \/>\ncorresponding<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48331\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-11.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 11\" width=\"545\" height=\"36\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-11.png 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-11-300x20.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Question 12.<br \/>\nalternate interior<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\n&#8220;Alternate Interior angles&#8221; are a pair of angles\u00a0on the inner side of each of those two lines but on opposite sides of the transversal.<br \/>\nHence,<br \/>\nFrom the given figure,<br \/>\nWe can conclude that the alternate interior angles are: \u22204 and \u22205; \u22203 and \u22206<\/p>\n<p>Question 13.<br \/>\nalternate exterior<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48332\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-13.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 13\" width=\"422\" height=\"27\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-13.png 422w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-13-300x19.png 300w\" sizes=\"(max-width: 422px) 100vw, 422px\" \/><\/p>\n<p>Question 14.<br \/>\nconsecutive interior<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe pair of angles on one side of the transversal and inside the two lines are called the &#8220;Consecutive interior angles&#8221;.<br \/>\nHence,<br \/>\nFrom the given figure,<br \/>\nWe can conclude that the consecutive interior angles are: \u22203 and \u22205; \u22204 and \u22206<\/p>\n<p><strong>USING STRUCTURE<\/strong><br \/>\nIn Exercises 15-18, classify the angle pair as corresponding. alternate interior, alternate exterior, or consecutive interior angles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37048\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-23.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 23\" width=\"175\" height=\"114\" \/><\/p>\n<p>Question 15.<br \/>\n\u22205 and \u22201<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48333\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-15.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 15\" width=\"370\" height=\"35\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-15.png 370w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-15-300x28.png 300w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><\/p>\n<p>Question 16.<br \/>\n\u222011 and \u222013<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe pair of angles on one side of the transversal and inside the two lines are called the &#8220;Consecutive interior angles&#8221;.<br \/>\nHence,<br \/>\nFrom the given figure,<br \/>\nWe can conclude that \u222011 and \u222013 are the &#8220;Consecutive interior angles&#8221;<\/p>\n<p>Question 17.<br \/>\n\u22206 and \u222013<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48334\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-17.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 17\" width=\"426\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-17.png 426w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-17-300x23.png 300w\" sizes=\"(max-width: 426px) 100vw, 426px\" \/><\/p>\n<p>Question 18.<br \/>\n\u22202 and \u222011<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\n&#8220;Vertical Angles&#8221; are the angles\u00a0opposite each other when two lines cross<br \/>\nHence, from the above figure,<br \/>\nWe can conclude that \u22202 and \u222011 are the &#8220;Vertical angles&#8221;<\/p>\n<p><strong>ERROR ANALYSIS<\/strong><br \/>\nIn Exercises 19 and 20. describe and correct the error in the conditional statement about lines.<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37047\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-24.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 24\" width=\"307\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-24.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-24-300x61.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48335\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-19.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 19\" width=\"597\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-19.png 597w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-19-300x43.png 300w\" sizes=\"(max-width: 597px) 100vw, 597px\" \/><\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37046\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-25.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 25\" width=\"324\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-25.png 324w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-25-300x79.png 300w\" sizes=\"(max-width: 324px) 100vw, 324px\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe &#8220;Perpendicular Postulate&#8221; states that if there is a line and a point not on the line, then there is exactly one line through the point perpendicular\u00a0to the given line.<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given statement is not correct<\/p>\n<p>Question 21.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nUse the photo to decide whether the statement is true or false. Explain Your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37045\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-26.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 26\" width=\"294\" height=\"224\" \/><br \/>\na. The plane containing the floor of the treehouse is parallel to the ground.<br \/>\nb. The lines containing the railings of the staircase, such as <img loading=\"lazy\" class=\"alignnone size-full wp-image-37044\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-27.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 27\" width=\"30\" height=\"25\" \/>, are skew to all lines in the plane containing the ground.<br \/>\nc. All the lines containing the balusters. such as <img loading=\"lazy\" class=\"alignnone size-full wp-image-37043\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-28.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 28\" width=\"32\" height=\"24\" \/>, are perpendicular to the plane containing the floor of the treehouse.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48336\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-21.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 21\" width=\"579\" height=\"181\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-21.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-21-300x94.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 22.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nIf two lines are intersected by a third line, is the third line necessarily a transversal? Justify your answer with a diagram.<br \/>\nAnswer:<br \/>\nNo, the third line does not necessarily be a transversal<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\n&#8220;Parallel lines&#8221; do not intersect each other<br \/>\n&#8220;Perpendicular lines&#8221; intersect at each other at right angles<br \/>\nThe third intersecting line can intersect at the same point that the two lines have intersected as shown below:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-79462\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-4.png\" alt=\"\" width=\"577\" height=\"481\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-4.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-4-300x250.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that the third line does not need to be a transversal<\/p>\n<p>Question 23.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nTwo lines are cut by a transversal. Is it possible for all eight angles formed to have the same measure? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48337\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-23.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 23\" width=\"570\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-23.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-23-300x46.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 24.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThink of each segment in the figure as part of a line.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37042\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-29.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 29\" width=\"128\" height=\"120\" \/><br \/>\na. Which lines are parallel to <img loading=\"lazy\" class=\"alignnone size-full wp-image-37041\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-30.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 30\" width=\"33\" height=\"24\" \/>?<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe lines that do not intersect to each other and are coplanar are called &#8220;Parallel lines&#8221;<br \/>\nHence, from the above figure,<br \/>\nWe can conclude that the line parallel to \\(\\overline{N Q}\\) is: \\(\\overline{M P}\\)<\/p>\n<p>b. Which lines intersect <img loading=\"lazy\" class=\"alignnone size-full wp-image-37041\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-30.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 30\" width=\"33\" height=\"24\" \/>?<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe lines that are coplanar and any two lines that have a common point are called &#8220;Intersecting lines&#8221;<br \/>\nHence, from the above figure,<br \/>\nWe can conclude that the lines that intersect \\(\\overline{N Q}\\) are: \\(\\overline{N K}\\), \\(\\overline{N M}\\), and \\(\\overline{Q P}\\)<\/p>\n<p>c. Which lines are skew to <img loading=\"lazy\" class=\"alignnone size-full wp-image-37041\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-30.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 30\" width=\"33\" height=\"24\" \/>?<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe lines that do not intersect or not parallel and non-coplanar are called &#8220;Skew lines&#8221;<br \/>\nHence, from the above figure,<br \/>\nWe can conclude that \\(\\overline{K L}\\), \\(\\overline{L M}\\), and \\(\\overline{L S}\\)<\/p>\n<p>d. Should you have named all the lines on the cube in parts (a)-(c) except \\(\\overline{N Q}\\)? Explain.<br \/>\nAnswer:<br \/>\nNo, we did not name all the lines on the cube in parts (a) &#8211; (c) except \\(\\overline{N Q}\\)<\/p>\n<p>In exercises 25-28. copy and complete the statement. List all possible correct answers.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-37040\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-31.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 31\" width=\"206\" height=\"128\" \/><\/p>\n<p>Question 25.<br \/>\n\u2220BCG and __________ are corresponding angles.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48338\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-25.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 25\" width=\"518\" height=\"32\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-25.png 518w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-25-300x19.png 300w\" sizes=\"(max-width: 518px) 100vw, 518px\" \/><\/p>\n<p>Question 26.<br \/>\n\u2220BCG and __________ are consecutive interior angles.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nWhen two lines are cut by a transversal, the pair of\u00a0angles on one side of the transversal and inside the two lines are called the &#8220;Consecutive interior angles&#8221;<br \/>\nHence,<br \/>\nFrom the given figure,<br \/>\nWe can conclude that the consecutive interior angles of \u2220BCG are: \u2220FCA and \u2220BCA<\/p>\n<p>Question 27.<br \/>\n\u2220FCJ and __________ are alternate interior angles.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48339\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-27.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 27\" width=\"540\" height=\"32\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-27.png 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-27-300x18.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Question 28.<br \/>\n\u2220FCA and __________ are alternate exterior angles.<br \/>\nAnswer:<br \/>\n&#8220;Alternate exterior angles&#8221; are the pair of angles\u00a0that lie on the outer side of the two parallel lines but on either side of the transversal line<br \/>\nHence,<br \/>\nFrom the above figure,<br \/>\nWe can conclude that \u2220FCA and \u2220JCB are alternate exterior angles<\/p>\n<p>Question 29.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims the uneven parallel bars in gymnastics are not really Parallel. She says one is higher than the other. so they cannot be on the same plane. Is she correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37039\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-32.png\" alt=\"\" width=\"275\" height=\"178\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48340\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-29.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 29\" width=\"578\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-29.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-29-300x30.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Maintaining Mathematical Proficiency<\/p>\n<p>Use the diagram to find the measure of all the angles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37038\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-33.png\" alt=\"\" width=\"152\" height=\"104\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-33.png 152w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-33-150x104.png 150w\" sizes=\"(max-width: 152px) 100vw, 152px\" \/><\/p>\n<p>Question 30.<br \/>\nm\u22201 = 76\u00b0<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe sum of the adjacent angles is: 180\u00b0<br \/>\nThe vertical angles are congruent i.e., the angle measures of the vertical angles are equal<br \/>\nNow,<br \/>\nFrom the figure,<br \/>\nThe adjacent angles are: \u22201 and \u22202; \u22202 and \u22203; \u22203 and \u22204; and \u22204 and \u22201<br \/>\nThe vertical angles are: \u22201 and \u22203; \u22202 and \u22204<br \/>\nNow,<br \/>\n\u22201 + \u22202 = 180\u00b0<br \/>\n\u22202 = 180\u00b0 &#8211; \u22201<br \/>\n= 180\u00b0 &#8211; 76\u00b0<br \/>\n= 104\u00b0<br \/>\nSo,<br \/>\n\u22203 = 76\u00b0 and \u22204 = 104\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that,<br \/>\n\u22201 = 76\u00b0, \u22202 = 104\u00b0, \u22203 = 76\u00b0, and \u22204 = 104\u00b0<\/p>\n<p>Question 31.<br \/>\nm\u22202 = 159\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48341\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-31.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 31\" width=\"573\" height=\"171\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-31.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.1-a-31-300x90.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<h3><a id=\"3.2_Parallel_Lines_and_Transversals\"><\/a>3.2 Parallel Lines and Transversals<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Exploring parallel Lines<\/p>\n<p>Work with a partner: Use dynamic geometry software to draw two parallel lines. Draw a third line that intersects both parallel lines. Find the measures of the eight angles that are formed. What can you conclude?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37366\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-34.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 34\" width=\"304\" height=\"241\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-34.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-34-300x238.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><br \/>\nAnswer:<br \/>\nBy using the dynamic geometry,<br \/>\nThe representation of the given coordinate plane along with parallel lines is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-79743\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-5.png\" alt=\"\" width=\"851\" height=\"571\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-5.png 851w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-5-300x201.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-5-768x515.png 768w\" sizes=\"(max-width: 851px) 100vw, 851px\" \/><br \/>\nHence, from the coordinate plane,<br \/>\nWe can observe that,<br \/>\n\u22203 = 53.7\u00b0 and \u22204 = 53.7\u00b0<br \/>\nWe know that,<br \/>\nThe angle measures of the vertical angles are congruent<br \/>\nSo,<br \/>\n\u22201 = 53.7\u00b0 and \u22205 = 53.7\u00b0<br \/>\nWe know that,<br \/>\nIn the parallel lines,<br \/>\nAll the angle measures are equal<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u22201 = \u22202 = \u22203 = \u22204 = \u22205 = \u22206 = \u22207 = 53.7\u00b0<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Writing conjectures<\/p>\n<p>Work with a partner. Use the results of Exploration 1 to write conjectures about the following pairs of angles formed by two parallel lines and a transversal.<br \/>\n<strong>ATTENDING TO PRECISION<\/strong><br \/>\nTo be proficient in math, you need to communicate precisely with others.<br \/>\na. corresponding angles<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37365\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-35.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 35\" width=\"172\" height=\"183\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nWhen two lines are crossed by another line (which is called the Transversal), the\u00a0angles in matching corners are called &#8220;Corresponding angles&#8221;<br \/>\nHence, from the given figure,<br \/>\nWe can conclude that<br \/>\nThe corresponding angles are: \u2220 and \u22205; \u22204 and \u22208<\/p>\n<p>b. alternate interior angles<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37364\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-36.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 36\" width=\"172\" height=\"182\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\n&#8220;Alternate Interior Angles&#8221; are a pair of angles\u00a0on the inner side of each of those two lines but on opposite sides of the transversal.<br \/>\nHence, from the above figure,<br \/>\nWe can conclude that<br \/>\nThe alternate interior angles are: \u22203 and \u22205; \u22202 and \u22208<\/p>\n<p>c. alternate exterior angles<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37363\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-37.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 37\" width=\"171\" height=\"180\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\n&#8220;Alternate exterior angles&#8221; are the pair of angles\u00a0that lie on the outer side of the two parallel lines but on either side of the transversal line.<br \/>\nHence, from the above figure,<br \/>\nWe can conclude that<br \/>\nThe alternate exterior angles are: \u22201 and \u22207; \u22206 and \u22204<\/p>\n<p>d. consecutive interior angles<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37362\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-38.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 38\" width=\"171\" height=\"183\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nWhen two lines are cut by a transversal, the pair of angles on one side of the transversal and inside the two lines are called the &#8220;Consecutive interior angles&#8221;<br \/>\nHence, from the above figure,<br \/>\nWe can conclude that<br \/>\nThe consecutive interior angles are: \u22202 and \u22205; \u22203 and \u22208<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 3.<br \/>\nWhen two parallel lines are cut by a transversal, which of the resulting pairs of angles are congruent?<br \/>\nAnswer:<br \/>\nIf two parallel lines are cut by a transversal, then the pairs of &#8220;Corresponding angles&#8221; are congruent.<br \/>\nIf two parallel lines are cut by a transversal, then the pairs of &#8220;Alternate interior angles&#8221; are congruent.<br \/>\nIf two parallel lines are cut by a transversal, then the pairs of &#8220;Alternate exterior angles&#8221; are congruent.<\/p>\n<p>Question 4.<br \/>\nIn Exploration 2. m\u22201 = 80\u00b0. Find the other angle measures.<br \/>\nAnswer:<br \/>\nIt is given that<br \/>\nIn Exploration 2,<br \/>\n\u22201 = 80\u00b0<br \/>\nWe know that,<br \/>\nExploration 2 comes from Exploration 1<br \/>\nFrom Exploration 1,<br \/>\nWe can say that all the angle measures are equal in Exploration 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u22201 = \u22202 = \u22203 = \u22204 = \u22205 = \u22206 = \u22207 = \u22208 = 80\u00b0<\/p>\n<h3><a id=\"Lesson_3.2_Parallel_Lines_and_Transversals\"><\/a>Lesson 3.2 Parallel Lines and Transversals<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Use the diagram<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37361\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-39.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 39\" width=\"164\" height=\"94\" \/><\/p>\n<p>Question 1.<br \/>\nGiven m\u22201 = 105\u00b0, find m\u22204, m\u22205, and m\u22208. Tell which theorem you use in each case.<br \/>\nAnswer:<br \/>\nIt is given that \u22201 = 105\u00b0<br \/>\nNow,<br \/>\nWe have to find \u22204, \u22205, and \u22208<br \/>\nNow,<br \/>\nTo find \u22204:<br \/>\nVerticle angle theorem:<br \/>\nVertical Angles Theorem\u00a0states that\u00a0vertical angles,\u00a0angles\u00a0that are opposite each other and formed by two intersecting straight lines, are congruent<br \/>\nSo,<br \/>\n\u22201 = \u22204<br \/>\nHence,<br \/>\n\u22204 = 105\u00b0<\/p>\n<p>To find \u22205:<br \/>\nAlternate Interior angles theorem:<br \/>\nThe Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal, the resulting\u00a0alternate interior angles\u00a0are congruent<br \/>\nSo,<br \/>\n\u22204 = \u22205<br \/>\nHence,<br \/>\n\u22205 = 105\u00b0<\/p>\n<p>To find \u22208:<br \/>\nVerticle angle theorem:<br \/>\nVertical Angles Theorem\u00a0states that\u00a0vertical angles,\u00a0angles\u00a0that are opposite each other and formed by two intersecting straight lines, are congruent<br \/>\nSo,<br \/>\n\u22205 = \u22208<br \/>\nHence,<br \/>\n\u22208 = 105\u00b0<\/p>\n<p>Question 2.<br \/>\nGiven m\u22203 = 68\u00b0 and m\u22208 = (2x + 4)\u00b0, what is the value of x? Show your steps.<br \/>\nAnswer:<br \/>\nIt is given that<br \/>\n\u22203 = 68\u00b0 and \u22208 = (2x + 4)\u00b0<br \/>\nFrom the given figure,<br \/>\nWe can observe that \u22203 and \u22208 are consecutive exterior angles.<br \/>\nSo,<br \/>\nAccording to the consecutive exterior angles theorem,<br \/>\nIf parallel lines are cut by a transversal line, then\u00a0consecutive exterior angles\u00a0are supplementary.<br \/>\nSo,<br \/>\n\u22203 + \u22208 = 180\u00b0<br \/>\n68\u00b0 + (2x + 4)\u00b0 = 180\u00b0<br \/>\n2x + 72\u00b0 = 180\u00b0<br \/>\n2x\u00b0 = 180\u00b0 &#8211; 72\u00b0<br \/>\n2x\u00b0 = 108\u00b0<br \/>\nx = \\(\\frac{108}{2}\\)<br \/>\nx = 54\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 54\u00b0<\/p>\n<p>Question 3.<br \/>\nIn the proof in Example 4, if you use the third statement before the second statement. could you still prove the theorem? Explain.<br \/>\nAnswer:<br \/>\nIn Example 4, the given theorem is &#8220;Alternate interior angle theorem&#8221;<br \/>\nIf you even interchange the second and third statements, you could still prove the theorem as the second line before interchange is not necessary<br \/>\nHence, from the above,<br \/>\nWe can conclude that if you use the third statement before the second statement, you could still prove the theorem<\/p>\n<p>Question 4.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nIn Example 5. yellow light leaves a drop at an angle of m\u22202 = 41\u00b0. What is m\u22201? How do you know?<br \/>\nAnswer:<br \/>\nIn Example 5,<br \/>\nIf we observe \u22201 and \u22202, then they are alternate interior angles<br \/>\nNow,<br \/>\nAccording to Alternate interior angle theorem,<br \/>\n\u22201 = \u22202<br \/>\nIt is given that,<br \/>\n\u22202 = 41\u00b0<br \/>\nSo,<br \/>\n\u22201 = 41\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u22201 = 41\u00b0<\/p>\n<h3><a id=\"Exercise_3.2_Parallel_Lines_and_Transversals\"><\/a>Exercise 3.2 Parallel Lines and Transversals<\/h3>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nHow are the Alternate Interior Angles Theorem (Theorem 3.2) and the Alternate Exterior<br \/>\nAngles Theorem (Theorem 3.3) alike? How are they different?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48342\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-1.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 1\" width=\"575\" height=\"198\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-1.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-1-300x103.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WHICH ONE did DOESN\u2019T BELONG?<\/strong><br \/>\nWhich pair of angle measures does not belong with the other three? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37360\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-40.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 40\" width=\"304\" height=\"143\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-40.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-40-300x141.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><br \/>\nm\u22201 and m\u22203<br \/>\nm\u22202 and m\u22204<br \/>\nm\u22202 and m\u22203<br \/>\nm\u22201 and m\u22205<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37360\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-40.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 40\" width=\"304\" height=\"143\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-40.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-40-300x141.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><br \/>\nFrom the given figure,<br \/>\n\u22201 and \u22203 are the vertical angles<br \/>\n\u22202 and \u22204 are the alternate interior angles<br \/>\n\u22202 and \u22203 are the consecutive interior angles<br \/>\n\u22201 and \u22205 are the alternate exterior angles<br \/>\nSo,<br \/>\nFrom the above,<br \/>\nWe can observe that all the angles except \u22201 and \u22203 are the interior and exterior angles<br \/>\nHence, from the above,<br \/>\nWe can conclude that \u22201 and \u22203 pair does not belong with the other three<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3-6, find m\u22201 and m\u22202. Tell which theorem you use in each case.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37359\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-41.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 41\" width=\"130\" height=\"101\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48343\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-3.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 3\" width=\"625\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-3.png 625w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-3-300x30.png 300w\" sizes=\"(max-width: 625px) 100vw, 625px\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37358\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-42.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 42\" width=\"174\" height=\"110\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37358\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-42.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 42\" width=\"174\" height=\"110\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that,<br \/>\n\u22201 = \u22202 (By using the Vertical Angles theorem)<br \/>\n\u22202 = 150\u00b0 (By using the Alternate exterior angles theorem)<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u22201 = \u22202 = 150\u00b0<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37357\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-43.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 43\" width=\"133\" height=\"102\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48344\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-5.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 5\" width=\"630\" height=\"117\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-5.png 630w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-5-300x56.png 300w\" sizes=\"(max-width: 630px) 100vw, 630px\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37356\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-44.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 44\" width=\"178\" height=\"100\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37356\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-44.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 44\" width=\"178\" height=\"100\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that,<br \/>\n\u22201 + \u22202 = 180\u00b0 (By using the consecutive interior angles theorem)<br \/>\n\u22202 = 140\u00b0 (By using the Vertical angles theorem)<br \/>\nSo,<br \/>\n\u22201 = 180\u00b0 &#8211; 140\u00b0<br \/>\n\u22201 = 40\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u22201 = 40\u00b0 and \u22202 = 140\u00b0<\/p>\n<p>In Exercises 7-10. find the value of x. Show your steps.<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37355\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-45.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 45\" width=\"154\" height=\"98\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48345\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-7.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 7\" width=\"381\" height=\"151\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-7.png 381w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-7-300x119.png 300w\" sizes=\"(max-width: 381px) 100vw, 381px\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37354\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-46.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 46\" width=\"144\" height=\"87\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37354\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-46.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 46\" width=\"144\" height=\"87\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\n72\u00b0 + (7x + 24)\u00b0 = 180\u00b0 (By using the Consecutive interior angles theory)<br \/>\n(7x + 24)\u00b0 = 180\u00b0 &#8211; 72\u00b0<br \/>\n(7x + 24)\u00b0 = 108\u00b0<br \/>\n7x\u00b0 = 108\u00b0 &#8211; 24\u00b0<br \/>\n7x\u00b0 = 84\u00b0<br \/>\nx\u00b0 = \\(\\frac{84}{7}\\)<br \/>\nx\u00b0 = 12\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 12\u00b0<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37353\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-47.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 47\" width=\"160\" height=\"122\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48346\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-9.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 9\" width=\"577\" height=\"314\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-9.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-9-300x163.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37352\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-48.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 48\" width=\"149\" height=\"127\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37352\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-48.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 48\" width=\"149\" height=\"127\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\n(8x + 6)\u00b0 = 118\u00b0 (By using the Vertical Angles theorem)<br \/>\n8x\u00b0 = 118\u00b0 &#8211; 6\u00b0<br \/>\n8x\u00b0 = 112\u00b0<br \/>\nx\u00b0 = \\(\\frac{112}{8}\\)<br \/>\nx\u00b0 = 14\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 14\u00b0<\/p>\n<p>In Exercises 11 and 12. find m\u22201, m\u22202, and m\u22203. Explain our reasoning.<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37351\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-49.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 49\" width=\"169\" height=\"108\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48347\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-11.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 11\" width=\"571\" height=\"167\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-11.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-11-300x88.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37350\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-50.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 50\" width=\"142\" height=\"109\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37350\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-50.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 50\" width=\"142\" height=\"109\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\n\u22203 + 133\u00b0 = 180\u00b0 (By using the Consecutive Interior angles theorem)<br \/>\n\u22203 = 180\u00b0 &#8211; 133\u00b0<br \/>\n\u22203 = 47\u00b0<br \/>\nNow,<br \/>\nWe can observe that<br \/>\n\u22202 + \u22203 = 180\u00b0<br \/>\n\u22202 = 180\u00b0 &#8211; \u22203<br \/>\n\u22202 = 180\u00b0 &#8211; 47\u00b0<br \/>\n\u22202 = 133\u00b0<br \/>\nNow,<br \/>\nWe can observe that<br \/>\n\u22201 = \u22202<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u22201 = \u22202 = 133\u00b0 and \u22203 = 47\u00b0<\/p>\n<p>Question 13.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in the students reasoning<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37349\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-51.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 51\" width=\"329\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-51.png 329w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-51-300x101.png 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48348\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-13.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 13\" width=\"590\" height=\"115\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-13.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-13-300x58.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p>Question 14.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nUse the diagram<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37348\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-52.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 52\" width=\"134\" height=\"79\" \/><br \/>\na. Name two pairs of congruent angles when \\(\\overline{A D}\\) and \\(\\overline{B C}\\) are parallel? Explain your reasoning?<br \/>\nAnswer:<br \/>\nLet the congruent angle be \u2220P<br \/>\nSo,<br \/>\nFrom the figure,<br \/>\nWe can observe that the pair of angle when \\(\\overline{A D}\\) and \\(\\overline{B C}\\) are parallel is: \u2220APB and \u2220DPB<\/p>\n<p>b. Name two pairs of supplementary angles when \\(\\overline{A B}\\) and \\(\\overline{D C}\\) are parallel. Explain your reasoning.<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nThe two pairs of supplementary angles when \\(\\overline{A B}\\) and \\(\\overline{D C}\\) are parallel is: \u2220ACD and \u2220BDC<\/p>\n<p><strong>PROVING A THEOREM<\/strong><br \/>\nIn Exercises 15 and 16, prove the theorem.<\/p>\n<p>Question 15.<br \/>\nAlternate Exterior Angles Theorem (Thm. 3.3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48349\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-15.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 15\" width=\"531\" height=\"585\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-15.png 531w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-15-272x300.png 272w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><\/p>\n<p>Question 16.<br \/>\nConsecutive Interior Angles Theorem (Thm. 3.4)<br \/>\nAnswer:<br \/>\nStatement of consecutive Interior angles theorem:<br \/>\nIf two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary<br \/>\nProof:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-80194\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-6.png\" alt=\"\" width=\"580\" height=\"636\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-6.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-6-274x300.png 274w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 17.<br \/>\n<strong>PROBLEM-SOLVING<\/strong><br \/>\nA group of campers ties up their food between two parallel trees, as shown. The rope is pulled taut. forming a straight line. Find m\u22202. Explain our reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37347\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-53.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 53\" width=\"215\" height=\"232\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48350\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-17.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 17\" width=\"575\" height=\"220\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-17.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-17-300x115.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 18.<br \/>\n<strong>DRAWING CONCLUSIONS<\/strong><br \/>\nYou are designing a box like the one shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37346\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-54.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 54\" width=\"398\" height=\"144\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-54.png 398w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-54-300x109.png 300w\" sizes=\"(max-width: 398px) 100vw, 398px\" \/><br \/>\na. The measure of \u22201 is 70\u00b0. Find m\u22202 and m\u22203.<br \/>\nb. Explain why \u2220ABC is a straight angle.<br \/>\nc. If m\u22201 is 60\u00b0, will \u2220ABC still he a straight angle? Will the opening of the box be more steep or less steep? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nIs it possible for consecutive interior angles to be congruent? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48351\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-19.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 19\" width=\"587\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-19.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-19-300x31.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 20.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nThe postulates and theorems in this book represent Euclidean geometry. In spherical geometry, all points are points on the surface of a sphere. A line is a circle on the sphere whose diameter is equal to the diameter of the sphere. In spherical geometry, is it possible that a transversal intersects two parallel lines? Explain your reasoning.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nAccording to Euclidean geometry,<br \/>\nFor a parallel line, there will be no intersecting point<br \/>\nBut, In spherical geometry, even though there is some resemblance between circles and lines, there is no possibility to form parallel lines as the lines will intersect at least at 1 point on the circle which is called a tangent<br \/>\nHence, from the above,<br \/>\nWe can conclude that it is not possible that a transversal intersects two parallel lines<\/p>\n<p><strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nIn Exercises 21 and 22, write and solve a system of linear equations to find the values of x and y.<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37345\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-55.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 55\" width=\"158\" height=\"94\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48352\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-21.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 21\" width=\"479\" height=\"197\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-21.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-21-300x123.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37344\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-56.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 56\" width=\"152\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-56.png 152w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-56-150x87.png 150w\" sizes=\"(max-width: 152px) 100vw, 152px\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37344\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-56.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 56\" width=\"152\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-56.png 152w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-56-150x87.png 150w\" sizes=\"(max-width: 152px) 100vw, 152px\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that the given pairs of angles are consecutive interior angles<br \/>\nSo,<br \/>\n2y\u00b0 + 4x\u00b0 = 180\u00b0<br \/>\n(2x + 12)\u00b0 + (y + 6)\u00b0 = 180\u00b0<br \/>\n2x\u00b0 + y\u00b0 + 18\u00b0 = 180\u00b0<br \/>\n2x\u00b0 + y\u00b0 = 180\u00b0 &#8211; 18\u00b0<br \/>\n2x\u00b0 + y\u00b0 = 162\u00b0&#8212;&#8212;&#8212;(1)<br \/>\n4x\u00b0 + 2y\u00b0 = 180\u00b0&#8212;&#8212;&#8211;(2)<br \/>\nSolve eq. (1) and eq. (2) to get the values of x and y<br \/>\n2x\u00b0 = 18\u00b0<br \/>\nx\u00b0 = \\(\\frac{18}{2}\\)<br \/>\nx\u00b0 = 9\u00b0<br \/>\nNow,<br \/>\ny\u00b0 = 162\u00b0 &#8211; 2 (9\u00b0)<br \/>\ny\u00b0 = 162\u00b0 &#8211; 18\u00b0<br \/>\ny\u00b0 = 144\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the values of x and y are: 9\u00b0 and 14\u00b0 respectively<\/p>\n<p>Question 23.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nDuring a game of pool. your friend claims to be able to make the shot Shown in the diagram by hitting the cue ball so that m\u22201 = 25\u00b0. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37343\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-57.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 57\" width=\"338\" height=\"187\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-57.png 338w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-57-300x166.png 300w\" sizes=\"(max-width: 338px) 100vw, 338px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48353\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-23.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 23\" width=\"588\" height=\"151\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-23.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-23-300x77.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 24.<br \/>\n<strong>REASONING<\/strong><br \/>\nIn diagram. \u22204 \u2245\u22205 and \\(\\overline{S E}\\) bisects \u2220RSF. Find m\u22201. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37342\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-58.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 58\" width=\"259\" height=\"115\" \/><br \/>\nAnswer:<br \/>\nIt is given that \u22204 \u2245\u22205 and \\(\\overline{S E}\\) bisects \u2220RSF<br \/>\nSo,<br \/>\n\u2220FSE = \u2220ESR<br \/>\nFrom \u0394ESR,<br \/>\nWe know that,<br \/>\nThe sum of the angle measures of a triangle is: 180\u00b0<br \/>\nSo,<br \/>\n\u22203 + \u22204 + \u22205 = 180\u00b0<br \/>\nSo,<br \/>\n\u22203 = 60\u00b0 (Since \u22204 \u2245 \u22205 and the triangle is not a right triangle)<br \/>\nFrom the given figure,<br \/>\nWe can observe that,<br \/>\n\u22201 = \u22203 (By using the Corresponding angles theorem)<br \/>\nSo,<br \/>\n\u22201 = 60\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that \u22201 = 60\u00b0<\/p>\n<p>Maintaining Mathematical Proficiency<\/p>\n<p>Write the converse of the conditional statement. Decide whether it is true or false.<\/p>\n<p>Question 25.<br \/>\nIf two angles are vertical angles. then they are congruent.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48354\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-25.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 25\" width=\"543\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-25.png 543w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-25-300x31.png 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/p>\n<p>Question 26.<br \/>\nIf you go to the zoo, then you will see a tiger.<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nIf you go to the zoo, then you will see a tiger<br \/>\nThe converse of the given statement is:<br \/>\nIf you will see a tiger, then you go to the zoo&#8212;&#8212;&#8212;-&gt; False<\/p>\n<p>Question 27.<br \/>\nIf two angles form a linear pair. then they are supplementary.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48355\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-27.png\" alt=\"Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 27\" width=\"587\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-27.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-3.2-a-27-300x29.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 28.<br \/>\nIf it is warm outside, then we will go to the park.<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nIf it is warm outside, then we will go to the park<br \/>\nThe converse of the given statement is:<br \/>\nIf you will go to the park, then it is warm outside &#8212;&#8212;&#8212;&#8212;&#8212;-&gt; False<\/p>\n<h3><a id=\"3.3_Proofs_with_Parallel_Lines\"><\/a>3.3 Proofs with Parallel Lines<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Exploring Converses<\/p>\n<p>Work with a partner: Write the converse of each conditional statement. Draw a diagram to represent the converse. Determine whether the converse is true. Justify your conclusion.<br \/>\n<strong>CONSTRUCTING VIABLE ARGUMENTS<\/strong><br \/>\nTo be proficient in math, you need to make conjectures and build a logical progression of statements to explore the truth of your conjectures.<\/p>\n<p>a. Corresponding Angles Theorem (Theorem 3.1): If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37539\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-59.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 59\" width=\"172\" height=\"165\" \/><br \/>\nConverse:<br \/>\nIf the pairs of corresponding angles are<\/p>\n<p>congruent, then the two parallel lines are<\/p>\n<p>cut by a transversal.<\/p>\n<p>Answer:<br \/>\nThe Converse of the Corresponding Angles Theorem:<br \/>\nThe Converse of the Corresponding Angles Theorem says that if two\u00a0lines\u00a0and a transversal form\u00a0congruent\u00a0corresponding angles, then the\u00a0lines\u00a0are parallel.<br \/>\nSo,<br \/>\nWhen we compare the converses we obtained from the given statement and the actual converse,<br \/>\nWe can conclude that both converses are the same<br \/>\nHence,<br \/>\nWe can conclude that the converse we obtained from the given statement is true<br \/>\nNow,<br \/>\nProof of Converse of Corresponding Angles Theorem:<br \/>\nConsider the 2 lines L1 and L2 intersected by a transversal line L3 creating 2 corresponding angles 1 and 2 which are congruent<br \/>\nWe want to prove L1 and L2 are parallel and we will prove this by using &#8220;Proof of Contradiction&#8221;<br \/>\nNow,<br \/>\nAccording to Contradiction,<br \/>\nAssume L1 is not parallel to L2<br \/>\nThen, according to the parallel line axiom, there is a different line than L2 that passes through the intersection point of L2 and L3 (point A in the drawing), which is parallel to L1.<br \/>\nLet\u2019s draw that line, and call it P. Let\u2019s also call the angle formed by the traversal line and this new line angle 3, and we see that if we add some other angle, call it angle 4, to it, it will be the same as angle 2.<br \/>\nNow,<br \/>\nP || L1<br \/>\nSo,<br \/>\n\u22201\u00a0\u2245 \u22203,<br \/>\nas corresponding angles formed by a transversal of parallel lines, and so,<br \/>\nm\u22201=m\u22203<br \/>\nThis contradicts what was given,\u00a0\u00a0that angles 1 and 2 are congruent.<br \/>\nThis contradiction means our assumption <em>(\u201c<\/em>L1 is not parallel to L2<em>\u201d<\/em>) is false, and so L1 must be parallel to L2.<br \/>\nThe representation of the Converse of Corresponding Angles Theorem is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-80435\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-9.png\" alt=\"\" width=\"338\" height=\"250\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-9.png 338w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-9-300x222.png 300w\" sizes=\"(max-width: 338px) 100vw, 338px\" \/><\/p>\n<p>b. Alternate Interior Angles Theorem (Theorem 3.2): If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37538\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-60.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 60\" width=\"172\" height=\"166\" \/><br \/>\nConverse:<br \/>\nIf the pairs of alternate interior angles are<\/p>\n<p>congruent, then the two parallel lines are<\/p>\n<p>cut by a transversal.<\/p>\n<p>Answer:<br \/>\nThe converse of the Alternate Interior angles Theorem:<br \/>\nThe &#8220;Converse of the Alternate Interior Angles Theorem&#8221; states that if two lines are cut by a transversal and the alternate interior angles\u00a0are congruent, then the lines are parallel<br \/>\nSo,<br \/>\nWhen we compare the actual converse and the converse according to the given statement,<br \/>\nwe can conclude that the converse we obtained from the given statement is false<\/p>\n<p>c. Alternate Exterior Angles Theorem (Theorem 3.3): If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37537\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-61.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 61\" width=\"169\" height=\"166\" \/><br \/>\nConverse:<br \/>\nIf the pairs of alternate exterior angles<\/p>\n<p><span style=\"font-size: 16px;\">are congruent, then the two parallel <\/span><\/p>\n<p><span style=\"font-size: 16px;\">lines are cut by a transversal.\u00a0<\/span><\/p>\n<p>Answer:<br \/>\nThe Converse of the alternate exterior angles Theorem:<br \/>\nThe &#8220;Converse of the Alternate Exterior Angles Theorem&#8221; states that if alternate exterior angles\u00a0of two lines crossed by a transversal are congruent, then the two lines are parallel.<br \/>\nSo,<br \/>\nWhen we compare the converses we obtained from the given statement and the actual converse,<br \/>\nWe can conclude that both converses are the same<br \/>\nHence,<br \/>\nWe can conclude that the converse we obtained from the given statement is true<br \/>\nNow,<br \/>\nProof of Alternate exterior angles Theorem:<br \/>\nGiven: \u22201 \u2245 \u22202<br \/>\nProve: l || m<br \/>\nThe flow proof for the Converse of Alternate exterior angles Theorem is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-80493\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-11.png\" alt=\"\" width=\"607\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-11.png 607w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-11-300x31.png 300w\" sizes=\"(max-width: 607px) 100vw, 607px\" \/><br \/>\nThe representation of the Converse of the Exterior angles Theorem is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-80496\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-13.png\" alt=\"\" width=\"281\" height=\"194\" \/><\/p>\n<p>d. Consecutive Interior Angles Theorem (Theorem 3.4): If two parallel lines are cut by a transversal. then the pairs of consecutive interior angles are supplementary.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37536\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-62.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 62\" width=\"167\" height=\"164\" \/><br \/>\nConverse:<br \/>\nIf the pairs of consecutive interior angles<\/p>\n<p>are supplementary, then the two parallel lines<\/p>\n<p>are cut by a transversal<\/p>\n<p>Answer:<br \/>\nThe Converse of the Consecutive Interior angles Theorem:<br \/>\nThe &#8220;Converse of the consecutive Interior angles Theorem&#8221; states that if the consecutive interior angles on the same side of a transversal line intersecting two lines are supplementary, then the two lines are parallel.<br \/>\nSo,<br \/>\nWhen we compare the converses we obtained from the given statement and the actual converse,<br \/>\nWe can conclude that both converses are the same<br \/>\nHence,<br \/>\nWe can conclude that the converse we obtained from the given statement is true<br \/>\nNow,<br \/>\nProof of the Converse of the Consecutive Interior angles Theorem:<br \/>\na.\u00a0 m\u22205 + m\u22204 = 180\u00b0 \/\/From the given statement<br \/>\nb.\u00a0 m\u22201 + m\u22204 = 180\u00b0 \/\/ Linear pair of angles are supplementary<br \/>\nc. m\u22205=m\u22201 \/\/ (1), (2), transitive property of equality<br \/>\nd.\u00a0 AB||CD \/\/ Converse of the Corresponding Angles Theorem<br \/>\nThe representation of the Converse of the Consecutive Interior angles Theorem is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-80509\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-14.png\" alt=\"\" width=\"316\" height=\"233\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-14.png 316w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-14-300x221.png 300w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 2.<br \/>\nFor which of the theorems involving parallel lines and transversals is the converse true?<br \/>\nAnswer:<br \/>\nFrom Exploration 1,<br \/>\nThe theorems involving parallel lines and transversals that the converse is true are:<br \/>\na. Corresponding Angles Theorem<br \/>\nb. Alternate Exterior angles Theorem<br \/>\nc. Consecutive Interior angles Theorem<\/p>\n<p>Question 3.<br \/>\nIn Exploration 1, explain how you would prove any of the theorems that you found to be true.<br \/>\nAnswer:<br \/>\nFor the proofs of the theorems that you found to be true, refer to Exploration 1<\/p>\n<h3><a id=\"Lesson_3.3_Proofs_with_Parallel_Lines\"><\/a>Lesson 3.3 Proofs with Parallel Lines<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nIs there enough information in the diagram to conclude that m || n? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37535\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-63.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 63\" width=\"164\" height=\"119\" \/><br \/>\nAnswer:<br \/>\nYes, there is enough information in the diagram to conclude m || n.<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37535\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-63.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 63\" width=\"164\" height=\"119\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that the given angles are the consecutive exterior angles<br \/>\nNow,<br \/>\nWe have to prove that m || n<br \/>\nSo,<br \/>\nWe will use &#8220;Converse of Consecutive Exterior angles Theorem&#8221; to prove m || n<br \/>\nProof of the Converse of the Consecutive Exterior angles Theorem:<br \/>\na.\u00a0 m\u22201 + m\u22208 = 180\u00b0 \/\/From the given statement<br \/>\nb.\u00a0 m\u22201 + m\u22204 = 180\u00b0 \/\/ Linear pair of angles are supplementary<br \/>\nc. m\u22205=m\u22201 \/\/ (1), (2), transitive property of equality<br \/>\nd.\u00a0 AB||CD \/\/ Converse of the Corresponding Angles Theorem<br \/>\nThe representation of the Converse of the Consecutive Interior angles Theorem is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-81035\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-1.jpg\" alt=\"\" width=\"306\" height=\"214\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-1.jpg 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-1-300x210.jpg 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><\/p>\n<p>Question 2.<br \/>\nExplain why the Corresponding Angles Converse is the converse of the Corresponding Angles Theorem (Theorem 3.1).<br \/>\nAnswer:<br \/>\nCorresponding Angles Theorem:<br \/>\nThe &#8220;Corresponding Angles Postulate&#8221; states that, when two parallel lines are cut by a transversal, the resulting corresponding angles\u00a0are congruent<br \/>\nConverse:<br \/>\nWhen the corresponding angles are congruent, the two parallel lines are cut by a transversal<br \/>\nNow,<br \/>\nThe Converse of Corresponding Angles Theorem:<br \/>\nIf the corresponding angles formed are congruent, then two lines l and m are cut by a transversal.<br \/>\nSo,<br \/>\nWhen we observe the Converse of the Corresponding Angles Theorem we obtained and the actual definition, both are the same<br \/>\nHence, from the above,<br \/>\nWe can conclude that the Corresponding Angles Converse is the converse of the Corresponding Angles Theorem<\/p>\n<p>Question 3.<br \/>\nIf you use the diagram below to prove the Alternate Exterior Angles Converse. what Given and Prove statements would you use?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37534\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-64.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 64\" width=\"157\" height=\"103\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37534\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-64.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 64\" width=\"157\" height=\"103\" \/><br \/>\nIt is given that the given angles are the alternate exterior angles<br \/>\nNow,<br \/>\nAlternate Exterior angle Theorem:<br \/>\nIf two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent<br \/>\nThe Converse of the Alternate Exterior Angles Theorem:<br \/>\nThe \u201cConverse of the Alternate Exterior Angles Theorem\u201d states that if alternate exterior angles\u00a0of two lines crossed by a transversal are congruent, then the two lines are parallel.<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nFor the Converse of the alternate exterior angles Theorem,<br \/>\nThe given statement is: \u22201 \u2245 8<br \/>\nTo prove: l || k<\/p>\n<p>Question 4.<br \/>\nCopy and complete the following paragraph proof of the Alternate Interior Angles Converse using the diagram in Example 2.<\/p>\n<p>It is given that \u22204 \u2245\u22205. By the _______ . \u22201 \u2245 \u22204. Then by the Transitive Property of Congruence (Theorem 2.2), _______ . So, by the _______ , g || h.<br \/>\nAnswer:<br \/>\nThe completed proof of the Alternate Interior Angles Converse using the diagram in Example 2 is:<br \/>\nIt is given that \u22204 \u2245\u22205.<br \/>\nBy the Vertical Angles Congruence Theorem (Theorem 2.6). \u22201 \u2245 \u22204.<br \/>\nThen by the Transitive Property of Congruence (Theorem 2.2), \u22201 \u2245\u22205.<br \/>\nSo, by the Corresponding Angles Converse, g || h.<\/p>\n<p>Question 5.<br \/>\nEach step is parallel to the step immediately above it. The bottom step is parallel to the ground. Explain why the top step is parallel t0 the ground.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37533\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-65.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 65\" width=\"191\" height=\"277\" \/><br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can observe that not any step is intersecting at each other<br \/>\nIn the same way, when we observe the floor from any step,<br \/>\nWe can say that they are also parallel<br \/>\nHence, from the above,<br \/>\nWe can conclude that the\u00a0 top step is also parallel to the ground since they do not intersect each other at any point<\/p>\n<p>Question 6.<br \/>\nIn the diagram below. p || q and q || r. Find m\u22208. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37532\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-66.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 66\" width=\"149\" height=\"129\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37532\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-66.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 66\" width=\"149\" height=\"129\" \/><br \/>\nFrom the figure,<br \/>\nWe can observe that the given angles are the consecutive exterior angles<br \/>\nWe know that,<br \/>\nAccording to the Consecutive Exterior angles Theorem,<br \/>\n\u22208 + 115\u00b0 = 180\u00b0<br \/>\n\u22208 = 180\u00b0 &#8211; 115\u00b0<br \/>\n\u22208 = 65\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u22208 = 65\u00b0<\/p>\n<h3><a id=\"Exercise_3.3_Proofs_with_Parallel_Lines\"><\/a>Exercise 3.3 Proofs with Parallel Lines<\/h3>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nTwo lines are cut by a transversal. Which angle pairs must be congruent for the lines to be parallel?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48356\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-1.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 1\" width=\"574\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-1.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-1-300x29.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nUse the theorems from Section 3.2 and the converses of those theorems in this section to write three biconditional statements about parallel lines and transversals.<br \/>\nAnswer:<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3-8. find the value of x that makes m || n. Explain your reasoning.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37530\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-67.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 67\" width=\"135\" height=\"88\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48357\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-3.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 3\" width=\"563\" height=\"175\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-3.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-3-300x93.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37529\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-68.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 68\" width=\"162\" height=\"88\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37529\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-68.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 68\" width=\"162\" height=\"88\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that the given angles are the corresponding angles<br \/>\nNow,<br \/>\nAccording to Corresponding Angles Theorem,<br \/>\n(2x + 15)\u00b0 = 135\u00b0<br \/>\n2x\u00b0 = 135\u00b0 &#8211; 15\u00b0<br \/>\n2x\u00b0 = 120\u00b0<br \/>\nx\u00b0 = \\(\\frac{120}{2}\\)<br \/>\nx\u00b0 = 60\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 60\u00b0<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37528\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-69.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 69\" width=\"148\" height=\"89\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48358\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-5.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 5\" width=\"529\" height=\"265\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-5.png 529w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-5-300x150.png 300w\" sizes=\"(max-width: 529px) 100vw, 529px\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37527\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-70.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 70\" width=\"163\" height=\"93\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37527\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-70.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 70\" width=\"163\" height=\"93\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that the given angles are the corresponding angles<br \/>\nNow,<br \/>\nAccording to Corresponding Angles Theorem,<br \/>\n(180 &#8211; x)\u00b0 = x\u00b0<br \/>\n180\u00b0 = x\u00b0\u00a0 + x\u00b0<br \/>\n2x\u00b0 = 180\u00b0<br \/>\nx\u00b0 = \\(\\frac{180}{2}\\)<br \/>\nx\u00b0 = 90\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 90\u00b0<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37526\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-71.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 71\" width=\"147\" height=\"83\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48359\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-7.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 7\" width=\"521\" height=\"216\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-7.png 521w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-7-300x124.png 300w\" sizes=\"(max-width: 521px) 100vw, 521px\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37525\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-72.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 72\" width=\"171\" height=\"91\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37525\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-72.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 72\" width=\"171\" height=\"91\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that the given angles are the corresponding angles<br \/>\nNow,<br \/>\nAccording to Corresponding Angles Theorem,<br \/>\n(2x + 20)\u00b0 = 3x\u00b0<br \/>\n20\u00b0 = 3x\u00b0\u00a0 &#8211; 2x\u00b0<br \/>\nx\u00b0 = 20\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 20\u00b0<\/p>\n<p>In Exercises 9 and 10, use a compass and straightedge to construct a line through point P that is parallel to line m.<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37524\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-73.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 73\" width=\"162\" height=\"71\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48360\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-9.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 9\" width=\"540\" height=\"268\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-9.png 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-9-300x149.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37523\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-74.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 74\" width=\"142\" height=\"99\" \/><br \/>\nAnswer:<br \/>\nLet A and B be two points on line m.<br \/>\nDraw \\(\\overline{A P}\\) and construct an angle \u22201 on n at P so that \u2220PAB and \u22201 are corresponding angles<br \/>\nHence,<br \/>\nThe representation of the complete figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-81072\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-2.jpg\" alt=\"\" width=\"310\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-2.jpg 310w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-2-300x159.jpg 300w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><\/p>\n<p><strong>PROVING A THEOREM<\/strong><br \/>\nIn Exercises 11 and 12. prove the theorem.<br \/>\nQuestion 11.<br \/>\nAlternate Exterior Angles Converse (Theorem 3.7)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48361\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-11.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 11\" width=\"586\" height=\"413\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-11.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-11-300x211.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 12.<br \/>\nConsecutive Interior Angles Converse (Theorem 3.8)<br \/>\nAnswer:<br \/>\nProof of the Converse of the Consecutive Interior angles Theorem:<br \/>\nGiven: m\u22205 + m\u22204 = 180\u00b0<br \/>\nProve: AB || CD<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-80509\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-14.png\" sizes=\"(max-width: 316px) 100vw, 316px\" srcset=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-14.png 316w, https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-14-300x221.png 300w\" alt=\"\" width=\"316\" height=\"233\" \/><br \/>\nNow,<br \/>\na.\u00a0 m\u22205 + m\u22204 = 180\u00b0 \/\/From the given statement<br \/>\nb.\u00a0 m\u22201 + m\u22204 = 180\u00b0 \/\/ Linear pair of angles are supplementary<br \/>\nc. m\u22205=m\u22201 \/\/ (1), (2), transitive property of equality<br \/>\nd.\u00a0 AB||CD \/\/ Converse of the Corresponding Angles Theorem<\/p>\n<p>In Exercises 13-18. decide whether there is enough information to prove that m || n. If so, state the theorem you would use.<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37522\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-75.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 75\" width=\"147\" height=\"87\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48362\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-13.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 13\" width=\"486\" height=\"30\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-13.png 486w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-13-300x19.png 300w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37521\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-76.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 76\" width=\"150\" height=\"87\" \/><br \/>\nAnswer:<br \/>\nYes, there is enough information to prove m || n<br \/>\nThe theorem we can use to prove that m || n is: Alternate Exterior angles Converse theorem<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37520\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-77.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 77\" width=\"129\" height=\"107\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48363\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-15.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 15\" width=\"86\" height=\"24\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37519\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-78.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 78\" width=\"144\" height=\"82\" \/><br \/>\nAnswer:<br \/>\nNo, there is no enough information to prove m || n<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37518\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-79.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 79\" width=\"152\" height=\"84\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-79.png 152w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-79-150x84.png 150w\" sizes=\"(max-width: 152px) 100vw, 152px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48364\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-17.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 17\" width=\"69\" height=\"26\" \/><\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37517\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-80.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 80\" width=\"156\" height=\"88\" \/><br \/>\nAnswer:<br \/>\nYes, there is enough information to prove m || n<br \/>\nThe theorem we can use to prove that m || n is: Alternate Exterior angles Converse theorem<\/p>\n<p><strong>ERROR ANALYSIS<\/strong><br \/>\nIn Exercises 19 and 20, describe and correct the error in the reasoning.<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37516\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-81.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 81\" width=\"263\" height=\"135\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48365\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-19.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 19\" width=\"583\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-19.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-19-300x45.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37515\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-82.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 82\" width=\"213\" height=\"147\" \/><br \/>\nAnswer:<br \/>\nThe given figure shows that angles 1 and 2 are Consecutive Interior angles<br \/>\nIt also shows that a and b are cut by a transversal and they have the same length<br \/>\nSo,<br \/>\nFrom the converse of the Consecutive Interior angles Theorem,<br \/>\nWe can conclude that a || b<\/p>\n<p>In Exercises 21-24. are <img loading=\"lazy\" class=\"alignnone size-full wp-image-37514\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-83.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 83\" width=\"32\" height=\"24\" \/> and <img loading=\"lazy\" class=\"alignnone size-full wp-image-37513\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-84.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 84\" width=\"36\" height=\"23\" \/> parallel? Explain your reasoning.<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37512\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-85.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 85\" width=\"137\" height=\"89\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48366\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-21.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 21\" width=\"590\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-21.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-21-300x62.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37511\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-86.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 86\" width=\"156\" height=\"105\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37511\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-86.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 86\" width=\"156\" height=\"105\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nThe sum of the given angle measures is: 180\u00b0<br \/>\nFrom the given figure,<br \/>\nWe can observe that the given angles are consecutive exterior angles<br \/>\nSo,<br \/>\nFrom the Consecutive Exterior angles Converse,<br \/>\nWe can conclude that AC || DF<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37510\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-87.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 87\" width=\"144\" height=\"101\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48367\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-23.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 23\" width=\"571\" height=\"82\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-23.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-23-300x43.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37509\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-88.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 88\" width=\"152\" height=\"100\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-88.png 152w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-88-150x100.png 150w\" sizes=\"(max-width: 152px) 100vw, 152px\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37509\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-88.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 88\" width=\"152\" height=\"100\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-88.png 152w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-88-150x100.png 150w\" sizes=\"(max-width: 152px) 100vw, 152px\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that the sum of the angle measures of all the pairs i.e., (115 + 65)\u00b0, (115 + 65)\u00b0, and (65 + 65)\u00b0 is not 180\u00b0<br \/>\nSince,<br \/>\nThe sum of the angle measures are not supplementary, according to the Consecutive Exterior Angles Converse,<br \/>\nAC is not parallel to DF<\/p>\n<p>Question 25.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nThe map shows part of Denser, Colorado, Use the markings on the map. Are the numbered streets parallel to one another? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37508\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-89.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 89\" width=\"374\" height=\"207\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-89.png 374w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-89-300x166.png 300w\" sizes=\"(max-width: 374px) 100vw, 374px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48368\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-25.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 25\" width=\"604\" height=\"222\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-25.png 604w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-25-300x110.png 300w\" sizes=\"(max-width: 604px) 100vw, 604px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nEach rung of the ladder is parallel to the rung directly above it. Explain why the top rung is parallel to the bottom rung.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37507\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-90.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 90\" width=\"116\" height=\"159\" \/><br \/>\nAnswer:<br \/>\nWhen we observe the ladder,<br \/>\nThe rungs are not intersecting at any point i.e., they have different points<br \/>\nWe know that,<br \/>\nThe parallel lines do not have any intersecting points<br \/>\nHence, from the above,<br \/>\nWe can conclude that the top rung is parallel to the bottom rung<\/p>\n<p>Question 27.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe diagram of the control bar of the kite shows the angles formed between the Control bar and the kite lines. How do you know that n is parallel to m?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37506\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-91.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 91\" width=\"376\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-91.png 376w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-91-300x168.png 300w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48369\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-27.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 27\" width=\"576\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-27.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-27-300x58.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>REASONING<\/strong><br \/>\nUse the diagram. Which rays are parallel? Which rays are not parallel? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37505\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-92.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 92\" width=\"283\" height=\"116\" \/><br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>ATTENDING TO PRECISION<\/strong><br \/>\nUse the diagram. Which theorems allow you to conclude that m || n? Select all that apply. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37504\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-93.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 93\" width=\"183\" height=\"127\" \/><br \/>\n(A) Corresponding Angles Converse (Thm 3.5)<br \/>\n(B) Alternate Interior Angles Converse (Thm 3.6)<br \/>\n(C) Alternate Exterior Angles Converse (Thm 3.7)<br \/>\n(D) Consecutive Interior Angles Converse (Thm 3.8)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48370\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-29.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 29\" width=\"605\" height=\"391\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-29.png 605w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-29-300x194.png 300w\" sizes=\"(max-width: 605px) 100vw, 605px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nOne way to build stairs is to attach triangular blocks to angled support, as shown. The sides of the angled support are parallel. If the support makes a 32\u00b0 angle with the floor, what must m\u22201 so the top of the step will be parallel to the floor? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37503\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-94.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 94\" width=\"308\" height=\"186\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-94.png 308w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-94-300x181.png 300w\" sizes=\"(max-width: 308px) 100vw, 308px\" \/><br \/>\nAnswer:<br \/>\nIt is given that the sides of the angled support are parallel and the support makes a 32\u00b0 angle with the floor<br \/>\nSo,<br \/>\nTo make the top of the step where \u22201 is present to be parallel to the floor, the angles must be &#8220;Alternate Interior angles&#8221;<br \/>\nWe know that,<br \/>\nThe &#8220;Alternate Interior angles&#8221; are congruent<br \/>\nSo,<br \/>\n\u22201 = 32\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u22201 = 32\u00b0<\/p>\n<p>Question 31.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nIn the diagram, how many angles must be given to determine whether j || k? Give four examples that would allow you to conclude that j || k using the theorems from this lesson.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37502\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-95.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 95\" width=\"140\" height=\"119\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48371\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-31.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 31\" width=\"559\" height=\"279\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-31.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-31-300x150.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nDraw a diagram of at least two lines cut by at least one transversal. Mark your diagram so that it cannot be proven that any lines are parallel. Then explain how your diagram would need to change in order to prove that lines are parallel.<br \/>\nAnswer:<br \/>\nThe diagram that represents the figure that it can not be proven that any lines are parallel is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-81251\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-3.jpg\" alt=\"\" width=\"165\" height=\"88\" \/><br \/>\nFrom the above,<br \/>\nThe diagram can be changed by the transformation of transversals into parallel lines and a parallel line into transversal<br \/>\nHence,<br \/>\nThe diagram that represents the figure that it can be proven that the lines are parallel is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-81262\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-17.png\" alt=\"\" width=\"373\" height=\"235\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-17.png 373w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-17-300x189.png 300w\" sizes=\"(max-width: 373px) 100vw, 373px\" \/><\/p>\n<p><strong>PROOF<\/strong><br \/>\nIn Exercises 33-36, write a proof.<\/p>\n<p>Question 33.<br \/>\nGiven m\u22201 = 115\u00b0, m\u22202 = 65\u00b0<br \/>\nProve m||n<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37501\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-96.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 96\" width=\"190\" height=\"115\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48372\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-33.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 33\" width=\"568\" height=\"563\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-33.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-33-300x297.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-33-150x150.png 150w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 34.<br \/>\nGiven \u22201 and \u22203 are supplementary.<br \/>\nProve m||n<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37500\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-97.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 97\" width=\"164\" height=\"110\" \/><br \/>\nAnswer:<br \/>\nGiven: \u22201 and \u22203 are supplementary<br \/>\nProve: m || n<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-81300\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-4.jpg\" alt=\"\" width=\"573\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-4.jpg 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-4-300x35.jpg 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 35.<br \/>\nGiven \u22201 \u2245 \u22202, \u22203 \u2245 \u22204<br \/>\nProve \\(\\overline{A B} \\| \\overline{C D}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37499\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-98.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 98\" width=\"201\" height=\"114\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48373\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-35.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 35\" width=\"566\" height=\"501\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-35.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-35-300x266.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 36.<br \/>\nGiven a||b, \u22202 \u2245 \u22203<br \/>\nProve c||d<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37498\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-99.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 99\" width=\"223\" height=\"102\" \/><br \/>\nAnswer:<br \/>\nGiven: a || b, \u22202 \u2245 \u22203<br \/>\nProve: c || d<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-81351\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-5.jpg\" alt=\"\" width=\"576\" height=\"360\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-5.jpg 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-5-300x188.jpg 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 37.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour classmate decided that <img loading=\"lazy\" class=\"alignnone size-full wp-image-37497\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-100.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 100\" width=\"69\" height=\"24\" \/> based on the diagram. Is your classmate correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37496\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-101.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 101\" width=\"194\" height=\"126\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48374\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-37.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 37\" width=\"569\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-37.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-37-300x49.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nAre the markings on the diagram enough to conclude that any lines are parallel? If so. which ones? If not, what other information is needed?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37495\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-102.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 102\" width=\"173\" height=\"108\" \/><br \/>\nAnswer:<br \/>\nThe given diagram is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37495\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-102.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 102\" width=\"173\" height=\"108\" \/><br \/>\nFrom the given diagram,<br \/>\nWe can observe that<br \/>\n\u22201 and \u22204; \u22202 and \u22203 are the pairs of corresponding angles<br \/>\nWe know that,<br \/>\nAccording to the Converse of the Corresponding angles Theorem,<br \/>\nIf the corresponding angles are congruent, then the two lines that cut by a transversal are parallel lines<br \/>\nHence,<br \/>\nWe can conclude that p and q; r and s are the pairs of parallel lines<\/p>\n<p>Question 39.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nUse these steps to prove the Transitive Property of Parallel Lines Theorem<br \/>\na. Cops the diagram with the Transitive Property of Parallel Lines Theorem on page 141.<br \/>\nb. Write the Given and Prove statements.<br \/>\nc. Use the properties of angles formed by parallel lines cut by a transversal to prove the theorem.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48375\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-39.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 39\" width=\"581\" height=\"698\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-39.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-39-250x300.png 250w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nUse the diagram<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37494\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-103.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 103\" width=\"242\" height=\"117\" \/><br \/>\na. Find the value of x that makes p || q.<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can observe that when p || q,<br \/>\nThe angles are: (2x + 2)\u00b0 and (x + 56)\u00b0<br \/>\nWe can observe that the given angles are corresponding angles<br \/>\nHence,<br \/>\n(2x + 2)\u00b0 = (x + 56)\u00b0<br \/>\n2x &#8211; x = 56\u00b0 &#8211; 2\u00b0<br \/>\nx\u00b0 = 54\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x when p || q is: 54\u00b0<\/p>\n<p>b. Find the value of y that makes r || s.<br \/>\nAnswer:<br \/>\nWe can observe that when r || s,<br \/>\nThe angles are (y + 7)\u00b0 and (3y &#8211; 17)\u00b0<br \/>\nWe can observe that the given angles are corresponding angles<br \/>\nHence,<br \/>\n(y + 7)\u00b0 = (3y &#8211; 17)\u00b0<br \/>\ny &#8211; 3y = -17\u00b0 &#8211; 7\u00b0<br \/>\n-2y\u00b0 = -24\u00b0<br \/>\ny = \\(\\frac{24}{2}\\)<br \/>\ny = 12\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y when r || s is: 12\u00b0<\/p>\n<p>c. Can r be parallel to s and can p, be parallel to q at the same time? Explain your reasoning.<br \/>\nAnswer:<br \/>\nNo, p ||q and r ||s will not be possible at the same time because when p || q, r, and s can act as transversal and when r || s, p, and q can act as transversal<\/p>\n<p>Maintaining Mathematical Proficiency<br \/>\nUse the Distance Formula to find the distance between the two points.<\/p>\n<p>Question 41.<br \/>\n(1, 3) and (- 2, 9)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48376\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-41.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 41\" width=\"305\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-41.png 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-41-300x105.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><\/p>\n<p>Question 42.<br \/>\n(- 3, 7) and (8, &#8211; 6)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\n(-3, 7), and (8, -6)<br \/>\nCompare the given points with (x1, y1), and (x2, y2)<br \/>\nWe know that,<br \/>\nd = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nd = \\(\\sqrt{(8 + 3)\u00b2 + (7 + 6)\u00b2}\\)<br \/>\nd = \\(\\sqrt{(11)\u00b2 + (13)\u00b2}\\)<br \/>\nd = \\(\\sqrt{290}\\)<br \/>\nd = 17.02<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance between the given 2 points is: 17.02<\/p>\n<p>Question 43.<br \/>\n(5, &#8211; 4) and (0, 8)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48377\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-43.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 43\" width=\"305\" height=\"144\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-43.png 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-3.3-a-43-300x142.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><\/p>\n<p>Question 44.<br \/>\n(13, 1) and (9, &#8211; 4)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\n(13, 1), and (9, -4)<br \/>\nCompare the given points with (x1, y1), and (x2, y2)<br \/>\nWe know that,<br \/>\nd = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nd = \\(\\sqrt{(13 &#8211; 9)\u00b2 + (1 + 4)\u00b2}\\)<br \/>\nd = \\(\\sqrt{(4)\u00b2 + (5)\u00b2}\\)<br \/>\nd = \\(\\sqrt{41}\\)<br \/>\nd = 6.40<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance between the given 2 points is: 6.40<\/p>\n<h3><a id=\"3.1_-_3.3_Study_Skills:_Analyzing_Your_Errors\"><\/a>3.1 &#8211; 3.3 Study Skills: Analyzing Your Errors<\/h3>\n<p><strong>Mathematical Practices<\/strong><\/p>\n<p>Question 1.<br \/>\nDraw the portion of the diagram that you used to answer Exercise 26 on page 130.<br \/>\nAnswer:<br \/>\nThe portion of the diagram that you used to answer Exercise 26 on page 130 is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37040\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-31.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 31\" width=\"206\" height=\"128\" \/><\/p>\n<p>Question 2.<br \/>\nIn Exercise 40 on page 144. explain how you started solving the problem and why you started that way.<br \/>\nAnswer:<br \/>\nIn Exercise 40 on page 144,<br \/>\nYou started solving the problem by considering the 2 lines parallel and two lines as transversals<br \/>\nSo,<br \/>\nIf p and q are the parallel lines, then r and s are the transversals<br \/>\nIf r and s are the parallel lines, then p and q are the transversals<\/p>\n<h3><a id=\"3.1_-_3.3_Quiz\"><\/a>3.1 &#8211; 3.3 Quiz<\/h3>\n<p>Think of each segment in the diagram as part of a line. Which lines(s) or plane(s) contain point G and appear to fit the description?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-37552\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-104.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 104\" width=\"188\" height=\"214\" \/><\/p>\n<p>Question 1.<br \/>\nline(s) parallel to <img loading=\"lazy\" class=\"alignnone size-full wp-image-37551\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-105.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 105\" width=\"35\" height=\"25\" \/>.<br \/>\nAnswer:<br \/>\nThe line parallel to \\(\\overline{E F}\\) is: \\(\\overline{D H}\\)<\/p>\n<p>Question 2.<br \/>\nline(s) perpendicular to <img loading=\"lazy\" class=\"alignnone size-full wp-image-37551\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-105.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 105\" width=\"35\" height=\"25\" \/>.<br \/>\nAnswer:<br \/>\nThe lines perpendicular to \\(\\overline{E F}\\) are: \\(\\overline{F B}\\) and \\(\\overline{F G}\\)<\/p>\n<p>Question 3.<br \/>\nline(s) skew to <img loading=\"lazy\" class=\"alignnone size-full wp-image-37551\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-105.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 105\" width=\"35\" height=\"25\" \/>.<br \/>\nAnswer:<br \/>\nThe lines skew to \\(\\overline{E F}\\) are: \\(\\overline{C D}\\), \\(\\overline{C G}\\), and \\(\\overline{A E}\\)<\/p>\n<p>Question 4.<br \/>\nplane(s) parallel to plane ADE<br \/>\nAnswer:<br \/>\nThe plane parallel to plane ADE is: Plane GCB<\/p>\n<p>Identify all pairs of angles of the given type.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-37550\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-106.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 106\" width=\"178\" height=\"135\" \/><\/p>\n<p>Question 5.<br \/>\nconsecutive interior<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nWhen two lines are cut by a transversal, the pair of\u00a0angles\u00a0on one side of the transversal and inside the two lines are called the\u00a0consecutive interior angles.<br \/>\nHence, from the given figure,<br \/>\nWe can conclude that the consecutive interior angles are: 3 and 5; 4 and 6<\/p>\n<p>Question 6.<br \/>\nalternate interior<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nAlternate Interior Angles\u00a0are a pair of\u00a0angles\u00a0on the inner side of each of those two lines but on opposite sides of the transversal.<br \/>\nHence, from the given figure,<br \/>\nWe can conclude that the alternate interior angles are: 3 and 6; 4 and 5<\/p>\n<p>Question 7.<br \/>\ncorresponding<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nWhen two lines are crossed by another line (which is called the Transversal), the\u00a0angles\u00a0in matching corners are called\u00a0corresponding angles.<br \/>\nHence, from the given figure,<br \/>\nWe can conclude that the corresponding angles are: 1 and 5; 3 and 7; 2 and 4; 6 and 8<\/p>\n<p>Question 8.<br \/>\nalternate exterior<br \/>\nAnswer:<br \/>\nAlternate exterior angles\u00a0are the pair of\u00a0angles\u00a0that lie on the outer side of the two parallel lines but on either side of the transversal line<br \/>\nHence, from the above figure,<br \/>\nWe can conclude that the alternate exterior angles are: 1 and 8; 7 and 2<\/p>\n<p>Find m\u22201 and m\u22202. Tell which theorem you use in each case.<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37549\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-107.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 107\" width=\"176\" height=\"107\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37549\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-107.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 107\" width=\"176\" height=\"107\" \/><br \/>\nFrom the given figure,<br \/>\nBy using the linear pair theorem,<br \/>\n\u22201 + 138\u00b0 = 180\u00b0<br \/>\n\u22201 = 180\u00b0 &#8211; 138\u00b0<br \/>\n\u22201 = 42\u00b0<br \/>\nNow,<br \/>\nBy using the Alternate Exterior Angles Theorem,<br \/>\n\u22201 = \u22202<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u22201 = \u22202 = 42\u00b0<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37548\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-108.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 108\" width=\"172\" height=\"101\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37548\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-108.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 108\" width=\"172\" height=\"101\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nBy using the Vertical Angles Theorem,<br \/>\n\u22202 = 123\u00b0<br \/>\nNow,<br \/>\nBy using the vertical Angles Theorem,<br \/>\n\u22201 = \u22202<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u22201 = \u22202 = 123\u00b0<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37547\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-109.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 109\" width=\"173\" height=\"104\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37547\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-109.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 109\" width=\"173\" height=\"104\" \/><br \/>\nFrom the given figure,<br \/>\nBy using the linear pair theorem,<br \/>\n\u22201 + 57\u00b0 = 180\u00b0<br \/>\n\u22201 = 180\u00b0 &#8211; 57\u00b0<br \/>\n\u22201 = 123\u00b0<br \/>\nNow,<br \/>\nBy using the consecutive interior angles theorem,<br \/>\n\u22201 + \u22202 = 180\u00b0<br \/>\n\u22202 = 180\u00b0 &#8211; 123\u00b0<br \/>\n\u22202 = 57\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u22201 = 123\u00b0 and \u22202 = 57\u00b0<\/p>\n<p>Decide whether there is enough information to prove that m || n. If so, state the theorem you would use.<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37546\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-110.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 110\" width=\"171\" height=\"99\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37546\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-110.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 110\" width=\"171\" height=\"99\" \/><br \/>\nWe know that,<br \/>\nBy using the &#8220;Consecutive Interior angles Converse&#8221;,<br \/>\nIf the angle measure of the angles is a supplementary angle, then the lines cut by a transversal are parallel<br \/>\nNow,<br \/>\n69\u00b0 + 111\u00b0 = 180\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that m || n by using the Consecutive Interior angles Theorem<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37545\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-111.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 111\" width=\"164\" height=\"130\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37545\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-111.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 111\" width=\"164\" height=\"130\" \/><br \/>\nWe know that,<br \/>\nBy using the Corresponding Angles Theorem,<br \/>\nIf the corresponding angles are congruent, then the lines cut by a transversal are parallel<br \/>\nHence, from the above,<br \/>\nWe can conclude that m || n by using the Corresponding Angles Theorem<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37544\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-112.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 112\" width=\"203\" height=\"131\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37544\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-112.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 112\" width=\"203\" height=\"131\" \/><br \/>\nFrom the given figure,<br \/>\nIt is given that l || m and l || n,<br \/>\nSo,<br \/>\nWe know that,<br \/>\nBy using the parallel lines property,<br \/>\nIf a || b and b || c, then a || c<br \/>\nHence, from the above,<br \/>\nWe can conclude that m || n<\/p>\n<p>Question 15.<br \/>\nCellular phones use bars like the ones shown to indicate how much signal strength a phone receives from the nearest service tower. Each bar is parallel to the bar directly next to it.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37543\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-113.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 113\" width=\"118\" height=\"179\" \/><br \/>\na. Explain why the tallest bar is parallel to the shortest bar.<br \/>\nAnswer:<br \/>\nFrom the given bars,<br \/>\nWe can observe that there is no intersection between any bars<br \/>\nIf we represent the bars in the coordinate plane, we can observe that the number of intersection points between any bar is: 0<br \/>\nWe know that,<br \/>\nThe number of intersection points for parallel lines is: 0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the tallest bar is parallel to the shortest bar<\/p>\n<p>b. Imagine that the left side of each bar extends infinitely as a line.<br \/>\nIf m\u22201 = 58\u00b0, then what is m\u22202?<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can observe that \u22201 and \u22202 are the consecutive interior angles<br \/>\nWe know that,<br \/>\nThe sum of the angle measure between 2 consecutive interior angles is: 180\u00b0<br \/>\nSo,<br \/>\n\u22201 + \u2220 2 = 180\u00b0<br \/>\nIt is given that \u22201 = 58\u00b0<br \/>\nSo,<br \/>\n\u22202 = 180\u00b0 &#8211; 58\u00b0<br \/>\n\u22202 = 122\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u22202 = 122\u00b0<\/p>\n<p>Question 16.<br \/>\nThe diagram shows lines formed on a tennis court.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37542\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-114.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 114\" width=\"450\" height=\"186\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-114.png 450w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-3-Parallel-and-Perpendicular-Lines-114-300x124.png 300w\" sizes=\"(max-width: 450px) 100vw, 450px\" \/><br \/>\na. Identify two pairs of parallel lines so that each pair is in a different plane.<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can observe that there are a total of 5 lines.<br \/>\nHence,<br \/>\nThe two pairs of parallel lines so that each pair is in a different plane are: q and p; k and m<\/p>\n<p><span style=\"font-size: 16px;\">b. Identify two pairs of perpendicular lines.<br \/>\n<\/span>Answer:<br \/>\nFro the given figure,<br \/>\nWe can observe that there are 2 perpendicular lines<br \/>\nHence, from the above,<br \/>\nThe two pairs of perpendicular lines are l and n<\/p>\n<p>c. Identify two pairs of skew line<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can observe that there are 2 pairs of skew lines<br \/>\nHence,<br \/>\nThe 2 pair of skew lines are: q and p; l and m<\/p>\n<p>d. Prove that \u22201 \u2245 \u22202.<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can observe that \u22201 and \u22202 are the alternate exterior angles<br \/>\nWe know that,<br \/>\nAccording to the Alternate Exterior angles Theorem,<br \/>\nIf the line cut by a transversal is parallel, then the corresponding angles are congruent<br \/>\nHence,<br \/>\nAccording to the above theorem,<br \/>\nWe can conclude that \u22201 \u2245 \u22202<\/p>\n<h3><a id=\"3.4_Proofs_with_Perpendicular_Lines\"><\/a>3.4 Proofs with Perpendicular Lines<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Writing Conjectures<\/p>\n<p>Work with a partner: Fold a piece of pair in half twice. Label points on the two creases. as shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38075\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-115.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 115\" width=\"219\" height=\"260\" \/><br \/>\na. Write a conjecture about \\(\\overline{A B}\\) and \\(\\overline{C D}\\). Justify your conjecture.<br \/>\nAnswer:<br \/>\nThe conjecture about \\(\\overline{A B}\\) and \\(\\overline{c D}\\) is:<br \/>\nIf two\u00a0lines\u00a0intersect to form a linear pair of congruent angles, then the\u00a0lines\u00a0are\u00a0perpendicular.<\/p>\n<p>b. Write a conjecture about \\(\\overline{A O}\\) and \\(\\overline{O B}\\) Justify your conjecture.<br \/>\nAnswer:<br \/>\nThe conjecture about \\(\\overline{A O}\\) and \\(\\overline{O B}\\) is:<br \/>\nIn a plane, if two\u00a0lines\u00a0are\u00a0perpendicular\u00a0to the same\u00a0line, then they are parallel to each other.<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Exploring a segment Bisector<\/p>\n<p>Work with a partner: Fold and crease a piece of paper. as shown. Label the ends of the crease as A and B.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38074\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-116.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 116\" width=\"243\" height=\"230\" \/><br \/>\na. Fold the paper again so that point A coincides with point B. Crease the paper on that fold.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38074\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-116.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 116\" width=\"243\" height=\"230\" \/><\/p>\n<p>b. Unfold the paper and examine the four angles formed by the two creases. What can you conclude about the four angles?<br \/>\nAnswer:<br \/>\nWhen we unfold the paper and examine the four angles formed by the two creases, we can conclude that the four angles formed are the right angles i.e., 90\u00b0<\/p>\n<p><strong>Exploration 3<\/strong><\/p>\n<p>Writing a conjecture<\/p>\n<p>Work with a partner.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38073\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-117.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 117\" width=\"300\" height=\"240\" \/><br \/>\na. Draw \\(\\overline{A B}\\), as shown.<br \/>\nb. Draw an arc with center A on each side of AB. Using the same compass selling, draw an arc with center B on each side \\(\\overline{A B}\\). Label the intersections of arcs C and D.<br \/>\nc. Draw \\(\\overline{C D}\\). Label its intersection with \\(\\overline{A B}\\) as O. Write a conjecture about the resulting diagram. Justify your conjecture.<br \/>\n<strong>CONSTRUCTING VIABLE ARGUMENTS<\/strong><br \/>\nTo be proficient in math, you need to make conjectures and build a logical progression of statements to explore the truth of your conjectures.<br \/>\nAnswer:<br \/>\nThe resultant diagram is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-82222\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-18.png\" alt=\"\" width=\"447\" height=\"269\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-18.png 447w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-18-300x181.png 300w\" sizes=\"(max-width: 447px) 100vw, 447px\" \/><br \/>\nFrom the above diagram,<br \/>\nWe can conclude that<br \/>\nThe angles formed at all the intersection points are: 90\u00b0<br \/>\nThe lengths of the line segments are equal i.e., AO = OB and CO = OD<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 4.<br \/>\nWhat conjectures can you make about perpendicular lines?<br \/>\nAnswer:<br \/>\nThe conjectures about perpendicular lines are:<br \/>\na. If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.<br \/>\nb. In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line. c. In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.<\/p>\n<p>Question 5.<br \/>\nIn Exploration 3. find AO and OB when AB = 4 units.<br \/>\nAnswer:<br \/>\nFrom Exploration 2,<br \/>\nWe can observe that,<br \/>\nAB = AO + OB<br \/>\nAO = OB<br \/>\nIt is given that<br \/>\nAB = 4 units<br \/>\nHence,<br \/>\nThe values of AO and OB are: 2 units<\/p>\n<h3><a id=\"Lesson_3.4_Proofs_with_Perpendicular_Lines\"><\/a>Lesson 3.4 Proofs with Perpendicular Lines<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nFind the distance from point E to <img loading=\"lazy\" class=\"alignnone size-full wp-image-38072\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-118.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 118\" width=\"35\" height=\"27\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38071\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-119.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 119\" width=\"177\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-119.png 177w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-119-150x150.png 150w\" sizes=\"(max-width: 177px) 100vw, 177px\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38071\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-119.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 119\" width=\"177\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-119.png 177w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-119-150x150.png 150w\" sizes=\"(max-width: 177px) 100vw, 177px\" \/><br \/>\nIt is given that E is \u22a5 to \\(\\overline{F H}\\)<br \/>\nSo,<br \/>\nTo find the distance between E and \\(\\overline{F H}\\), we need to find the distance between E and G i.e., EG<br \/>\nNow,<br \/>\nFrom the coordinate plane,<br \/>\nE (-4, -3), G (1, 2)<br \/>\nCompare the given points with<br \/>\nE (x1, y1), G (x2, y2)<br \/>\nSo,<br \/>\nEG = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nEG = \\(\\sqrt{(1 + 4)\u00b2 + (2 + 3)\u00b2}\\)<br \/>\nEG = \\(\\sqrt{(5)\u00b2 + (5)\u00b2}\\)<br \/>\nEG = \\(\\sqrt{50}\\)<br \/>\nEG = 7.07<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance from point E to \\(\\overline{F H}\\) is: 7.07<\/p>\n<p>Question 2.<br \/>\nProve the Perpendicular Transversal Theorem using the diagram in Example 2 and the Alternate Exterior Angles Theorem (Theorem 3.3).<br \/>\nAnswer:<br \/>\nPerpendicular transversal theorem:<br \/>\nIn a plane, if a line is perpendicular to one of the two parallel lines, then it is perpendicular to the other line also<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-82268\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-19.png\" alt=\"\" width=\"309\" height=\"172\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-19.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-19-300x167.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><br \/>\nProof:<br \/>\nGiven: k || l, t \u22a5 k<br \/>\nProve: t \u22a5 l<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-82269\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-20.png\" alt=\"\" width=\"453\" height=\"508\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-20.png 453w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-20-268x300.png 268w\" sizes=\"(max-width: 453px) 100vw, 453px\" \/><br \/>\nAlternate Exterior Angles Theorem:<br \/>\nThe Alternate Exterior Angles Theorem states that, when two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-82301\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-21.png\" alt=\"\" width=\"276\" height=\"221\" \/><br \/>\nProof:<br \/>\nGiven: k || l<br \/>\nProve: \u22201 \u2245 \u22207 and \u22204 \u2245 \u22206<br \/>\nSince <span style=\"white-space: nowrap;\">k || l,<\/span>\u00a0by the Corresponding Angles Postulate,<br \/>\n\u22201 \u2245 \u22205<br \/>\nAlso, by the Vertical Angles Theorem,<br \/>\n\u22205 \u2245 \u22207<br \/>\nThen, by the Transitive Property of Congruence,<br \/>\n\u22201 \u2245 \u22207<br \/>\nYou can prove that\u00a0<span id=\"MathJax-Element-8-Frame\" class=\"MathJax\" style=\"display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mrow&gt;&lt;mo&gt;&amp;#x2220;&lt;\/mo&gt;&lt;mn&gt;4&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/math&gt;\"><span id=\"MathJax-Span-51\" class=\"math\" role=\"math\"><span id=\"MathJax-Span-52\" class=\"mrow\"><span id=\"MathJax-Span-53\" class=\"mrow\"><span id=\"MathJax-Span-54\" class=\"mo\">\u2220<\/span><span id=\"MathJax-Span-55\" class=\"mn\">4<\/span><\/span><\/span><\/span><\/span>\u00a0and\u00a0<span id=\"MathJax-Element-9-Frame\" class=\"MathJax\" style=\"display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mrow&gt;&lt;mo&gt;&amp;#x2220;&lt;\/mo&gt;&lt;mn&gt;6&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/math&gt;\"><span id=\"MathJax-Span-56\" class=\"math\" role=\"math\"><span id=\"MathJax-Span-57\" class=\"mrow\"><span id=\"MathJax-Span-58\" class=\"mrow\"><span id=\"MathJax-Span-59\" class=\"mo\">\u2220<\/span><span id=\"MathJax-Span-60\" class=\"mn\">6<\/span><\/span><\/span><\/span><\/span>\u00a0are congruent using the same method.<\/p>\n<p>Use the lines marked in the photo.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-82305\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-22.png\" alt=\"\" width=\"326\" height=\"223\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-22.png 326w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-22-300x205.png 300w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><\/p>\n<p><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" style=\"display: inline-table; font-style: normal; font-weight: 400; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: 0px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; color: #393939; font-family: 'Noto Sans', sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; background-color: #ffffff; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mrow&gt;&lt;mo&gt;&amp;#x2220;&lt;\/mo&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;mo&gt;&amp;#x2245;&lt;\/mo&gt;&lt;mo&gt;&amp;#x2220;&lt;\/mo&gt;&lt;mn&gt;7&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/math&gt;\"><span id=\"MathJax-Span-6\" class=\"math\" role=\"math\"><span id=\"MathJax-Span-7\" class=\"mrow\"><span id=\"MathJax-Span-8\" class=\"mrow\"><span id=\"MathJax-Span-9\" class=\"mo\"><\/span><\/span><\/span><\/span><\/span>Question 3.<br \/>\nIs b || a? Explain your reasoning.<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nThere is not any intersection between a and b<br \/>\nHence, from the above,<br \/>\nWe can conclude that b || a<\/p>\n<p>Question 4.<br \/>\nIs b \u22a5 c? Explain your reasoning.<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can observe that the angle between b and c is 90\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that b is perpendicular to c<\/p>\n<h3><a id=\"Exercise_3.4_Proofs_with_Perpendicular_Lines\"><\/a>Exercise 3.4 Proofs with Perpendicular Lines<\/h3>\n<p>Vocabulary and core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nThe perpendicular bisector of a segment is the line that passes through the _______________ of the segment at a _______________ angle.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48378\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 1\" width=\"587\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-1.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-1-300x31.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find &#8220;both\u201d answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38070\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-120.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 120\" width=\"191\" height=\"174\" \/><br \/>\nFind the distance from point X to <img loading=\"lazy\" class=\"alignnone size-full wp-image-38069\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-121.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 121\" width=\"34\" height=\"32\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38070\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-120.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 120\" width=\"191\" height=\"174\" \/><br \/>\nTo find the distance from point X to \\(\\overline{W Z}\\),<br \/>\nWe have to find the distance between X and Y i.e., XY<br \/>\nNow,<br \/>\nThe given points are:<br \/>\nX (-3, 3), Y (3, 1)<br \/>\nCompare the given points with<br \/>\n(x1, y1), (x2, y2)<br \/>\nNow,<br \/>\nXY = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nXY = \\(\\sqrt{(3 + 3)\u00b2 + (3 &#8211; 1)\u00b2}\\)<br \/>\nXY = \\(\\sqrt{(6)\u00b2 + (2)\u00b2}\\)<br \/>\nXY = 6.32<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance from point X to \\(\\overline{W Z}\\) is: 6.32<\/p>\n<p>Find XZ<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nX (-3, 3), Z (4, 4)<br \/>\nCompare the given points with<br \/>\n(x1, y1), (x2, y2)<br \/>\nNow,<br \/>\nXZ = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nXZ = \\(\\sqrt{(4 + 3)\u00b2 + (3 &#8211; 4)\u00b2}\\)<br \/>\nXZ = \\(\\sqrt{(7)\u00b2 + (1)\u00b2}\\)<br \/>\nXZ = 7.07<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of XZ is: 7.07<\/p>\n<p>Find the length of \\(\\overline{X Y}\\)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nX (-3, 3), Y (3, 1)<br \/>\nCompare the given points with<br \/>\n(x1, y1), (x2, y2)<br \/>\nNow,<br \/>\nXY = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nXY = \\(\\sqrt{(3 + 3)\u00b2 + (3 &#8211; 1)\u00b2}\\)<br \/>\nXY = \\(\\sqrt{(6)\u00b2 + (2)\u00b2}\\)<br \/>\nXY = 6.32<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of XY is: 6.32<\/p>\n<p>Find the distance from line l to point X.<br \/>\nAnswer:<br \/>\nTo find the distance from line l to point X,<br \/>\nWe have to find the distance between X and Y i.e., XY<br \/>\nNow,<br \/>\nThe given points are:<br \/>\nX (-3, 3), Y (3, 1)<br \/>\nCompare the given points with<br \/>\n(x1, y1), (x2, y2)<br \/>\nNow,<br \/>\nXY = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nXY = \\(\\sqrt{(3 + 3)\u00b2 + (3 &#8211; 1)\u00b2}\\)<br \/>\nXY = \\(\\sqrt{(6)\u00b2 + (2)\u00b2}\\)<br \/>\nXY = 6.32<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance from line l to point X is: 6.32<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3 and 4. find the distance from point A to <img loading=\"lazy\" class=\"alignnone size-full wp-image-38068\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-122.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 122\" width=\"30\" height=\"20\" \/>.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38067\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-123.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 123\" width=\"176\" height=\"194\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48379\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 3\" width=\"481\" height=\"139\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-3.png 481w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-3-300x87.png 300w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-124.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 124\" width=\"172\" height=\"173\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-124.png 172w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-124-150x150.png 150w\" sizes=\"(max-width: 172px) 100vw, 172px\" \/><br \/>\nAnswer:<br \/>\nTo find the distance from point A to \\(\\overline{X Z}\\),<br \/>\nWe have to find the distance between A and Y i.e., AY<br \/>\nNow,<br \/>\nThe given points are:<br \/>\nX (3, 3), Y (2, -1.5)<br \/>\nCompare the given points with<br \/>\n(x1, y1), (x2, y2)<br \/>\nNow,<br \/>\nXY = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nXY = \\(\\sqrt{(3 + 1.5)\u00b2 + (3 &#8211; 2)\u00b2}\\)<br \/>\nXY = \\(\\sqrt{(4.5)\u00b2 + (1)\u00b2}\\)<br \/>\nXY = 4.60<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance from point A to \\(\\overline{X Z}\\) is: 4.60<\/p>\n<p><strong>CONSTRUCTION<\/strong><br \/>\nIn Exercises 5-8, trace line m and point P. Then use a compass and straightedge to construct a line perpendicular to line m through point P.<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38065\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-125.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 125\" width=\"152\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-125.png 152w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-125-150x93.png 150w\" sizes=\"(max-width: 152px) 100vw, 152px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48380\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 5\" width=\"553\" height=\"352\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-5.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-5-300x191.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38064\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-126.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 126\" width=\"143\" height=\"126\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38064\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-126.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 126\" width=\"143\" height=\"126\" \/><br \/>\nNow,<br \/>\nUsing P as the center, draw two arcs intersecting with line m.<br \/>\nLabel the intersections as points X and Y.<br \/>\nUsing X and Y as centers and an appropriate radius, draw arcs that intersect.<br \/>\nLabel the intersection as Z. Draw \\(\\overline{P Z}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-82879\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-23.png\" alt=\"\" width=\"435\" height=\"232\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-23.png 435w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-23-300x160.png 300w\" sizes=\"(max-width: 435px) 100vw, 435px\" \/><\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38063\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-127.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 127\" width=\"129\" height=\"101\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48381\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-7.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 7\" width=\"584\" height=\"406\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-7.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-7-300x209.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38062\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-128.png\" alt=\"Math \" width=\"156\" height=\"46\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38062\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-128.png\" alt=\"Math \" width=\"156\" height=\"46\" \/><br \/>\nNow,<br \/>\nUsing P as the center and any radius, draw arcs intersecting m and label those intersections as X and Y.<br \/>\nUsing X as the center, open the compass so that it is greater than half of XP and draw an arc.<br \/>\nUsing Y as the center and retaining the same compass setting, draw an arc that intersects with the first<br \/>\nLabel the point of intersection as Z. Draw \\(\\overline{P Z}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-82883\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-24.png\" alt=\"\" width=\"407\" height=\"274\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-24.png 407w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-24-300x202.png 300w\" sizes=\"(max-width: 407px) 100vw, 407px\" \/><\/p>\n<p><strong>CONSTRUCTION<\/strong><br \/>\nIn Exercises 9 and 10, trace \\(\\overline{A B}\\). Then use a compass and straightedge to construct the perpendicular bisector of \\(\\overline{A B}\\)<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38061\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-129.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 129\" width=\"140\" height=\"82\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48382\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-9.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 9\" width=\"540\" height=\"244\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-9.png 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-9-300x136.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-130.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 130\" width=\"189\" height=\"82\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-130.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 130\" width=\"189\" height=\"82\" \/><br \/>\nNow,<br \/>\nUsing a compass setting greater than half of AB, draw two arcs using A and B as centers<br \/>\nConnect the points of intersection of the arcs with a straight line<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-82885\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-25.png\" alt=\"\" width=\"283\" height=\"167\" \/><\/p>\n<p><strong>ERROR ANALYSIS<\/strong><br \/>\nIn Exercises 11 and 12, describe and correct the error in the statement about the diagram.<br \/>\nQuestion 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38059\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-131.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 131\" width=\"278\" height=\"134\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48383\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-11.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 11\" width=\"574\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-11.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-11-300x59.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38058\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-132.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 132\" width=\"290\" height=\"150\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nAccording to the Perpendicular Transversal theorem,<br \/>\nThe distance from the perpendicular to the line is given as the distance between the point and the non-perpendicular line<br \/>\nSo,<br \/>\nFrom the given figure,<br \/>\nThe distance from point C to AB is the distance between point C and A i.e., AC<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance from point C to AB is: 12 cm<\/p>\n<p><strong>PROVING A THEOREM\u00a0<\/strong><br \/>\nIn Exercises 13 and 14, prove the theorem.<br \/>\nQuestion 13.<br \/>\nLinear Pair Perpendicular Theorem (Thm. 3. 10)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48384\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-13.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 13\" width=\"572\" height=\"672\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-13.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-13-255x300.png 255w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 14.<br \/>\nLines Perpendicular to a Transversal Theorem (Thm. 3.12)<br \/>\nAnswer:<br \/>\nIn a plane, if a line is perpendicular to one of the two parallel lines, then it is perpendicular to the other line also<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-82268\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-19.png\" sizes=\"(max-width: 309px) 100vw, 309px\" srcset=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-19.png 309w, https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-19-300x167.png 300w\" alt=\"\" width=\"309\" height=\"172\" \/><br \/>\nProof:<br \/>\nGiven: k || l, t \u22a5 k<br \/>\nProve: t \u22a5 l<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-82269\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-20.png\" sizes=\"(max-width: 453px) 100vw, 453px\" srcset=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-20.png 453w, https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-20-268x300.png 268w\" alt=\"\" width=\"453\" height=\"508\" \/><\/p>\n<p><strong>PROOF<\/strong><br \/>\nIn Exercises 15 and 16, use the diagram to write a proof of the statement.<\/p>\n<p>Question 15.<br \/>\nIf two intersecting lines are perpendicular. then they intersect to form four right angles.<br \/>\nGiven a \u22a5 b<br \/>\nProve \u22201, \u22202, \u22203, and \u22204 are right angles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38057\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-133.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 133\" width=\"180\" height=\"126\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48385\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-15.1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 15.1\" width=\"589\" height=\"606\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-15.1.png 589w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-15.1-292x300.png 292w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48386\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-15.2.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 15.2\" width=\"578\" height=\"393\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-15.2.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-15.2-300x204.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 16.<br \/>\nIf two sides of two adjacent acute angles are perpendicular, then the angles are complementary.<br \/>\nGiven \\(\\overrightarrow{B A}\\) \u22a5\\(\\vec{B}\\)C<br \/>\nProve \u22201 and \u22202 are complementary<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38056\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-134.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 134\" width=\"146\" height=\"143\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 17-22, determine which lines, if any, must be parallel. Explain your reasoning.<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38055\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-135.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 135\" width=\"149\" height=\"112\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48387\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-17.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 17\" width=\"584\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-17.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-17-300x57.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38054\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-136.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 136\" width=\"160\" height=\"115\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38054\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-136.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 136\" width=\"160\" height=\"115\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that a is perpendicular to both the lines b and c<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nBy using the Perpendicular transversal theorem,<br \/>\na is both perpendicular to b and c and b is parallel to c<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38051\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-139.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 139\" width=\"149\" height=\"109\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48388\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-19.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 19\" width=\"594\" height=\"91\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-19.png 594w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-19-300x46.png 300w\" sizes=\"(max-width: 594px) 100vw, 594px\" \/><\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38050\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-140.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 140\" width=\"159\" height=\"110\" \/><br \/>\nAnswer:<br \/>\nThe given figure is;<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38050\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-140.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 140\" width=\"159\" height=\"110\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\na is perpendicular to d and b is perpendicular to c<br \/>\nFor parallel lines, we can&#8217;t say anything<br \/>\nHence, from the above,<br \/>\nBy using the Perpendicular transversal theorem,<br \/>\na is perpendicular to d and b isperpendicular to c<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38049\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-141.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 141\" width=\"158\" height=\"171\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48389\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-21.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 21\" width=\"583\" height=\"66\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-21.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-21-300x34.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38048\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-142.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 142\" width=\"177\" height=\"156\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38048\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-142.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 142\" width=\"177\" height=\"156\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nw \u22a5 v and w\u22a5 y<br \/>\nSo,<br \/>\nWe can say that w and v are parallel lines by &#8220;Perpendicular Transversal Theorem&#8221;<br \/>\nWe can observe that<br \/>\nz \u22a5 x and w \u22a5 z<br \/>\nSo,<br \/>\nWe can say that w and x are parallel lines by &#8220;Perpendicular Transversal theorem&#8221;<\/p>\n<p>Question 23.<br \/>\n<strong>USING STRUCTURE<\/strong><br \/>\nFind all the unknown angle measures in the diagram. Justify your answer for cacti angle measure.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38047\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-143.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 143\" width=\"194\" height=\"130\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48390\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-23.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 23\" width=\"572\" height=\"337\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-23.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-23-300x177.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 24.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims that because you can find the distance from a point to a line, you should be able to find the distance between any two lines. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\nNo, your friend is not correct<\/p>\n<p>Explanation:<br \/>\nIt is given that your friend claims that because you can find the distance from a point to a line, you should be able to find the distance between any two lines<br \/>\nNow,<br \/>\nThis can be proven by following the below steps:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-82897\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-26.png\" alt=\"\" width=\"737\" height=\"263\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-26.png 737w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-26-300x107.png 300w\" sizes=\"(max-width: 737px) 100vw, 737px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that your friend is not correct<\/p>\n<p>Question 25.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nFind the value of x when a \u22a5 b and b || c.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38046\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-144.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 144\" width=\"276\" height=\"97\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48391\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-25.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 25\" width=\"567\" height=\"347\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-25.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-25-300x184.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nYou are trying to cross a stream from point A. Which point should you jump to in order to jump the shortest distance? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38045\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-145.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 145\" width=\"316\" height=\"162\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-145.png 316w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-145-300x154.png 300w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nPoint A is perpendicular to Point C<br \/>\nWe know that,<br \/>\nAccording to Perpendicular Transversal Theorem,<br \/>\nThe distance between the perpendicular points is the shortest<br \/>\nHence, from the above,<br \/>\nWe can conclude that in order to jump the shortest distance, you have to jump to point C from point A<\/p>\n<p>Question 27.<br \/>\n<strong>ATTENDING TO PRECISION<\/strong><br \/>\nIn which of the following diagrams is \\(\\overline{A C}\\) || \\(\\overline{B D}\\) and \\(\\overline{A C}\\) \u22a5 \\(\\overline{C D}\\)? Select all that apply.<br \/>\n(A) <img loading=\"lazy\" class=\"alignnone size-full wp-image-38044\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-146.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 146\" width=\"111\" height=\"111\" \/><br \/>\n(B) <img loading=\"lazy\" class=\"alignnone size-full wp-image-38043\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-147.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 147\" width=\"103\" height=\"125\" \/><br \/>\n(C) <img loading=\"lazy\" class=\"alignnone size-full wp-image-38042\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-148.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 148\" width=\"109\" height=\"114\" \/><br \/>\n(D) <img loading=\"lazy\" class=\"alignnone size-full wp-image-38041\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-149.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 149\" width=\"119\" height=\"101\" \/><br \/>\n(E) <img loading=\"lazy\" class=\"alignnone size-full wp-image-38040\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-150.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 150\" width=\"181\" height=\"110\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48392\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-27.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 27\" width=\"402\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-27.png 402w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-27-300x25.png 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nThe postulates and theorems in this book represent Euclidean geometry. In spherical geometry, all points are points on the surface of a sphere. A line is a circle on the sphere whose diameter is equal to the diameter of the sphere. In spherical geometry. how many right angles are formed by two perpendicular lines? Justify your answer.<br \/>\nAnswer:<br \/>\nIt is given that in spherical geometry, all points are points on the surface of a sphere. A line is a circle on the sphere whose diameter is equal to the diameter of the sphere.<br \/>\nWe know that,<br \/>\nIn Euclidean geometry, the two perpendicular lines form 4 right angles whereas, In spherical geometry, the two perpendicular lines form 8 right angles according to the &#8220;Parallel lines Postulate&#8221; in spherical geometry.<br \/>\nHence, from the above,<br \/>\nWe can conclude that 8 right angles are formed by two perpendicular lines in spherical geometry<\/p>\n<p>Question 29.<br \/>\n<strong>CONSTRUCTION<\/strong><br \/>\nConstruct a square of side length AB<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38039\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-151.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 151\" width=\"175\" height=\"31\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48393\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-29.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 29\" width=\"343\" height=\"253\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-29.png 343w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-29-300x221.png 300w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nThe painted line segments that brain the path of a crosswalk are usually perpendicular to the crosswalk. Sketch what the segments in the photo would look like if they were perpendicular to the crosswalk. Which type of line segment requires less paint? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38038\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-152.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 152\" width=\"330\" height=\"322\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-152.png 330w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-152-300x293.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nTwo lines, a and b, are perpendicular to line c. Line d is parallel to line c. The distance between lines a and b is x meters. The distance between lines c and d is y meters. What shape is formed by the intersections of the four lines?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48394\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-31.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 31\" width=\"593\" height=\"117\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-31.png 593w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-31-300x59.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nFind the distance between the lines with the equations y = \\(\\frac{3}{2}\\) + 4 and &#8211; 3x + 2y = &#8211; 1.<br \/>\nAnswer:<br \/>\nThe given equations are:<br \/>\ny = \\(\\frac{3}{2}\\) + 4 and -3x + 2y = -1<br \/>\ny = \\(\\frac{3}{2}\\) + 4 and y = \\(\\frac{3}{2}\\)x &#8211; \\(\\frac{1}{2}\\)<br \/>\nCompare the given equations with<br \/>\ny = mx + c<br \/>\nSo,<br \/>\nm1 = m2 = \\(\\frac{3}{2}\\)<br \/>\nc1 = 4<br \/>\nc2= &#8211;\\(\\frac{1}{2}\\)<br \/>\nWe know that,<br \/>\nThe distance between the two parallel lines is:<br \/>\nd = | c1 &#8211; c2 |<br \/>\nSo,<br \/>\nThe distance between the given 2 parallel lines = | c1 &#8211; c2 |<br \/>\n= | 4 + \\(\\frac{1}{2}\\) |<br \/>\n= \\(\\frac{9}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance between the given lines is: \\(\\frac{7}{2}\\)<\/p>\n<p>Question 33.<br \/>\n<strong>WRITING<\/strong><br \/>\nDescribe how you would find the distance from a point to a plane. Can you find the distance from a line to a plane? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48395\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-33.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 33\" width=\"569\" height=\"226\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-33.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-33-300x119.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Maintaining Mathematical Proficiency<\/p>\n<p>Simplify the ratio.<\/p>\n<p>Question 34.<br \/>\n\\(\\frac{6-(-4)}{8-3}\\)<br \/>\nAnswer:<br \/>\nThe given expression is:<br \/>\n\\(\\frac{6 &#8211; (-4)}{8 &#8211; 3}\\)<br \/>\n= \\(\\frac{6 + 4}{8 &#8211; 3}\\)<br \/>\n= \\(\\frac{10}{5}\\)<br \/>\n= 2<br \/>\nHence,f rom the above,<br \/>\nWe can conclude that the value of the given expression is: 2<\/p>\n<p>Question 35.<br \/>\n\\(\\frac{3-5}{4-1}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48396\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-35.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 35\" width=\"147\" height=\"56\" \/><\/p>\n<p>Question 36.<br \/>\n\\(\\frac{8-(-3)}{7-(-2)}\\)<br \/>\nAnswer:<br \/>\nThe given expression is:<br \/>\n\\(\\frac{8 &#8211; (-3)}{7 &#8211; (-2)}\\)<br \/>\n= \\(\\frac{8 + 3}{7 + 2}\\)<br \/>\n= \\(\\frac{11}{9}\\)<br \/>\nHence,f rom the above,<br \/>\nWe can conclude that the value of the given expression is: \\(\\frac{11}{9}\\)<\/p>\n<p>Question 37.<br \/>\n\\(\\frac{13-4}{2-(-1)}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48397\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-37.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 37\" width=\"194\" height=\"54\" \/><\/p>\n<p>Identify the slope and the y-intercept of the line.<\/p>\n<p>Question 38.<br \/>\ny = 3x + 9<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = 3x + 9 &#8212;&#8212;-(1)<br \/>\nCompare the above equation with<br \/>\ny = mx + c<br \/>\nWhere,<br \/>\nm is the slope<br \/>\nc is the y-intercept<br \/>\nBy comparing eq. (1) with the y = mx + c,<br \/>\nm = 3 and c = 9<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe slope is: 3<br \/>\nThe y-intercept is: 9<\/p>\n<p>Question 39.<br \/>\ny = &#8211;\\(\\frac{1}{2}\\)x + 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48398\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-39.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 39\" width=\"280\" height=\"42\" \/><\/p>\n<p>Question 40.<br \/>\ny = \\(\\frac{1}{6}\\)x &#8211; 8<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = \\(\\frac{1}{6}\\)x &#8211; 8<br \/>\nCompare the above equation with<br \/>\ny = mx + c<br \/>\nSo,<br \/>\nm = \\(\\frac{1}{6}\\) and c = -8<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe slope is: \\(\\frac{1}{6}\\)<br \/>\nThe y-intercept is: -8<\/p>\n<p>Question 41.<br \/>\ny = &#8211; 8x &#8211; 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48399\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-41.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 41\" width=\"319\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-41.png 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-3.4-a-41-300x31.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><\/p>\n<h3><a id=\"3.5_Equations_of_Parallel_and_Perpendicular_Lines\"><\/a>3.5 Equations of Parallel and Perpendicular Lines<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Writing Equations of Parallel and Perpendicular Lines<\/p>\n<p>Work with a partner: Write an equation of the line that is parallel or perpendicular to the given line and passes through the given point. Use a graphing calculator to verify your answer. What is the relationship between the slopes?<br \/>\na.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38429\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-153.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 153\" width=\"193\" height=\"138\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38429\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-153.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 153\" width=\"193\" height=\"138\" \/><br \/>\nWe know that,<br \/>\nFrom the given figure,<br \/>\nWe can observe that the given lines are parallel lines<br \/>\nNow,<br \/>\nThe equation for another line is:<br \/>\ny = \\(\\frac{3}{2}\\)x + c<br \/>\nSubstitute (0, 2) in the above equation<br \/>\nSo,<br \/>\n2 = 0 + c<br \/>\nc = 2<br \/>\nSo,<br \/>\nThe equation for another parallel line is:<br \/>\ny = \\(\\frac{3}{2}\\)x + 2<br \/>\nWhen we compare the given equation with the obtained equation,<br \/>\nWe can observe that the slopes are the same and the y-intercepts are different<br \/>\nWe know that,<br \/>\nThe lines that have the same slope and different y-intercepts are &#8220;Parallel lines&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that the parallel lines are:<br \/>\ny = \\(\\frac{3}{2}\\)x &#8211; 1<br \/>\ny = \\(\\frac{3}{2}\\)x + 2<\/p>\n<p>b.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38428\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-154.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 154\" width=\"223\" height=\"137\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38428\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-154.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 154\" width=\"223\" height=\"137\" \/><br \/>\nWe know that,<br \/>\nFrom the given figure,<br \/>\nWe can observe that the given lines are perpendicular lines<br \/>\nThe equation for another line is:<br \/>\ny = \\(\\frac{3}{2}\\)x + c<br \/>\nWe know that,<br \/>\nThe slope of perpendicular lines is: -1<br \/>\nSo,<br \/>\nm1m2 = -1<br \/>\n\\(\\frac{3}{2}\\) . m2 = -1<br \/>\nSo,<br \/>\nm2 = &#8211;\\(\\frac{2}{3}\\)<br \/>\nSo,<br \/>\ny = &#8211;\\(\\frac{2}{3}\\)x + c<br \/>\nSubstitute (0, 1) in the above equation<br \/>\nSo,<br \/>\n1 = 0 + c<br \/>\nc = 1<br \/>\nSo,<br \/>\nThe equation for another perpendicular line is:<br \/>\ny = &#8211;\\(\\frac{2}{3}\\)x + 1<br \/>\nWhen we compare the given equation with the obtained equation,<br \/>\nWe can observe that the product of the slopes are -1 and the y-intercepts are different<br \/>\nWe know that,<br \/>\nThe lines that have the slopes product -1 and different y-intercepts are &#8220;Perpendicular lines&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that the perpendicular lines are:<br \/>\ny = \\(\\frac{3}{2}\\)x &#8211; 1<br \/>\ny = &#8211;\\(\\frac{2}{3}\\)x + 1<\/p>\n<p>c.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38427\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-155.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 155\" width=\"221\" height=\"137\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38427\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-155.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 155\" width=\"221\" height=\"137\" \/><br \/>\nWe know that,<br \/>\nFrom the given figure,<br \/>\nWe can observe that the given lines are parallel lines<br \/>\nNow,<br \/>\nThe equation for another line is:<br \/>\ny = \\(\\frac{1}{2}\\)x + c<br \/>\nSubstitute (2, -2) in the above equation<br \/>\nSo,<br \/>\n-2 = \\(\\frac{1}{2}\\) (2) + c<br \/>\n-2 = 1 + c<br \/>\nc = 2 &#8211; 1<br \/>\nc = -3<br \/>\nSo,<br \/>\nThe equation for another parallel line is:<br \/>\ny = \\(\\frac{1}{2}\\)x &#8211; 3<br \/>\nWhen we compare the given equation with the obtained equation,<br \/>\nWe can observe that the slopes are the same and the y-intercepts are different<br \/>\nWe know that,<br \/>\nThe lines that have the same slope and different y-intercepts are &#8220;Parallel lines&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that the parallel lines are:<br \/>\ny = \\(\\frac{1}{2}\\)x + 2<br \/>\ny = \\(\\frac{1}{2}\\)x &#8211; 3<\/p>\n<p>d.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38426\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-156.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 156\" width=\"216\" height=\"138\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38426\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-156.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 156\" width=\"216\" height=\"138\" \/><br \/>\nWe know that,<br \/>\nFrom the given figure,<br \/>\nWe can observe that the given lines are perpendicular lines<br \/>\nThe equation for another line is:<br \/>\ny = \\(\\frac{1}{2}\\)x + c<br \/>\nWe know that,<br \/>\nThe slope of perpendicular lines is: -1<br \/>\nSo,<br \/>\nm1m2 = -1<br \/>\n\\(\\frac{1}{2}\\) . m2 = -1<br \/>\nSo,<br \/>\nm2 = -2<br \/>\nSo,<br \/>\ny = -2x + c<br \/>\nSubstitute (2, -3) in the above equation<br \/>\nSo,<br \/>\n-3 = -2 (2) + c<br \/>\n-3 = -4 + c<br \/>\nc = 4 &#8211; 3<br \/>\nc = 1<br \/>\nSo,<br \/>\nThe equation for another perpendicular line is:<br \/>\ny = -2x + 1<br \/>\nWhen we compare the given equation with the obtained equation,<br \/>\nWe can observe that the product of the slopes are -1 and the y-intercepts are different<br \/>\nWe know that,<br \/>\nThe lines that have the slopes product -1 and different y-intercepts are &#8220;Perpendicular lines&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that the perpendicular lines are:<br \/>\ny = \\(\\frac{1}{2}\\)x + 2<br \/>\ny = -2x + 1<\/p>\n<p>e.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38425\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-157.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 157\" width=\"216\" height=\"136\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38425\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-157.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 157\" width=\"216\" height=\"136\" \/><br \/>\nWe know that,<br \/>\nFrom the given figure,<br \/>\nWe can observe that the given lines are parallel lines<br \/>\nNow,<br \/>\nThe equation for another line is:<br \/>\ny = -2x + c<br \/>\nSubstitute (0, -2) in the above equation<br \/>\nSo,<br \/>\n-2 = 0 + c<br \/>\nc = -2<br \/>\nSo,<br \/>\nThe equation for another parallel line is:<br \/>\ny = -2x &#8211; 2<br \/>\nWhen we compare the given equation with the obtained equation,<br \/>\nWe can observe that the slopes are the same and the y-intercepts are different<br \/>\nWe know that,<br \/>\nThe lines that have the same slope and different y-intercepts are &#8220;Parallel lines&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that the parallel lines are:<br \/>\ny = -2x + 2<br \/>\ny = -2x &#8211; 2<\/p>\n<p>f.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38424\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-158.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 158\" width=\"216\" height=\"134\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38424\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-158.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 158\" width=\"216\" height=\"134\" \/><br \/>\nWe know that,<br \/>\nFrom the given figure,<br \/>\nWe can observe that the given lines are perpendicular lines<br \/>\nThe equation for another line is:<br \/>\ny = -2x + c<br \/>\nWe know that,<br \/>\nThe slope of perpendicular lines is: -1<br \/>\nSo,<br \/>\nm1m2 = -1<br \/>\n-2 . m2 = -1<br \/>\nSo,<br \/>\nm2 = \\(\\frac{1}{2}\\)<br \/>\nSo,<br \/>\ny = \\(\\frac{1}{2}\\)x + c<br \/>\nSubstitute (4, 0) in the above equation<br \/>\nSo,<br \/>\n0 = \\(\\frac{1}{2}\\) (4) + c<br \/>\n0 = 2 + c<br \/>\nc = 0 &#8211; 2<br \/>\nc = -2<br \/>\nSo,<br \/>\nThe equation for another perpendicular line is:<br \/>\ny = \\(\\frac{1}{2}\\)x &#8211; 2<br \/>\nWhen we compare the given equation with the obtained equation,<br \/>\nWe can observe that the product of the slopes are -1 and the y-intercepts are different<br \/>\nWe know that,<br \/>\nThe lines that have the slopes product -1 and different y-intercepts are &#8220;Perpendicular lines&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that the perpendicular lines are:<br \/>\ny = \\(\\frac{1}{2}\\)x &#8211; 2<br \/>\ny = -2x + 2<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Writing Equations of Parallel and Perpendicular Lines<\/p>\n<p>Work with a partner: Write the equations of the parallel or perpendicular lines. Use a graphing calculator to verify your answers.<\/p>\n<p>a.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38423\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-159.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 159\" width=\"191\" height=\"135\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38423\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-159.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 159\" width=\"191\" height=\"135\" \/><br \/>\nFrom the given graph,<br \/>\nWe can observe that<br \/>\nThe given lines are the parallel lines<br \/>\nNow,<br \/>\nThe coordinates of the line of the first equation are: (-1.5, 0), and (0, 3)<br \/>\nThe coordinates of the line of the second equation are: (1, 0), and (0, -2)<br \/>\nCompare the given coordinates with<br \/>\nA (x1, y1), and B (x2, y2)<br \/>\nWe know that,<br \/>\nSlope (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nNow,<br \/>\nThe slope of the line of the first equation is:<br \/>\nm = \\(\\frac{3 &#8211; 0}{0 + 1.5}\\)<br \/>\nm = \\(\\frac{3}{1.5}\\)<br \/>\nm = 2<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe standard linear equation is:<br \/>\ny = mx + c<br \/>\nSo,<br \/>\ny = 2x + c<br \/>\nWe know that,<br \/>\nFor parallel lines,<br \/>\nThe slopes are the same but the y-intercepts are different<br \/>\nHence,<br \/>\nThe given parallel line equations are:<br \/>\ny = 2x + c1<br \/>\ny = 2x + c2<\/p>\n<p>b.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38422\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-160.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 160\" width=\"190\" height=\"138\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38422\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-160.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 160\" width=\"190\" height=\"138\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nThe given lines are perpendicular lines<br \/>\nSo,<br \/>\nThe coordinates of the line of the first equation are: (0, -3), and (-1.5, 0)<br \/>\nThe coordinates of the line of the second equation are: (-4, 0), and (0, 2)<br \/>\nCompare the given coordinates with<br \/>\nA (x1, y1), and B (x2, y2)<br \/>\nWe know that,<br \/>\nSlope (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nNow,<br \/>\nThe slope of the line of the first equation is:<br \/>\nm = \\(\\frac{0 + 3}{0 &#8211; 1.5}\\)<br \/>\nm = \\(\\frac{3}{-1.5}\\)<br \/>\nm = \\(\\frac{-30}{15}\\)<br \/>\nm = -2<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe standard linear equation is:<br \/>\ny = mx + c<br \/>\nSo,<br \/>\ny = -2x + c<br \/>\nWe know that,<br \/>\nFor perpediclar lines,<br \/>\nThe product of the slopes is -1 and the y-intercepts are different<br \/>\nSo,<br \/>\nm1 \u00d7 m2 = -1<br \/>\n-2 \u00d7 m2 = -1<br \/>\nm2 = \\(\\frac{1}{2}\\)<br \/>\nHence,<br \/>\nThe given perpendicular line equations are:<br \/>\ny = -2x + c1<br \/>\ny = \\(\\frac{1}{2}\\)x + c2<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 3.<br \/>\nHow can you write an equation of a line that is parallel or perpendicular to a given line and passes through a given point?<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nTo be proficient in math, you need to analyze relationships mathematically to draw conclusions.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe standard form of a linear equation is:<br \/>\ny = mx + c<br \/>\nNow,<br \/>\nFor parallel lines,<br \/>\nWe know that,<br \/>\nThe slopes are the same and the y-intercepts are different<br \/>\nSo,<br \/>\nTo find the y-intercept of the equation that is parallel to the given equation, substitute the given point and find the value of c<br \/>\nNow,<br \/>\nFor perpendicular lines,<br \/>\nwe know that,<br \/>\nThe product of the slopes is -1<br \/>\nSo,<br \/>\nThe slope of the equation that is perpendicular to the given equation is: &#8211;\\(\\frac{1}{m}\\)<br \/>\nTo find the y-intercept of the equation that is perpendicular to the given equation, substitute the given point and find the value of c<\/p>\n<p>Question 4.<br \/>\nWrite an equation of the line that is (a) parallel and (b) perpendicular to the line y = 3x + 2 and passes through the point (1, -2).<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = 3x + 2<br \/>\nThe given point is: (1, -2)<br \/>\na) Parallel line equation:<br \/>\nWe know that,<br \/>\nThe slope of the parallel equations are the same<br \/>\nSo,<br \/>\nThe slope of the equation that is parallel t the given equation is: 3<br \/>\nNow,<br \/>\nThe equation that is parallel to the given equation is:<br \/>\ny = 3x + c<br \/>\nSubstitute (1, -2) in the above equation<br \/>\nSo,<br \/>\n-2 = 3 (1) + c<br \/>\n-2 &#8211; 3 = c<br \/>\nc = -5<br \/>\nHence,<br \/>\nThe equation of the line that is parallel to the given equation is:<br \/>\ny = 3x &#8211; 5<br \/>\nb) Perpendicular line equation:<br \/>\nWe know that,<br \/>\nThe product of the slope of the perpendicular equations is: -1<br \/>\nSo,<br \/>\nm1 m2 = -1<br \/>\n3m2 = -1<br \/>\nSo,<br \/>\nm2 = &#8211;\\(\\frac{1}{3}\\)<br \/>\nSo,<br \/>\nThe slope of the equation that is parallel t the given equation is: &#8211;\\(\\frac{1}{3}\\)<br \/>\nNow,<br \/>\nThe equation that is perpendicular to the given equation is:<br \/>\ny = &#8211;\\(\\frac{1}{3}\\)x + c<br \/>\nSubstitute (1, -2) in the above equation<br \/>\nSo,<br \/>\n-2 = &#8211;\\(\\frac{1}{3}\\) (-2) + c<br \/>\n-2 &#8211; \\(\\frac{2}{3}\\) = c<br \/>\nc = &#8211;\\(\\frac{8}{3}\\)<br \/>\nHence,<br \/>\nThe equation of the line that is perpendicular to the given equation is:<br \/>\ny = &#8211;\\(\\frac{1}{3}\\)x &#8211;\\(\\frac{8}{3}\\)<\/p>\n<h3><a id=\"Lesson_3.5_Equations_of_Parallel_and_Perpendicular_Lines\"><\/a>Lesson 3.5 Equations of Parallel and Perpendicular Lines<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio.<\/p>\n<p>Question 1.<br \/>\nA(1, 3), B(8, 4); 4 to 1<br \/>\nAnswer:<br \/>\nThe given coordinates are: A (1, 3), and B (8, 4)<br \/>\nCompare the given points with<br \/>\nA (x1, y1), and B (x2, y2)<br \/>\nIt is given that<br \/>\nAP : PB = 4 : 1<br \/>\nSo,<br \/>\nWe have to divide AB into 5 parts<br \/>\nNow,<br \/>\nWe know that,<br \/>\nSlope (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\nSlope of AB = \\(\\frac{4 &#8211; 3}{8 &#8211; 1}\\)<br \/>\nSlope of AB = \\(\\frac{1}{7}\\)<br \/>\nNow,<br \/>\nTo find the coordinates of P, add slope to AP and PB<br \/>\nSo,<br \/>\nP = (4 + (4 \/ 5) \u00d7 7, 1 + (4 \/ 5) \u00d7 1)<br \/>\nP = (22.4, 1.8)<br \/>\nHence, from he above,<br \/>\nWe can conclude that<br \/>\nThe coordinates of P are (22.4, 1.8)<\/p>\n<p>Question 2.<br \/>\nA(- 2, 1), B(4, 5); 3 to 7<br \/>\nAnswer:<br \/>\nThe given coordinates are: A (-2, 1), and B (4, 5)<br \/>\nCompare the given points with<br \/>\nA (x1, y1), and B (x2, y2)<br \/>\nIt is given that<br \/>\nAP : PB = 3 : 7<br \/>\nSo,<br \/>\nWe have to divide AB into 10 parts<br \/>\nNow,<br \/>\nWe know that,<br \/>\nSlope (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\nSlope of AB = \\(\\frac{5 &#8211; 1}{4 + 2}\\)<br \/>\nSlope of AB = \\(\\frac{4}{6}\\)<br \/>\nSlope of AB = \\(\\frac{2}{3}\\)<br \/>\nNow,<br \/>\nTo find the coordinates of P, add slope to AP and PB<br \/>\nSo,<br \/>\nP = (3 + (\\(\\frac{3}{10}\\) \u00d7 3), 7 + (\\(\\frac{3}{10}\\) \u00d7 2))<br \/>\nP = (3.9, 7.6)<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe coordinates of P are (3.9, 7.6)<\/p>\n<p>Question 3.<br \/>\nDetermine which of the lines are parallel and which of the lines are perpendicular.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38421\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-161.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 161\" width=\"203\" height=\"172\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38421\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-161.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 161\" width=\"203\" height=\"172\" \/><br \/>\nFrom the given figure,<br \/>\nThe coordinates of line a are: (0, 2), and (-2, -2)<br \/>\nThe coordinates of line b are: (2, 3), and (0, -1)<br \/>\nThe coordinates of line c are: (4, 2), and (3, -1)<br \/>\nThe coordinates of line d are: (-3, 0), and (0, -1)<br \/>\nNow,<br \/>\nCompare the given coordinates with (x1, y1), and (x2, y2)<br \/>\nSo,<br \/>\nThe slope of line a (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{-2 &#8211; 2}{-2 &#8211; 0}\\)<br \/>\n= \\(\\frac{-4}{-2}\\)<br \/>\n= 2<\/p>\n<p>The slope of line b (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{-1 &#8211; 3}{0 &#8211; 2}\\)<br \/>\n= \\(\\frac{-4}{-2}\\)<br \/>\n= 2<\/p>\n<p>The slope of line c (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{-1 &#8211; 2}{3 &#8211; 4}\\)<br \/>\n= \\(\\frac{-3}{-1}\\)<br \/>\n= 3<\/p>\n<p>The slope of line d (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{-1 &#8211; 0}{0 + 3}\\)<br \/>\n= \\(\\frac{-1}{3}\\)<br \/>\n= &#8211;\\(\\frac{1}{3}\\)<br \/>\nWe know that,<br \/>\nThe parallel lines have the same slopes<br \/>\nThe perpendicular lines have the product of slopes equal to -1<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nLinea and Line b are parallel lines<br \/>\nLine c and Line d are perpendicular lines<\/p>\n<p>Question 4.<br \/>\nWrite an equation of the line that passes through the point (1, 5) and is<br \/>\n(a) parallel to the line y = 3x &#8211; 5 and<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = 3x &#8211; 5<br \/>\nThe given point is: (1, 5)<br \/>\nWe know that,<br \/>\nThe parallel lines have the same slope<br \/>\nCompare the given equation with<br \/>\ny = mx + c<br \/>\nSo,<br \/>\nThe slope of the parallel line that passes through (1, 5) is: 3<br \/>\nSo,<br \/>\nThe equation of the parallel line that passes through (1, 5) is<br \/>\ny = 3x + c<br \/>\nTo find the value of c, substitute (1, 5) in the above equation<br \/>\nSo,<br \/>\n5 = 3 (1) + c<br \/>\nc = 5 &#8211; 3<br \/>\nc = 2<br \/>\nHence,<br \/>\nThe equation of the parallel line that passes through (1, 5) is:<br \/>\ny = 3x + 2<\/p>\n<p>(b) perpendicular to the line y = 3x &#8211; 5.<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = 3x &#8211; 5<br \/>\nThe given point is: (1, 5)<br \/>\nWe know that,<br \/>\nThe product of the slopes of the perpendicular lines is equal to -1<br \/>\nNow,<br \/>\nCompare the given equation with<br \/>\ny = mx + c<br \/>\nSo,<br \/>\nm = 3<br \/>\nNow,<br \/>\nThe slope of the perpendicular line that passes through (1, 5) is:<br \/>\nm1m2 = -1<br \/>\n3m2 = -1<br \/>\nm2 = &#8211;\\(\\frac{1}{3}\\)<br \/>\nNow,<br \/>\nThe equation of the perpendicular line that passes through (1, 5) is:<br \/>\ny = &#8211;\\(\\frac{1}{3}\\)x + c<br \/>\nTo find the value of c, substitute (1, 5) in the above equation<br \/>\nSo,<br \/>\n5 = &#8211;\\(\\frac{1}{3}\\) + c<br \/>\nc = 5 + \\(\\frac{1}{3}\\)<br \/>\nc = \\(\\frac{16}{3}\\)<br \/>\nHence,<br \/>\nThe equation of the perpendicular line that passes through (1, 5) is:<br \/>\ny = &#8211;\\(\\frac{1}{3}\\)x + \\(\\frac{16}{3}\\)<\/p>\n<p>Question 5.<br \/>\nHow do you know that the lines x = 4 and y = 2 are perpendiculars?<br \/>\nAnswer:<br \/>\nThe given lines are:<br \/>\nx = 4 and y = 2<br \/>\nWe know that,<br \/>\nThe line x = 4 is a vertical line that has the right angle i.e., 90\u00b0<br \/>\nThe line y = 4 is a horizontal line that have the straight angle i.e., 0\u00b0<br \/>\nSo,<br \/>\nThe angle at the intersection of the 2 lines = 90\u00b0 &#8211; 0\u00b0 = 90\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the lines x = 4 and y = 2 are perpendicular lines<\/p>\n<p>Question 6.<br \/>\nFind the distance from the point (6, 4) to the line y = x + 4.<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = x + 4<br \/>\nCompare the given equation with<br \/>\nax + by + c = 0<br \/>\nSo,<br \/>\nx &#8211; y + 4 = 0<br \/>\nSo,<br \/>\na = 1, and b = -1<br \/>\nThe given point is: (6, 4)<br \/>\nWe know that,<br \/>\nThe distance from the point (x, y) to the line ax + by + c = 0 is:<br \/>\nd = | ax + by + c| \/\\(\\sqrt{a\u00b2 + b\u00b2}\\)<br \/>\nd = | x &#8211; y + 4 | \/ \\(\\sqrt{1\u00b2 + (-1)\u00b2}\\)<br \/>\nd = | x &#8211; y + 4 | \/ \\(\\sqrt{2}\\)}<br \/>\nSubstitute (6, 4) in the above equation<br \/>\nSo,<br \/>\nd = | 6 &#8211; 4 + 4 |\/ \\(\\sqrt{2}\\)}<br \/>\nd = 3\u221a2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance from the given point to the given line is: 3\u221a2<\/p>\n<p>Question 7.<br \/>\nFind the distance from the point (- 1, 6) to the line y = &#8211; 2x.<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = -2x<br \/>\nCompare the given equation with<br \/>\nax + by + c = 0<br \/>\nSo,<br \/>\n2x + y = 0<br \/>\nSo,<br \/>\na = 2, and b = 1<br \/>\nThe given point is: (-1, 6)<br \/>\nWe know that,<br \/>\nThe distance from the point (x, y) to the line ax + by + c = 0 is:<br \/>\nd = | ax + by + c| \/\\(\\sqrt{a\u00b2 + b\u00b2}\\)<br \/>\nd = | 2x + y | \/ \\(\\sqrt{2\u00b2 + (1)\u00b2}\\)<br \/>\nd = | 2x + y | \/ \\(\\sqrt{5}\\)}<br \/>\nSubstitute (-1, 6) in the above equation<br \/>\nSo,<br \/>\nd = | -2 + 6 |\/ \\(\\sqrt{5}\\)<br \/>\nd = \\(\\frac{4}{\u221a5}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance from the given point to the given line is: \\(\\frac{4}{\u221a5}\\)<\/p>\n<h3><a id=\"Exercise_3.5_Equations_of_Parallel_and_Perpendicular_Lines\"><\/a>Exercise 3.5 Equations of Parallel and Perpendicular Lines<\/h3>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nA _________ line segment AB is a segment that represents moving from point A to point B.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48400\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-1.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 1\" width=\"538\" height=\"52\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-1.png 538w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-1-300x29.png 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nHow are the slopes of perpendicular lines related?<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe &#8220;Perpendicular lines&#8221; are lines that intersect at right angles.<br \/>\nIf you multiply the\u00a0slopes\u00a0of two\u00a0perpendicular lines in the plane, you get \u22121 i.e., the slopes of perpendicular lines are opposite reciprocals<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3 &#8211; 6. find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio.<\/p>\n<p>Question 3.<br \/>\nA(8, 0), B(3, &#8211; 2); 1 to 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48401\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-3.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 3\" width=\"576\" height=\"307\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-3.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-3-300x160.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 4.<br \/>\nA(- 2, &#8211; 4), B(6, 1); 3 to 2<br \/>\nAnswer:<br \/>\nThe given coordinates are: A (-2, -4), and B (6, 1)<br \/>\nCompare the given points with<br \/>\nA (x1, y1), and B (x2, y2)<br \/>\nIt is given that<br \/>\nAP : PB = 3 : 2<br \/>\nSo,<br \/>\nWe have to divide AB into 5 parts<br \/>\nNow,<br \/>\nWe know that,<br \/>\nSlope (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\nSlope of AB = \\(\\frac{1 + 4}{6 + 2}\\)<br \/>\nSlope of AB = \\(\\frac{5}{8}\\)<br \/>\nNow,<br \/>\nTo find the coordinates of P, add slope to AP and PB<br \/>\nSo,<br \/>\nP = (3 + (3 \/ 5) \u00d7 8, 2 + (3 \/ 5) \u00d7 5)<br \/>\nP = (7.8, 5)<br \/>\nHence, from he above,<br \/>\nWe can conclude that<br \/>\nThe coordinates of P are (7.8, 5)<\/p>\n<p>Question 5.<br \/>\nA(1, 6), B(- 2, &#8211; 3); 5 to 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48402\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-5.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 5\" width=\"565\" height=\"359\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-5.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-5-300x191.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 6.<br \/>\nA(- 3, 2), B(5, &#8211; 4); 2 to 6<br \/>\nAnswer:<br \/>\nThe given coordinates are: A (-3, 2), and B (5, -4)<br \/>\nCompare the given points with<br \/>\nA (x1, y1), and B (x2, y2)<br \/>\nIt is given that<br \/>\nAP : PB = 2 : 6<br \/>\nSo,<br \/>\nWe have to divide AB into 8 parts<br \/>\nNow,<br \/>\nWe know that,<br \/>\nSlope (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\nSlope of AB = \\(\\frac{-4 &#8211; 2}{5 + 3}\\)<br \/>\nSlope of AB = \\(\\frac{-6}{8}\\)<br \/>\nNow,<br \/>\nTo find the coordinates of P, add slope to AP and PB<br \/>\nSo,<br \/>\nP = (2 + (2 \/ 8) \u00d7 8, 6 + (2 \/ 8) \u00d7 (-6))<br \/>\nP = (4, 4.5)<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe coordinates of P are (4, 4.5)<\/p>\n<p>In Exercises 7 and 8, determine which of the lines are parallel and which of the lines are perpendicular.<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38420\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-162.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 162\" width=\"177\" height=\"176\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-162.png 177w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-162-150x150.png 150w\" sizes=\"(max-width: 177px) 100vw, 177px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48403\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-7.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 7\" width=\"578\" height=\"327\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-7.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-7-300x170.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38419\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-163.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 163\" width=\"175\" height=\"173\" \/><br \/>\nAnswer:<\/p>\n<p>The given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38419\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-163.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 163\" width=\"175\" height=\"173\" \/><br \/>\nFrom the given figure,<br \/>\nThe coordinates of line a are: (2, 2), and (-2, 3)<br \/>\nThe coordinates of line b are: (3, -2), and (-3, 0)<br \/>\nThe coordinates of line c are: (2, 4), and (0, -2)<br \/>\nThe coordinates of line d are: (0, 6), and (-2, 0)<br \/>\nNow,<br \/>\nCompare the given coordinates with (x1, y1), and (x2, y2)<br \/>\nSo,<br \/>\nThe slope of line a (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{3 &#8211; 2}{-2 &#8211; 2}\\)<br \/>\n= \\(\\frac{1}{-4}\\)<br \/>\n= &#8211;\\(\\frac{1}{4}\\)<\/p>\n<p>The slope of line b (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{0 + 2}{-3 &#8211; 3}\\)<br \/>\n= \\(\\frac{2}{-6}\\)<br \/>\n= &#8211;\\(\\frac{1}{3}\\)<\/p>\n<p>The slope of line c (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{-4 &#8211; 2}{0 &#8211; 2}\\)<br \/>\n= \\(\\frac{-6}{-2}\\)<br \/>\n= 3<\/p>\n<p>The slope of line d (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{6 &#8211; 0}{0 + 2}\\)<br \/>\n= \\(\\frac{6}{2}\\)<br \/>\n= 3<br \/>\nWe know that,<br \/>\nThe parallel lines have the same slopes<br \/>\nThe perpendicular lines have the product of slopes equal to -1<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nLine c and Line d are parallel lines<br \/>\nLine b and Line c are perpendicular lines<\/p>\n<p>In Exercises 9 &#8211; 12, tell whether the lines through the given points are parallel, perpendicular, or neither. justify your answer.<\/p>\n<p>Question 9.<br \/>\nLine 1: (1, 0), (7, 4)<br \/>\nLine 2: (7, 0), (3, 6)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48404\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-9.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 9\" width=\"563\" height=\"229\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-9.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-9-300x122.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 10.<br \/>\nLine 1: (- 3, 1), (- 7, &#8211; 2)<br \/>\nLine 2: (2, &#8211; 1), (8, 4)<br \/>\nAnswer:<br \/>\nThe coordinates of line 1 are: (-3, 1), (-7, -2)<br \/>\nThe coordinates of line 2 are: (2, -1), (8, 4)<br \/>\nCompare the given coordinates with<br \/>\n(x1, y1), (x2, y2)<br \/>\nWe know that,<br \/>\nSlope (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\nSlope of line 1 = \\(\\frac{-2 &#8211; 1}{-7 + 3}\\)<br \/>\n= \\(\\frac{-3}{-4}\\)<br \/>\n= \\(\\frac{3}{4}\\)<br \/>\nSlope of line 2 = \\(\\frac{4 + 1}{8 &#8211; 2}\\)<br \/>\n= \\(\\frac{5}{6}\\)<br \/>\nHence,<br \/>\nBy comparing the slopes,<br \/>\nWe can conclude that the given lines are neither parallel nor perpendicular<\/p>\n<p>Question 11.<br \/>\nLine 1: (- 9, 3), (- 5, 7)<br \/>\nLine 2: (- 11, 6), (- 7, 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48405\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-11.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 11\" width=\"556\" height=\"226\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-11.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-11-300x122.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 12.<br \/>\nLine 1: (10, 5), (- 8, 9)<br \/>\nLine 2: (2, &#8211; 4), (11, &#8211; 6)<br \/>\nAnswer:<br \/>\nThe coordinates of line 1 are: (10, 5), (-8, 9)<br \/>\nThe coordinates of line 2 are: (2, -4), (11, -6)<br \/>\nCompare the given coordinates with<br \/>\n(x1, y1), (x2, y2)<br \/>\nWe know that,<br \/>\nSlope (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\nSlope of line 1 = \\(\\frac{9 &#8211; 5}{-8 &#8211; 10}\\)<br \/>\n= \\(\\frac{4}{-18}\\)<br \/>\n= &#8211;\\(\\frac{2}{9}\\)<br \/>\nSlope of line 2 = \\(\\frac{4 &#8211; 6}{11 &#8211; 2}\\)<br \/>\n= \\(\\frac{-2}{9}\\)<br \/>\n= &#8211;\\(\\frac{2}{9}\\)<br \/>\nHence,<br \/>\nBy comparing the slopes,<br \/>\nWe can conclude that the given lines are parallel<\/p>\n<p>In Exercises 13 &#8211; 16. write an equation of the line passing through point P that \u00a1s parallel to the given line. Graph the equations of the lines to check that they are parallel.<\/p>\n<p>Question 13.<br \/>\nP(0, &#8211; 1), y = &#8211; 2x + 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48406\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-13.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 13\" width=\"583\" height=\"348\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-13.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-13-300x179.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 14.<br \/>\nP(3, 8), y = \\(\\frac{1}{5}\\)(x + 4)<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = \\(\\frac{1}{5}\\) (x + 4)<br \/>\nThe given point is: P (3, 8)<br \/>\nSo,<br \/>\ny = \\(\\frac{1}{5}\\)x + \\(\\frac{4}{5}\\)<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe slopes are equal fot the parallel lines<br \/>\nSo,<br \/>\nThe equation that is parallel to the given equation is:<br \/>\ny = \\(\\frac{1}{5}\\)x + c<br \/>\nSubstitute P (3, 8) in the above equation to find the value of c<br \/>\nSo,<br \/>\n8 = \\(\\frac{1}{5}\\) (3) + c<br \/>\nc = 8 &#8211; \\(\\frac{3}{5}\\)<br \/>\nc = \\(\\frac{37}{5}\\)<br \/>\nHence,<br \/>\nThe parallel line equation that is parallel to the given equation is:<br \/>\ny = \\(\\frac{1}{5}\\)x + \\(\\frac{37}{5}\\)<br \/>\nThe representation of the parallel lines in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-83280\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-27.png\" alt=\"\" width=\"486\" height=\"536\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-27.png 486w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-27-272x300.png 272w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><\/p>\n<p>Question 15.<br \/>\nP(- 2, 6), x = &#8211; 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48407\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-15.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 15\" width=\"579\" height=\"384\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-15.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-15-300x199.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 16.<br \/>\nP(4, 0), &#8211; x + 2y = 12<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n-x + 2y = 12<br \/>\nThe given point is: P (4, 0)<br \/>\nSo,<br \/>\ny = \\(\\frac{1}{2}\\)x + 6<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe slopes are equal fot the parallel lines<br \/>\nSo,<br \/>\nThe equation that is parallel to the given equation is:<br \/>\ny = \\(\\frac{1}{2}\\)x + c<br \/>\nSubstitute P (4, 0) in the above equation to find the value of c<br \/>\nSo,<br \/>\n0 = \\(\\frac{1}{2}\\) (4) + c<br \/>\nc = 2 &#8211; 0<br \/>\nc = 2<br \/>\nHence,<br \/>\nThe parallel line equation that is parallel to the given equation is:<br \/>\ny = \\(\\frac{1}{2}\\)x + 2<br \/>\nThe representation of the parallel lines in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-83283\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-28.png\" alt=\"\" width=\"486\" height=\"530\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-28.png 486w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-28-275x300.png 275w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><\/p>\n<p>In Exercises 17 &#8211; 20. write an equation of the line passing through point P that is perpendicular to the given line. Graph the equations of the lines to check that they are perpendicular.<\/p>\n<p>Question 17.<br \/>\nP(0, 0), y = &#8211; 9x &#8211; 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48408\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-17.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 17\" width=\"492\" height=\"600\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-17.png 492w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-17-246x300.png 246w\" sizes=\"(max-width: 492px) 100vw, 492px\" \/><\/p>\n<p>Question 18.<br \/>\nP(4, &#8211; 6)y = &#8211; 3<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = -3<br \/>\nThe given point is: P (4, -6)<br \/>\nWe know that,<br \/>\nThe line that is perpendicular to y=n is:<br \/>\nx = n<br \/>\nSo,<br \/>\nThe line that is perpendicular to the given equation is:<br \/>\nx = n<br \/>\nSubstitute P (4, -6) in the above equation<br \/>\nSo,<br \/>\nx = 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe equation that is perpendicular to y = -3 is:<br \/>\nx = 4<br \/>\nThe representation of the perpendicular lines in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-83324\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-29.png\" alt=\"\" width=\"482\" height=\"501\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-29.png 482w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-29-289x300.png 289w\" sizes=\"(max-width: 482px) 100vw, 482px\" \/><\/p>\n<p>Question 19.<br \/>\nP(2, 3), y &#8211; 4 = &#8211; 2(x + 3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48409\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-19.1.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 19.1\" width=\"481\" height=\"490\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-19.1.png 481w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-19.1-294x300.png 294w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48410\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-19.2.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 19.2\" width=\"304\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-19.2.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-19.2-300x280.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><\/p>\n<p>Question 20.<br \/>\nP(- 8, 0), 3x &#8211; 5y = 6<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n3x &#8211; 5y = 6<br \/>\nThe given point is: P (-8, 0)<br \/>\nNow,<br \/>\n5y = 3x &#8211; 6<br \/>\ny = \\(\\frac{3}{5}\\)x &#8211; \\(\\frac{6}{5}\\)<br \/>\nWe know that,<br \/>\nThe product of the slopes of perpendicular lines is equal to -1<br \/>\nSo,<br \/>\nm = &#8211;\\(\\frac{5}{3}\\)<br \/>\nSo,<br \/>\nThe equation that is perpendicular to the given line equation is:<br \/>\ny = &#8211;\\(\\frac{5}{3}\\)x + c<br \/>\nSubstitute P(-8, 0) in the above equation<br \/>\n0 = &#8211;\\(\\frac{5}{3}\\) ( -8) + c<br \/>\nc = \\(\\frac{40}{3}\\)<br \/>\nHence,<br \/>\nThe equation that is perpendicular to the given equation is:<br \/>\ny = &#8211;\\(\\frac{5}{3}\\)x + \\(\\frac{40}{3}\\)<br \/>\nThe representation of the perpendicular lines in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-83382\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-30.png\" alt=\"\" width=\"485\" height=\"537\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-30.png 485w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-30-271x300.png 271w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><\/p>\n<p>In Exercises 21 &#8211; 24, find the distance from point A to the given line.<\/p>\n<p>Question 21.<br \/>\nA(- 1, 7), y = 3x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48411\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-21.1.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 21.1\" width=\"554\" height=\"620\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-21.1.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-21.1-268x300.png 268w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48412\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-21.2.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 21.2\" width=\"510\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-21.2.png 510w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-21.2-300x79.png 300w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><\/p>\n<p>Question 22.<br \/>\nA(- 9, &#8211; 3), y = x &#8211; 6<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = x &#8211; 6 &#8212;&#8212;-(1)<br \/>\nThe given point is: A (-9, -3)<br \/>\nCompare the given equation with<br \/>\ny = mx + c<br \/>\nWe know that,<br \/>\nThe product of the slopes of the perpendicular lines is equal to -1<br \/>\nSo,<br \/>\nm1m2 = -1<br \/>\n1 (m2) = -3<br \/>\nm2 = -1<br \/>\nSo,<br \/>\nThe equation that is perpendicular to the given line equation is:<br \/>\ny = -x + c<br \/>\nSubstitute A (-9, -3) in the above equation to find the value of c<br \/>\nSo,<br \/>\n-3 = 9 + c<br \/>\nc = -9 &#8211; 3<br \/>\nc = -12<br \/>\nHence,<br \/>\nThe equation that is perpendicular to the given line equation is:<br \/>\ny = -x &#8211; 12 &#8212;&#8212;(2)<br \/>\nNow,<br \/>\nWe have to find the point of intersection<br \/>\nSo,<br \/>\nEq. (1) = Eq. (2)<br \/>\nx &#8211; 6 = -x &#8211; 12<br \/>\nx + x = -12 + 6<br \/>\n2x = -6<br \/>\nx = \\(\\frac{-6}{2}\\)<br \/>\nx = -3<br \/>\nSo,<br \/>\ny = x &#8211; 6<br \/>\ny = -3 &#8211; 6<br \/>\ny = -9<br \/>\nSo,<br \/>\nThe point of intersection = (-3, -9)<br \/>\nNow,<br \/>\nThe points are: (-9, -3), (-3, -9)<br \/>\nSo,<br \/>\nd = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(9 &#8211; 3)\u00b2 + (9 &#8211; 3)\u00b2}\\)<br \/>\n= \\(\\sqrt{(6)\u00b2 + (6)\u00b2}\\)<br \/>\n= 8.48<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance from point A to the given line is: 8.48<\/p>\n<p>Question 23.<br \/>\nA(15, &#8211; 21), 5x + 2y = 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48413\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-23.1.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 23.1\" width=\"500\" height=\"620\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-23.1.png 500w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-23.1-242x300.png 242w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48414\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-23.2.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 23.2\" width=\"418\" height=\"572\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-23.2.png 418w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-23.2-219x300.png 219w\" sizes=\"(max-width: 418px) 100vw, 418px\" \/><\/p>\n<p>Question 24.<br \/>\nA(- \\(\\frac{1}{4}\\), 5), &#8211; x + 2y = 14<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n-x + 2y = 14<br \/>\ny = \\(\\frac{1}{2}\\)x + 7 &#8212;&#8212;-(1)<br \/>\nThe given point is: A (-\\(\\frac{1}{4}\\), 5)<br \/>\nCompare the given equation with<br \/>\ny = mx + c<br \/>\nWe know that,<br \/>\nThe product of the slopes of the perpendicular lines is equal to -1<br \/>\nSo,<br \/>\nm1m2 = -1<br \/>\n\\(\\frac{1}{2}\\) (m2) = -1<br \/>\nm2 = -2<br \/>\nSo,<br \/>\nThe equation that is perpendicular to the given line equation is:<br \/>\ny = -2x + c<br \/>\nSubstitute A (-\\(\\frac{1}{4}\\), 5) in the above equation to find the value of c<br \/>\nSo,<br \/>\n5 = -2 (-\\(\\frac{1}{4}\\)) + c<br \/>\nc = 5 &#8211; \\(\\frac{1}{2}\\)<br \/>\nc = \\(\\frac{9}{2}\\)<br \/>\nHence,<br \/>\nThe equation that is perpendicular to the given line equation is:<br \/>\ny = -2x + \\(\\frac{9}{2}\\) &#8212;&#8212;(2)<br \/>\nNow,<br \/>\nWe have to find the point of intersection<br \/>\nSo,<br \/>\nEq. (1) = Eq. (2)<br \/>\n\\(\\frac{1}{2}\\)x + 7 = -2x + \\(\\frac{9}{2}\\)<br \/>\n\\(\\frac{1}{2}\\)x + 2x = -7 + 9\/2<br \/>\n\\(\\frac{5}{2}\\)x = &#8211;\\(\\frac{5}{2}\\)<br \/>\nx = -1<br \/>\nSo,<br \/>\ny = -2x + 3<br \/>\ny = -2 (-1) + \\(\\frac{9}{2}\\)<br \/>\ny = \\(\\frac{13}{2}\\)<br \/>\nSo,<br \/>\nThe point of intersection = (-1, \\(\\frac{13}{2}\\))<br \/>\nNow,<br \/>\nThe points are: (-\\(\\frac{1}{4}\\), 5), (-1, \\(\\frac{13}{2}\\))<br \/>\nSo,<br \/>\nd = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3 \/ 2)\u00b2 + (3 \/ 4)\u00b2}\\)<br \/>\n= 1.67<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance from point A to the given line is: 1.67<\/p>\n<p>Question 25.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in determining whether the lines are parallel. perpendicular, or neither.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38418\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-164.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 164\" width=\"356\" height=\"131\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-164.png 356w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-164-300x110.png 300w\" sizes=\"(max-width: 356px) 100vw, 356px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48415\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-25.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 25\" width=\"579\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-25.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-25-300x45.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in writing an equation of the line that passes through the point (3, 4) and is parallel to the line y = 2x + 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38417\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-165.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 165\" width=\"245\" height=\"127\" \/><br \/>\nAnswer:<br \/>\nThe given equation of the line is:<br \/>\ny = 2x + 1<br \/>\nThe given point is: (3, 4)<br \/>\nWe know that,<br \/>\nThe slopes of the parallel lines are the same<br \/>\nNow,<br \/>\nCompare the given equation with<br \/>\ny = mx + c<br \/>\nSo,<br \/>\nm = 2<br \/>\nSo,<br \/>\nThe slope of the line that is aprallle to the given line equation is:<br \/>\nm = 2<br \/>\nSo,<br \/>\nThe equation of the line that is parallel to the given equation is:<br \/>\ny = 2x + c<br \/>\nTo find the value of c,<br \/>\nSubstitute (3, 4) in the above equation<br \/>\nSo,<br \/>\n4 = 2 (3) + c<br \/>\n4 &#8211; 6 = c<br \/>\nc = -2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the equation of the line that is parallel to the given line is:<br \/>\ny = 2x &#8211; 2<\/p>\n<p>In Exercises 27-30. find the midpoint of \\(\\overline{P Q}\\). Then write<br \/>\nan equation of the line that passes through the midpoint and is perpendicular to \\(\\overline{P Q}\\). This line is called the perpendicular bisector.<\/p>\n<p>Question 27.<br \/>\nP( &#8211; 4, 3), Q(4, &#8211; 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48416\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-27.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 27\" width=\"553\" height=\"325\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-27.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-27-300x176.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 28.<br \/>\nP(- 5, &#8211; 5), Q(3, 3)<br \/>\nAnswer:<br \/>\nThe given points are: P (-5, -5), Q (3, 3)<br \/>\nCompare the given points with (x1, y1), (x2, y2)<br \/>\nWe know that,<br \/>\nThe midpoint of PQ = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\n= (\\(\\frac{-5 + 3}{2}\\), \\(\\frac{-5 + 3}{2}\\))<br \/>\n= (\\(\\frac{-2}{2}\\), \\(\\frac{-2}{2}\\))<br \/>\n= (-1, -1)<br \/>\nNow,<br \/>\nThe slope of PQ = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{3 + 5}{3 + 5}\\)<br \/>\n= \\(\\frac{8}{8}\\)<br \/>\n= 1<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe product of the slopes of the perpendicular lines is equal to -1<br \/>\nSo,<br \/>\nm1m2 = -1<br \/>\nSo,<br \/>\nm2 = -1<br \/>\nWe know that,<br \/>\nThe equation of the perpendicular line that passes through the midpoint of PQ is:<br \/>\ny = -x + c<br \/>\nTo find the value of c,<br \/>\nSubstitute (-1, -1) in the above equation<br \/>\nSo,<br \/>\n-1 = -1 + c<br \/>\nc = 0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the equation of the line that is perpendicular bisector is:<br \/>\ny = -x<\/p>\n<p>Question 29.<br \/>\nP(0, 2), Q(6, &#8211; 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48417\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-29.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 29\" width=\"447\" height=\"457\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-29.png 447w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-29-293x300.png 293w\" sizes=\"(max-width: 447px) 100vw, 447px\" \/><\/p>\n<p>Question 30.<br \/>\nP(- 7, 0), Q(1, 8)<br \/>\nAnswer:<br \/>\nThe given points are: P (-7, 0), Q (1, 8)<br \/>\nCompare the given points with (x1, y1), (x2, y2)<br \/>\nWe know that,<br \/>\nThe midpoint of PQ = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\n= (\\(\\frac{8 + 0}{2}\\), \\(\\frac{-7 + 1}{2}\\))<br \/>\n= (\\(\\frac{8}{2}\\), \\(\\frac{-6}{2}\\))<br \/>\n= (4, -3)<br \/>\nNow,<br \/>\nThe slope of PQ = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{8 &#8211; 0}{1 + 7}\\)<br \/>\n= \\(\\frac{8}{8}\\)<br \/>\n= 1<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe product of the slopes of the perpendicular lines is equal to -1<br \/>\nSo,<br \/>\nm1m2 = -1<br \/>\nSo,<br \/>\nm2 = -1<br \/>\nWe know that,<br \/>\nThe equation of the perpendicular line that passes through the midpoint of PQ is:<br \/>\ny = -x + c<br \/>\nTo find the value of c,<br \/>\nSubstitute (4, -3) in the above equation<br \/>\nSo,<br \/>\n-3 = -4 + c<br \/>\nc = -3 + 4<br \/>\nc = 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the equation of the line that is perpendicular bisector is:<br \/>\ny = -x + 1<\/p>\n<p>Question 31.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYour school lies directly between your house and the movie theater. The distance from your house to the school is one-fourth of the distance from the school to the movie theater. What point on the graph represents your school?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38416\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-166.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 166\" width=\"209\" height=\"140\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48418\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-31.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 31\" width=\"565\" height=\"337\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-31.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-31-300x179.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>REASONING<\/strong><br \/>\nIs quadrilateral QRST a parallelogram? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38415\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-167.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 167\" width=\"160\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-167.png 160w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-167-150x150.png 150w\" sizes=\"(max-width: 160px) 100vw, 160px\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38415\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-167.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 167\" width=\"160\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-167.png 160w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-167-150x150.png 150w\" sizes=\"(max-width: 160px) 100vw, 160px\" \/><br \/>\nFrom the above figure,<br \/>\nThe coordinates of the quadrilateral QRST is:<br \/>\nQ (2, 6), R (6, 4), S (5, 1), and T (1, 3)<br \/>\nCompare the given points with (x1, y1), and (x2, y2)<br \/>\nNow,<br \/>\nWe know that,<br \/>\nIf both pairs of opposite sides of a quadrilateral are parallel, then it is a parallelogram<br \/>\nSo,<br \/>\nIf the slopes of the opposite sides of the quadrilateral are equal, then it is called as &#8220;Parallelogram&#8221;<br \/>\nWe know that,<br \/>\nSlope (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\nSlope of QR = \\(\\frac{4 &#8211; 6}{6 &#8211; 2}\\)<br \/>\nSlope of QR = \\(\\frac{-2}{4}\\)<br \/>\nSlope of QR = &#8211;\\(\\frac{1}{2}\\)<\/p>\n<p>Slope of RS = \\(\\frac{1 &#8211; 4}{5 &#8211; 6}\\)<br \/>\nSlope of RS = \\(\\frac{-3}{-1}\\)<br \/>\nSlope of RS = 3<\/p>\n<p>Slope of ST = \\(\\frac{3 &#8211; 1}{1 &#8211; 5}\\)<br \/>\nSlope of ST = \\(\\frac{2}{-4}\\)<br \/>\nSlope of ST = &#8211;\\(\\frac{1}{2}\\)<\/p>\n<p>Slope of TQ = \\(\\frac{3 &#8211; 6}{1 &#8211; 2}\\)<br \/>\nSlope of TQ = \\(\\frac{-3}{-1}\\)<br \/>\nSlope of TQ = 3<br \/>\nNow,<br \/>\nFrom the slopes,<br \/>\nWe can observe that the slopes of the opposite sides are equal i.e., the opposite sides are parallel<br \/>\nHence, from the above,<br \/>\nWe can conclude that the quadrilateral QRST is a parallelogram<\/p>\n<p><span style=\"font-size: 16px;\">Question 33.<\/span><\/p>\n<p><strong>REASONING<\/strong><br \/>\nA triangle has vertices L(0, 6), M(5, 8). and N(4, &#8211; 1), Is the triangle a right triangle? Explain \u2018your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48419\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-33.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 33\" width=\"557\" height=\"305\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-33.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-33-300x164.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA new road is being constructed parallel to the train tracks through points V. An equation of the line representing the train tracks is y = 2x. Find an equation of the line representing the new road.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38414\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-168.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 168\" width=\"139\" height=\"141\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38414\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-168.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 168\" width=\"139\" height=\"141\" \/><br \/>\nIt is given that a new road is being constructed parallel to the train tracks through points V. An equation of the line representing the train tracks is y = 2x.<br \/>\nSo,<br \/>\nFrom the figure,<br \/>\nV = (-2, 3)<br \/>\nWe know that,<br \/>\nThe slopes of the parallel lines are the same<br \/>\nSo,<br \/>\nBy comparing the given equation with<br \/>\ny = mx + c<br \/>\nWe get,<br \/>\nm = 2<br \/>\nSo,<br \/>\nThe equation of the line that is parallel to the line that represents the train tracks is:<br \/>\ny = 2x + c<br \/>\nNow,<br \/>\nTo find the value of c,<br \/>\nSubstitute (-2, 3) in the above equation<br \/>\nSo,<br \/>\n3 = 2 (-2) + x<br \/>\n3 + 4 = c<br \/>\nc = 7<br \/>\nHence, from the above,<br \/>\nWe can conclude that the equation of the line that is parallel to the line representing railway tracks is:<br \/>\ny = 2x + 7<\/p>\n<p>Question 35.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA bike path is being constructed perpendicular to Washington Boulevard through point P(2, 2). An equation of the line representing Washington Boulevard is y = &#8211;\\(\\frac{2}{3}\\)x. Find an equation of the line representing the bike path.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38413\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-169.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 169\" width=\"306\" height=\"204\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-169.png 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-169-300x200.png 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48420\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-35.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 35\" width=\"531\" height=\"283\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-35.png 531w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-35-300x160.png 300w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>PROBLEM-SOLVING<\/strong><br \/>\nA gazebo is being built near a nature trail. An equation of the line representing the nature trail is y = \\(\\frac{1}{3}\\)x &#8211; 4. Each unit in the coordinate plane corresponds to 10 feet. Approximately how far is the gazebo from the nature trail?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38412\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-170.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 170\" width=\"244\" height=\"141\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38412\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-170.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 170\" width=\"244\" height=\"141\" \/><br \/>\nIt is given that a gazebo is being built near a nature trail. An equation of the line representing the nature trail is y = \\(\\frac{1}{3}\\)x &#8211; 4. Each unit in the coordinate plane corresponds to 10 feet<br \/>\nSo,<br \/>\nIt can be observed that<br \/>\n1 unit either in the x-plane or y-plane = 10 feet<br \/>\nSo,<br \/>\ny = \\(\\frac{1}{3}\\)x &#8211; 4<br \/>\ny = \\(\\frac{1}{3}\\) (10) &#8211; 4<br \/>\ny = \\(\\frac{10 &#8211; 12}{3}\\)<br \/>\ny = &#8211;\\(\\frac{2}{3}\\)<br \/>\nWe know that,<br \/>\nThe distance won&#8217;t be in negative value,<br \/>\ny = \\(\\frac{2}{3}\\)<br \/>\ny = 0.66 feet<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance of the gazebo from the nature trail is: 0.66 feet<\/p>\n<p>Question 37.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nThe slope of line l is greater than 0 and less than 1. Write an inequality for the slope of a line perpendicular to l. Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48421\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-37.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 37\" width=\"568\" height=\"138\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-37.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-37-300x73.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nDetermine whether quadrilateral JKLM is a square. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38411\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-171.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 171\" width=\"177\" height=\"161\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38411\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-171.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 171\" width=\"177\" height=\"161\" \/><br \/>\nFrom the given figure,<br \/>\nThe coordinates of a quadrilateral are:<br \/>\nJ (0 0), K (0, n), L (n, n), M (n, 0)<br \/>\nCompare the given points with (x1, y1), and (x2, y2)<br \/>\nWe know that,<br \/>\nSlope (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\nSlope of JK = \\(\\frac{n &#8211; 0}{0 &#8211; 0}\\)<br \/>\n= Undefined<br \/>\nSlope of KL = \\(\\frac{n &#8211; n}{n &#8211; 0}\\)<br \/>\n= 0<br \/>\nSlope of LM = \\(\\frac{0 &#8211; n}{n &#8211; n}\\)<br \/>\n= Undefined<br \/>\nSlope of MJ = \\(\\frac{0 &#8211; 0}{n &#8211; 0}\\)<br \/>\n= 0<br \/>\nWe know that,<br \/>\nFor a square,<br \/>\nThe slopes of perpendicular lines are undefined and 0 respectively<br \/>\nHence, from the above,<br \/>\nWe can conclude that quadrilateral JKLM is a square<\/p>\n<p>Question 39.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nSuppose point P divides the directed line segment XY So that the ratio 0f XP to PY is 3 to 5. Describe the point that divides the directed line segment YX so that the ratio of YP Lo PX is 5 to 3.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48422\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-39.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 39\" width=\"537\" height=\"82\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-39.png 537w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-39-300x46.png 300w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour classmate claims that no two nonvertical parallel lines can have the same y-intercept. Is your classmate correct? Explain.<br \/>\nAnswer:<br \/>\nYes, your classmate is correct<\/p>\n<p>Explanation:<br \/>\nIt is given that your classmate claims that no two nonvertical parallel lines can have the same y-intercept<br \/>\nWe know that,<br \/>\nThe parallel lines have the same slope but have different y-intercepts and do not intersect<br \/>\nThe intersecting lines intersect each other and have different slopes and have the same y-intercept<br \/>\nHence, from the above,<br \/>\nWe can conclude that the claim of your classmate is correct<\/p>\n<p>Question 41.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nSolve each system of equations algebraically. Make a conjecture about what the solution(s) can tell you about whether the lines intersect. are parallel, or are the same line.<br \/>\na. y = 4x + 9<br \/>\n4x &#8211; y = 1<br \/>\nb. 3y + 4x = 16<br \/>\n2x &#8211; y = 18<br \/>\nc. y = &#8211; 5x + 6<br \/>\n10x + 2y = 12<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48423\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-41.1.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 41.1\" width=\"557\" height=\"580\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-41.1.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-41.1-288x300.png 288w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48424\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-41.2.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 41.2\" width=\"543\" height=\"369\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-41.2.png 543w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-41.2-300x204.png 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nFind a formula for the distance from the point (x<sub>0<span style=\"font-size: 16px;\">, Y<\/span><\/sub><sub>0<\/sub>) to the line ax + by = 0. Verify your formula using a point and a line.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-84020\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-35.png\" alt=\"\" width=\"517\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-35.png 517w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-35-300x78.png 300w\" sizes=\"(max-width: 517px) 100vw, 517px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-84021\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-36.png\" alt=\"\" width=\"539\" height=\"594\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-36.png 539w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-36-272x300.png 272w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-84023\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-37.png\" alt=\"\" width=\"548\" height=\"586\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-37.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-37-281x300.png 281w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-84024\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-38.png\" alt=\"\" width=\"582\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-38.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-38-300x146.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-84025\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-39.png\" alt=\"\" width=\"630\" height=\"703\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-39.png 630w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-39-269x300.png 269w\" sizes=\"(max-width: 630px) 100vw, 630px\" \/><br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nIn Exercises 43 and 44, find a value for k based on the given description.<\/p>\n<p>Question 43.<br \/>\nThe line through (- 1, k) and (- 7, &#8211; 2) is parallel to the line y = x + 1.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48425\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-43.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 43\" width=\"411\" height=\"276\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-43.png 411w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-43-300x201.png 300w\" sizes=\"(max-width: 411px) 100vw, 411px\" \/><\/p>\n<p>Question 44.<br \/>\nThe line through (k, 2) and (7, 0) is perpendicular to the line y = x &#8211; \\(\\frac{28}{5}\\).<br \/>\nAnswer:<br \/>\nThe given points are: (k, 2), and (7, 0)<br \/>\nThe given line that is perpendicular to the given points is:<br \/>\ny = x &#8211; \\(\\frac{28}{5}\\)<br \/>\nNow,<br \/>\nCompare the given points with (x1, y1), and (x2, y2)<br \/>\nSo,<br \/>\nSlope (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nm = \\(\\frac{0 &#8211; 2}{7 &#8211; k}\\)<br \/>\nm = \\(\\frac{-2}{7 &#8211; k}\\)<br \/>\nNow,<br \/>\nThe slope that is perpendicular to the given line is:<br \/>\nm = -1 [ Since we know that m1m2 = -1]<br \/>\nSo,<br \/>\n-1 = \\(\\frac{-2}{7 &#8211; k}\\)<br \/>\nk &#8211; 7 = -2<br \/>\nk = -2 + 7<br \/>\nk = 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of k is: 5<\/p>\n<p>Question 45.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nMake a conjecture about how to find the coordinates of a point that lies beyond point B along \\(\\vec{A}\\)B. Use an example to support your conjecture.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48426\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-45.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 45\" width=\"607\" height=\"387\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-45.png 607w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-45-300x191.png 300w\" sizes=\"(max-width: 607px) 100vw, 607px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>PROBLEM-SOLVING<\/strong><br \/>\nWhat is the distance between the lines y = 2x and y = 2x + 5? Verify your answer.<br \/>\nAnswer:<br \/>\nThe given lines are:<br \/>\ny = 2x and y = 2x + 5<br \/>\nCompare the given equations with<br \/>\ny = mx + c<br \/>\nNow,<br \/>\nTo find the distance between the two lines, we have to find the intersection point of the line<br \/>\nSo,<br \/>\nThe intersection of the line is the y-intercept<br \/>\nSo,<br \/>\nFrom y = 2x + 5,<br \/>\nThe intersection point is: (0, 5)<br \/>\nNow,<br \/>\nFor the intersection point of y = 2x,<br \/>\nFind the perpendicular line of y = 2x and find the intersection point of the two lines<br \/>\nWe know that,<br \/>\nThe product of the slopes of the perpendicular lines is equal to -1<br \/>\nSo,<br \/>\n2m2 = -1<br \/>\nm2 = &#8211;\\(\\frac{1}{2}\\)<br \/>\nSo,<br \/>\nThe perpendicular equation of y = 2x is:<br \/>\ny = &#8211;\\(\\frac{1}{2}\\)x + c<br \/>\nTo find the value of c in the above equation, substitue (0, 5) in the above equation<br \/>\nSo,<br \/>\n5 = c<br \/>\nc = 5<br \/>\nSo,<br \/>\nThe perpendicular line equation of y = 2x is:<br \/>\ny = &#8211;\\(\\frac{1}{2}\\)x + 5<br \/>\nNow,<br \/>\nFor the intersection point,<br \/>\n2x = &#8211;\\(\\frac{1}{2}\\)x + 5<br \/>\n2x + \\(\\frac{1}{2}\\)x = 5<br \/>\n\\(\\frac{5}{2}\\)x = 5<br \/>\nx = 2<br \/>\nSo,<br \/>\ny = 2x<br \/>\n= 2 (2)<br \/>\n= 4<br \/>\nSo,<br \/>\nThe intersection point of y = 2x is: (2, 4)<br \/>\nNow,<br \/>\nThe points are: (0, 5), and (2, 4)<br \/>\nCompare the given points with (x1, y1), and (x2, y2)<br \/>\nSo,<br \/>\nd = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4 &#8211; 5)\u00b2 + (2 &#8211; 0)\u00b2}\\)<br \/>\n= \\(\\sqrt{1 + 4}\\)<br \/>\n= 2.23<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance between the lines y = 2x and y = 2x + 5 is: 2.23<\/p>\n<p><strong>PROVING A THEOREM<\/strong><br \/>\nIn Exercises 47 and 48, use the slopes of lines to write a paragraph proof of the theorem.<\/p>\n<p>Question 47.<br \/>\nLines Perpendicular to a Transversal Theorem (Theorem 3.12): In a plane. if two lines are perpendicular to the same line. then they are parallel to each other.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48427\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-47.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 47\" width=\"583\" height=\"166\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-47.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-47-300x85.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 48.<br \/>\nTransitive Property of Parallel Lines Theorem (Theorem 3.9),\/+: If two lines are parallel to the same line, then they are parallel to each other.<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nIf two lines are parallel to the same line, then they are parallel to each other<br \/>\nProof:<br \/>\nLet the two parallel lines be E and F and the plane they lie be plane x<br \/>\nLet the two parallel lines that are parallel to the same line be G<br \/>\nHence,<br \/>\nAccording to the Transitive Property of parallel lines,<br \/>\nIf line E is parallel to line F and line F is parallel to line G, then line E is parallel to line G.<\/p>\n<p>Question 49.<br \/>\n<strong>PROOF<\/strong><br \/>\nProve the statement: If two lines are vertical. then they are parallel.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48428\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-49.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 49\" width=\"586\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-49.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-49-300x56.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 50.<br \/>\n<strong>PROOF<\/strong><br \/>\nProve the statement: If two lines are horizontal, then they are parallel.<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nIf two lines are horizontal, then they are parallel<br \/>\nProof:<br \/>\nIf two lines x and y are horizontal lines and they are cut by a vertical transversal z, then<br \/>\nx \u22a5 z and y \u22a5 z<br \/>\nHence,<br \/>\nx || y is proved by the Lines parallel to Transversal Theorem<\/p>\n<p>Question 51.<br \/>\n<strong>PROOF<\/strong><br \/>\nProve that horizontal lines are perpendicular to vertical lines.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48429\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-51.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 51\" width=\"570\" height=\"222\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-51.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-51-300x117.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Maintaining Mathematical Proficiency<\/p>\n<p>Plot the point in a coordinate plane.<\/p>\n<p>Question 52.<br \/>\nA(3, 6)<br \/>\nAnswer:<br \/>\nThe given point is: A(3, 6)<br \/>\nThe representation of the given point in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-83667\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-31.png\" alt=\"\" width=\"472\" height=\"473\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-31.png 472w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-31-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-31-150x150.png 150w\" sizes=\"(max-width: 472px) 100vw, 472px\" \/><\/p>\n<p>Question 53.<br \/>\nB(0, &#8211; 4)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48430\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-53.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 53\" width=\"211\" height=\"238\" \/><\/p>\n<p>Question 54.<br \/>\nC(5, 0)<br \/>\nAnswer:<br \/>\nThe given point is: C (5, 0)<br \/>\nThe representation of the given point in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-83668\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-32.png\" alt=\"\" width=\"473\" height=\"463\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-32.png 473w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-32-300x294.png 300w\" sizes=\"(max-width: 473px) 100vw, 473px\" \/><\/p>\n<p>Question 55.<br \/>\nD( &#8211; 1, &#8211; 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48431\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-55.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 55\" width=\"209\" height=\"170\" \/><\/p>\n<p>Copy and complete the table.<\/p>\n<p>Question 56.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38410\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-172.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 172\" width=\"309\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-172.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-172-300x75.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38410\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-172.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 172\" width=\"309\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-172.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-172-300x75.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><br \/>\nFrom the above table,<br \/>\nThe given equation is:<br \/>\ny = x + 9<br \/>\nHence,<br \/>\nThe completed table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-83671\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-6.jpg\" alt=\"\" width=\"312\" height=\"83\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-6.jpg 312w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-6-300x80.jpg 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><\/p>\n<p>Question 57.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38409\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-173.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 173\" width=\"304\" height=\"92\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-173.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-173-300x91.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48432\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-57.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 57\" width=\"598\" height=\"205\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-57.png 598w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-3-Parallel-and-Perpendicular-Lines-3.5-a-57-300x103.png 300w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><\/p>\n<h3><a id=\"3.4_-_3.5_Performance_Task:_Navajo_Rugs\"><\/a>3.4 &#8211; 3.5 Performance Task: Navajo Rugs<\/h3>\n<p><strong>Mathematical Practices<\/strong><\/p>\n<p>Question 1.<br \/>\nCompare the effectiveness of the argument in Exercise 24 on page 153 with the argument \u201cYou can find the distance between any two parallel lines\u201d What flaw(s) exist in the argument(s)? Does either argument use correct reasoning? Explain.<br \/>\nAnswer:<br \/>\nFrom the argument in Exercise 24 on page 153,<br \/>\nWe can say that<br \/>\nThe claim of your friend is not correct<br \/>\nWe know that,<br \/>\nIf we want to find the distance from the point to a given line, we need the perpendicular distance of a point and a line<br \/>\nHence, from the above,<br \/>\nWe can conclude that we can not find the distance between any two parallel lines if a point and a line is given to find the distance<\/p>\n<p>Question 2.<br \/>\nLook back at your construction of a square in Exercise 29 on page 154. How would your<br \/>\nconstruction change if you were to construct a rectangle?<br \/>\nAnswer:<br \/>\nFrom the construction of a square in Exercise 29 on page 154,<br \/>\nWe can observe that the length of all the line segments are equal<br \/>\nNow,<br \/>\nIf you were to construct a rectangle,<br \/>\nWe have to keep the lengths of the length of the rectangles the same and the widths of the rectangle also the same<\/p>\n<p>Question 3.<br \/>\nIn Exercise 31 on page 161, a classmate tells you that our answer is incorrect because you should have divided the segment into four congruent pieces. Respond to your classmates&#8217; argument by justifying your original answer.<br \/>\nAnswer:<br \/>\nIn Exercise 31 on page 161, from the coordinate plane,<br \/>\nWe can observe that we divided the total distance into the four congruent segments or pieces<br \/>\nHence, from the above,<br \/>\nWe can conclude that the argument of your friend that the answer is incorrect is not correct<\/p>\n<h3><a id=\"Parallel_and_Perpendicular_Lines_Chapter_Review\"><\/a>Parallel and Perpendicular Lines Chapter Review<\/h3>\n<h4>3.1 Pairs of Lines and Angles<\/h4>\n<p>Think of each segment in the figure as part of a line. Which line(s) or plane(s) appear to fit the description?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38457\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-174.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 174\" width=\"132\" height=\"151\" \/><br \/>\nQuestion 1.<br \/>\nline(s) perpendicular to <img loading=\"lazy\" class=\"alignnone size-full wp-image-38459\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-175-1.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 175\" width=\"35\" height=\"28\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe lines that are at 90\u00b0 are &#8220;Perpendicular lines&#8221;<br \/>\nHence,<br \/>\nFrom the above figure,<br \/>\nThe lines perpendicular to \\(\\overline{Q R}\\) are: \\(\\overline{R M}\\) and \\(\\overline{Q L}\\)<\/p>\n<p>Question 2.<br \/>\nline(s) parallel to <img loading=\"lazy\" class=\"alignnone size-full wp-image-38459\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-175-1.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 175\" width=\"35\" height=\"28\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe lines that do not have any intersection points are called &#8220;Parallel lines&#8221;<br \/>\nHence,<br \/>\nFrom the above figure,<br \/>\nThe line parallel to \\(\\overline{Q R}\\) is: \\(\\overline {L M}\\)<\/p>\n<p>Question 3.<br \/>\nline(s) skew to <img loading=\"lazy\" class=\"alignnone size-full wp-image-38459\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-175-1.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 175\" width=\"35\" height=\"28\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe lines that do not intersect and are not parallel and are not coplanar are &#8220;Skew lines&#8221;<br \/>\nHence,<br \/>\nFrom the above figure,<br \/>\nThe lines skew to \\(\\overline{Q R}\\) are: \\(\\overline{J N}\\), \\(\\overline{J K}\\), \\(\\overline{K L}\\), and \\(\\overline{L M}\\)<\/p>\n<p>Question 4.<br \/>\nplane(s) parallel to plane LMQ<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can conclude that the plane parallel to plane LMQ is: Plane JKL<\/p>\n<h4>3.2 Parallel Lines and Transversals<\/h4>\n<p>Find the values of x and y.<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38455\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-176.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 176\" width=\"142\" height=\"86\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38455\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-176.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 176\" width=\"142\" height=\"86\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that x and 35\u00b0 are the corresponding angles<br \/>\nWe know that,<br \/>\nBy using the Corresponding Angles Theorem,<br \/>\nx = 35\u00b0<br \/>\nNow,<br \/>\nWe can observe that 35\u00b0 and y are the consecutive interior angles<br \/>\nSo,<br \/>\n35\u00b0 + y = 180\u00b0<br \/>\ny = 180\u00b0 &#8211; 35\u00b0<br \/>\ny = 145\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nx\u00b0 = 35\u00b0 and y\u00b0 = 145\u00b0<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38454\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-177.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 177\" width=\"156\" height=\"92\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38454\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-177.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 177\" width=\"156\" height=\"92\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that 48\u00b0 and y are the consecutive interior angles and y and (5x &#8211; 17)\u00b0 are the corresponding angles<br \/>\nSo,<br \/>\nBy using the Consecutive Interior Angles Theorem,<br \/>\n48\u00b0 + y\u00b0 = 180\u00b0<br \/>\ny\u00b0 = 180\u00b0 &#8211; 48\u00b0<br \/>\ny\u00b0 = 132\u00b0<br \/>\nNow,<br \/>\nBy using the corresponding angles theorem,<br \/>\ny\u00b0 = (5x &#8211; 17)\u00b0<br \/>\n132\u00b0 = (5x &#8211; 17)\u00b0<br \/>\n5x = 132\u00b0 + 17\u00b0<br \/>\n5x = 149\u00b0<br \/>\nx = \\(\\frac{149}{5}\\)<br \/>\nx\u00b0 = 29.8\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nx\u00b0 = 29.8\u00b0 and y\u00b0 = 132\u00b0<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38453\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-178.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 178\" width=\"144\" height=\"89\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38453\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-178.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 178\" width=\"144\" height=\"89\" \/><br \/>\nFrom the above figure,<br \/>\nWe can observe that<br \/>\n2x\u00b0 and 2y\u00b0 are the alternate exterior angles<br \/>\n2y\u00b0 and 58\u00b0 are the alternate interior angles<br \/>\nSo,<br \/>\n2x\u00b0 = 2y\u00b0 = 58\u00b0<br \/>\nSo,<br \/>\nx\u00b0 = y\u00b0 =29\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nx\u00b0 = y\u00b0 = 29\u00b0<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38452\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-179.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 179\" width=\"177\" height=\"93\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38452\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-179.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 179\" width=\"177\" height=\"93\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\n(5y &#8211; 21)\u00b0 and 116\u00b0 are the corresponding angles<br \/>\nSo,<br \/>\n(5y &#8211; 21)\u00b0 = 116\u00b0<br \/>\n5y\u00b0 = 116\u00b0 + 21\u00b0<br \/>\n5y\u00b0 = 137\u00b0<br \/>\ny\u00b0 = \\(\\frac{137}{5}\\)<br \/>\ny\u00b0 = 27.4\u00b0<br \/>\nNow,<br \/>\nWe can observe that<br \/>\n(5y &#8211; 21)\u00b0 ad (6x + 32)\u00b0 are the alternate interior angles<br \/>\nSo,<br \/>\n(5y &#8211; 21)\u00b0 = (6x + 32)\u00b0<br \/>\n5 (28)\u00b0 &#8211; 21\u00b0 = (6x + 32)\u00b0<br \/>\n140 &#8211; 21 &#8211; 32 = 6x\u00b0<br \/>\n6x\u00b0 = 140\u00b0 &#8211; 53\u00b0<br \/>\n6x = 87\u00b0<br \/>\nx = \\(\\frac{87}{6}\\)<br \/>\nx\u00b0 = 14.5\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nx\u00b0 = 14.5\u00b0 and y\u00b0 = 27.4\u00b0<\/p>\n<h4>3.3 Proofs with Parallel Lines<\/h4>\n<p>Find the value of x that makes m || n.<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38451\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-180.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 180\" width=\"119\" height=\"93\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38451\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-180.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 180\" width=\"119\" height=\"93\" \/><br \/>\nWe know that,<br \/>\nm || n is true only when x and 73\u00b0 are the consecutive interior angles according to the &#8220;Converse of Consecutive Interior angles Theorem&#8221;<br \/>\nNow,<br \/>\nIt is given that m || n<br \/>\nSo,<br \/>\nx + 73\u00b0 = 180\u00b0<br \/>\nx = 180\u00b0 &#8211; 73\u00b0<br \/>\nx = 107\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 107\u00b0<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38450\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-181.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 181\" width=\"139\" height=\"98\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38450\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-181.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 181\" width=\"139\" height=\"98\" \/><br \/>\nWe know that,<br \/>\nm || n is true only when 147\u00b0 and (x + 14)\u00b0 are the corresponding angles by using the &#8220;Converse of the Alternate Exterior Angles Theorem&#8221;<br \/>\nNow,<br \/>\nIt is given that m || n<br \/>\nSo,<br \/>\n(x + 14)\u00b0= 147\u00b0<br \/>\nx\u00b0 = 147\u00b0 &#8211; 14\u00b0<br \/>\nx\u00b0 = 133\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 133\u00b0<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38449\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-182.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 182\" width=\"128\" height=\"106\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38449\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-182.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 182\" width=\"128\" height=\"106\" \/><br \/>\nm || n is true only when 3x\u00b0 and (2x + 20)\u00b0 are the corresponding angles by using the &#8220;Converse of the Corresponding Angles Theorem&#8221;<br \/>\nNow,<br \/>\nIt is given that m || n<br \/>\nSo,<br \/>\n(2x + 20)\u00b0= 3x\u00b0<br \/>\n3x\u00b0 &#8211; 2x\u00b0 = 20\u00b0<br \/>\nx\u00b0 = 20\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 20\u00b0<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38448\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-183.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 183\" width=\"174\" height=\"98\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38448\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-183.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 183\" width=\"174\" height=\"98\" \/><br \/>\nWe know that,<br \/>\nm || n is true only when (7x &#8211; 11)\u00b0 and (4x + 58)\u00b0 are the alternate interior angles by the &#8220;Convesre of the Consecutive Interior Angles Theorem&#8221;<br \/>\nNow,<br \/>\nIt is given that m || n<br \/>\nSo,<br \/>\n(7x &#8211; 11)\u00b0 = (4x + 58)\u00b0<br \/>\n7x\u00b0 &#8211; 4x\u00b0 = 58\u00b0 + 11\u00b0<br \/>\n3x\u00b0 = 69\u00b0<br \/>\nx\u00b0 = \\(\\frac{69}{3}\\)<br \/>\nx\u00b0 = 23\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 23\u00b0<\/p>\n<h4>3.4 Proofs with Perpendicular Lines<\/h4>\n<p>Determine which lines, if any, must be parallel. Explain your reasoning.<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38447\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-184.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 184\" width=\"131\" height=\"103\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38447\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-184.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 184\" width=\"131\" height=\"103\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nx \u22a5 z and y \u22a5 z<br \/>\nWe know that,<br \/>\nAccording to the Perpendicular Transversal Theorem,<br \/>\nIn a plane, if a line is perpendicular to one of two parallel\u00a0lines, then it is perpendicular to the other line also.<br \/>\nHence, from the above,<br \/>\nWe can conclude that x and y are parallel lines<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38446\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-185.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 185\" width=\"151\" height=\"123\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38446\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-185.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 185\" width=\"151\" height=\"123\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nw \u22a5 y and z \u22a5 x<br \/>\nWe can also observe that w and z is not both \u22a5 to x and y<br \/>\nWe know that,<br \/>\nAccording to the Perpendicular Transversal Theorem,<br \/>\nIn a plane, if a line is perpendicular to one of two parallel\u00a0lines, then it is perpendicular to the other line also.<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are not any parallel lines in the given figure<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38445\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-186.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 186\" width=\"167\" height=\"106\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38445\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-186.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 186\" width=\"167\" height=\"106\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nm \u22a5 a, n \u22a5 a, l\u00a0\u22a5 b, and n \u22a5 b<br \/>\nWe know that,<br \/>\nAccording to the Perpendicular Transversal Theorem,<br \/>\nIn a plane, if a line is perpendicular to one of two parallel\u00a0lines, then it is perpendicular to the other line also.<br \/>\nHence, from the above,<br \/>\nWe can conclude that m and n are parallel lines<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38444\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-187.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 187\" width=\"145\" height=\"105\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38444\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-3-Parallel-and-Perpendicular-Lines-187.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 187\" width=\"145\" height=\"105\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\na \u22a5 n, b \u22a5 n, and c \u22a5 m<br \/>\nWe know that,<br \/>\nAccording to the Perpendicular Transversal Theorem,<br \/>\nIn a plane, if a line is perpendicular to one of two parallel\u00a0lines, then it is perpendicular to the other line also.<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are not any parallel lines in the given figure<\/p>\n<h4>3.5 Equations of Parallel and Perpendicular Lines<\/h4>\n<p>Write an equation of the line passing through the given point that is parallel to the given line.<\/p>\n<p>Question 17.<br \/>\nA(3, &#8211; 4),y = &#8211; x + 8<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = -x + 8<br \/>\nThe given point is: A (3, -4)<br \/>\nSo,<br \/>\ny = -x + 8<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe slopes are equal fot the parallel lines<br \/>\nSo,<br \/>\nThe equation that is parallel to the given equation is:<br \/>\ny = -x + c<br \/>\nSubstitute A (3, -4) in the above equation to find the value of c<br \/>\nSo,<br \/>\n-4 = -3 + c<br \/>\nc = -4 + 3<br \/>\nc = -1<br \/>\nHence,<br \/>\nThe parallel line equation that is parallel to the given equation is:<br \/>\ny = -x &#8211; 1<\/p>\n<p><span style=\"font-size: 16px;\">Question 18.<br \/>\n<\/span>A(- 6, 5), y = \\(\\frac{1}{2}\\)x &#8211; 7<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = \\(\\frac{1}{2}\\)x &#8211; 7<br \/>\nThe given point is: A (-6, 5)<br \/>\nSo,<br \/>\ny = \\(\\frac{1}{2}\\)x &#8211; 7<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe slopes are equal fot the parallel lines<br \/>\nSo,<br \/>\nThe equation that is parallel to the given equation is:<br \/>\ny = \\(\\frac{1}{2}\\)x + c<br \/>\nSubstitute A (-6, 5) in the above equation to find the value of c<br \/>\nSo,<br \/>\n5 = \\(\\frac{1}{2}\\) (-6) + c<br \/>\nc = 5 + 3<br \/>\nc = 8<br \/>\nHence,<br \/>\nThe parallel line equation that is parallel to the given equation is:<br \/>\ny = \\(\\frac{1}{2}\\)x + 8<\/p>\n<p>Question 19.<br \/>\nA(2, 0), y = 3x &#8211; 5<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = 3x &#8211; 5<br \/>\nThe given point is: A (2, 0)<br \/>\nSo,<br \/>\ny = 3x &#8211; 5<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe slopes are equal for the parallel lines<br \/>\nSo,<br \/>\nThe equation that is parallel to the given equation is:<br \/>\ny = 3x + c<br \/>\nSubstitute A (2, 0) in the above equation to find the value of c<br \/>\nSo,<br \/>\n0 = 3 (2) + c<br \/>\nc = 6 &#8211; 0<br \/>\nc = 6<br \/>\nHence,<br \/>\nThe parallel line equation that is parallel to the given equation is:<br \/>\ny = 3x &#8211; 6<\/p>\n<p><span style=\"font-size: 16px;\">Question 20.<br \/>\n<\/span>A(3, &#8211; 1), y = \\(\\frac{1}{3}\\)x + 10<br \/>\nAnswer:<br \/>\nThe given point is: A (3, -1)<br \/>\nThe given equation is:,<br \/>\ny = \\(\\frac{1}{3}\\)x + 10<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe slopes are equal fot the parallel lines<br \/>\nSo,<br \/>\nThe equation that is parallel to the given equation is:<br \/>\ny = \\(\\frac{1}{3}\\)x + c<br \/>\nSubstitute A (3, -1) in the above equation to find the value of c<br \/>\nSo,<br \/>\n-1 = \\(\\frac{1}{3}\\) (3) + c<br \/>\nc = -1 &#8211; 1<br \/>\nc = -2<br \/>\nHence,<br \/>\nThe parallel line equation that is parallel to the given equation is:<br \/>\ny = \\(\\frac{1}{3}\\)x &#8211; 2<\/p>\n<p>Write an equation of the line passing through the given point that is perpendicular to the given line.<\/p>\n<p>Question 21.<br \/>\nA(6, &#8211; 1), y = &#8211; 2x + 8<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = -2x + 8<br \/>\nThe given point is:A (6, -1)<br \/>\nNow,<br \/>\ny = -2x + 8<br \/>\nWe know that,<br \/>\nThe product of the slopes of perpendicular lines is equal to -1<br \/>\nSo,<br \/>\nm = \\(\\frac{1}{2}\\)<br \/>\nSo,<br \/>\nThe equation that is perpendicular to the given line equation is:<br \/>\ny = \\(\\frac{1}{2}\\)x + c<br \/>\nSubstitute A (6, -1) in the above equation<br \/>\n-1 = \\(\\frac{1}{2}\\) ( 6) + c<br \/>\nc = -1 &#8211; 3<br \/>\nc = -4<br \/>\nHence,<br \/>\nThe equation that is perpendicular to the given equation is:<br \/>\ny = \\(\\frac{1}{2}\\)x &#8211; 4<\/p>\n<p>Question 22.<br \/>\nA(0, 3), y = &#8211; \\(\\frac{1}{2}\\)x &#8211; 6<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = &#8211;\\(\\frac{1}{2}\\)x &#8211; 6<br \/>\nThe given point is: A (0, 3)<br \/>\nNow,<br \/>\ny = \\(\\frac{1}{2}\\)x &#8211; 6<br \/>\nWe know that,<br \/>\nThe product of the slopes of perpendicular lines is equal to -1<br \/>\nSo,<br \/>\nm = 2<br \/>\nSo,<br \/>\nThe equation that is perpendicular to the given line equation is:<br \/>\ny = 2x + c<br \/>\nSubstitute A (0, 3) in the above equation<br \/>\n3 = 2 ( 0) + c<br \/>\nc = 3<br \/>\nHence,<br \/>\nThe equation that is perpendicular to the given equation is:<br \/>\ny = 2x + 3<\/p>\n<p>Question 23.<br \/>\nA(8, 2),y = 4x &#8211; 7<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = 4x &#8211; 7<br \/>\nThe given point is: A (8, 2)<br \/>\nNow,<br \/>\ny = 4x &#8211; 7<br \/>\nWe know that,<br \/>\nThe product of the slopes of perpendicular lines is equal to -1<br \/>\nSo,<br \/>\nm = &#8211;\\(\\frac{1}{4}\\)<br \/>\nSo,<br \/>\nThe equation that is perpendicular to the given line equation is:<br \/>\ny = &#8211;\\(\\frac{1}{4}\\)x + c<br \/>\nSubstitute A (8, 2) in the above equation<br \/>\n2 = &#8211;\\(\\frac{1}{4}\\) (8) + c<br \/>\nc = 2 + 2<br \/>\nc = 4<br \/>\nHence,<br \/>\nThe equation that is perpendicular to the given equation is:<br \/>\ny = &#8211;\\(\\frac{1}{4}\\)x + 4<\/p>\n<p>Question 24.<br \/>\nA(-1, 5), y = \\(\\frac{1}{7}\\)x + 4<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = \\(\\frac{1}{7}\\)x + 4<br \/>\nThe given point is: A (-1, 5)<br \/>\nNow,<br \/>\ny = \\(\\frac{1}{7}\\)x + 4<br \/>\nWe know that,<br \/>\nThe product of the slopes of perpendicular lines is equal to -1<br \/>\nSo,<br \/>\nm = -7<br \/>\nSo,<br \/>\nthe equation that is perpendicular to the given line equation is:<br \/>\ny = -7x + c<br \/>\nSubstitute A (-1, 5) in the above equation<br \/>\n5 = -7 ( -1) + c<br \/>\nc = 5 &#8211; 7<br \/>\nc = -2<br \/>\nHence,<br \/>\nThe equation that is perpendicular to the given equation is:<br \/>\ny = -7x &#8211; 2<\/p>\n<p>Find the distance front point A to the given line.<\/p>\n<p>Question 25.<br \/>\nA(2, &#8211; 1), y = &#8211; x + 4<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = -x + 4 &#8212;&#8212;-(1)<br \/>\nThe given point is: A (2, -1)<br \/>\nCompare the given equation with<br \/>\ny = mx + c<br \/>\nWe know that,<br \/>\nThe product of the slopes of the perpendicular lines is equal to -1<br \/>\nSo,<br \/>\nm1m2 = -1<br \/>\n(-1) (m2) = -1<br \/>\nm2 = 1<br \/>\nSo,<br \/>\nThe equation that is perpendicular to the given line equation is:<br \/>\ny = x + c<br \/>\nSubstitute A (2, -1) in the above equation to find the value of c<br \/>\nSo,<br \/>\n-1 = 2 + c<br \/>\nc = -1 &#8211; 2<br \/>\nc = -3<br \/>\nHence,<br \/>\nThe equation that is perpendicular to the given line equation is:<br \/>\ny = x &#8211; 3 &#8212;&#8212;(2)<br \/>\nNow,<br \/>\nWe have to find the point of intersection<br \/>\nSo,<br \/>\nEq. (1) = Eq. (2)<br \/>\n-x + 4 = x &#8211; 3<br \/>\n-x &#8211; x = -3 &#8211; 4<br \/>\n2x = 7<br \/>\nx = \\(\\frac{7}{2}\\)<br \/>\nSo,<br \/>\ny = x &#8211; 3<br \/>\ny = \\(\\frac{7}{2}\\) &#8211; 3<br \/>\ny = \\(\\frac{1}{2}\\)<br \/>\nSo,<br \/>\nThe point of intersection = (\\(\\frac{7}{2}\\), \\(\\frac{1}{2}\\))<br \/>\nNow,<br \/>\nThe points are: (2, -1), (\\(\\frac{7}{2}\\), \\(\\frac{1}{2}\\))<br \/>\nSo,<br \/>\nd = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3 \/ 2)\u00b2 + (3 \/ 2)\u00b2}\\)<br \/>\n= 2.12<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance from point A to the given line is: 2.12<\/p>\n<p>Question 26.<br \/>\nA(- 2, 3), y = \\(\\frac{1}{2}\\)x + 1<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = \\(\\frac{1}{2}\\)x + 1 &#8212;&#8212;-(1)<br \/>\nThe given point is: A (-2, 3)<br \/>\nCompare the given equation with<br \/>\ny = mx + c<br \/>\nWe know that,<br \/>\nThe product of the slopes of the perpendicular lines is equal to -1<br \/>\nSo,<br \/>\nm1m2 = -1<br \/>\n(\\(\\frac{1}{2}\\)) (m2) = -1<br \/>\nm2 = -2<br \/>\nSo,<br \/>\nThe equation that is perpendicular to the given line equation is:<br \/>\ny = -2x + c<br \/>\nSubstitute A (-2, 3) in the above equation to find the value of c<br \/>\nSo,<br \/>\n3 = -2 (-2) + c<br \/>\nc = 3 &#8211; 4<br \/>\nc = -1<br \/>\nHence,<br \/>\nThe equation that is perpendicular to the given line equation is:<br \/>\ny = -2x &#8211; 1 &#8212;&#8212;(2)<br \/>\nNow,<br \/>\nWe have to find the point of intersection<br \/>\nSo,<br \/>\nEq. (1) = Eq. (2)<br \/>\n\\(\\frac{1}{2}\\)x + 1 = -2x &#8211; 1<br \/>\n\\(\\frac{5}{2}\\)x = 2<br \/>\nx = \\(\\frac{4}{5}\\)<br \/>\nSo,<br \/>\ny = -2x &#8211; 1<br \/>\ny = &#8211;\\(\\frac{8}{5}\\) &#8211; 1<br \/>\ny = &#8211;\\(\\frac{13}{5}\\)<br \/>\nSo,<br \/>\nThe point of intersection = (\\(\\frac{4}{5}\\), &#8211;\\(\\frac{13}{5}\\))<br \/>\nNow,<br \/>\nThe points are: (-2, 3), (\\(\\frac{4}{5}\\), &#8211;\\(\\frac{13}{5}\\))<br \/>\nSo,<br \/>\nd = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{31.36 + 7.84}\\)<br \/>\n= 6.26<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance from point A to the given line is: 6.26<\/p>\n<h3><a id=\"Parallel_and_Perpendicular_Lines_Test\"><\/a>Parallel and Perpendicular Lines Test<\/h3>\n<p>Find the values of x and y. State which theorem(s) you used.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38470\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-188.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 188\" width=\"172\" height=\"136\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38470\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-188.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 188\" width=\"172\" height=\"136\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nx and 61\u00b0 are the vertical angles<br \/>\n61\u00b0 and y\u00b0 are the alternate interior angles<br \/>\nWe know that,<br \/>\nAccording to the &#8220;Alternate Interior Angles theorem&#8221;, the alternate interior angles are congruent<br \/>\nAccording to the &#8220;Vertical Angles Theorem&#8221;, the vertical angles are congruent<br \/>\nHence,<br \/>\nx\u00b0 = y\u00b0 = 61\u00b0<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38469\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-189.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 189\" width=\"210\" height=\"140\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38469\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-189.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 189\" width=\"210\" height=\"140\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\n8x\u00b0 and 96\u00b0 are the alternate interior angles<br \/>\n(11y + 19)\u00b0 and 96\u00b0 are the corresponding angles<br \/>\nWe know that,<br \/>\nAccording to the &#8220;Alternate Interior Angles Theorem&#8221;, the alternate interior angles are congruent<br \/>\nAccording to the &#8220;Corresponding Angles Theorem&#8221;, the corresponding angles are congruent<br \/>\nSo,<br \/>\n8x\u00b0 = 96\u00b0<br \/>\nx\u00b0 = \\(\\frac{96}{8}\\)<br \/>\nx\u00b0 = 12\u00b0<br \/>\nNow,<br \/>\n(11y + 19)\u00b0 = 96\u00b0<br \/>\n11y\u00b0 = 96\u00b0 &#8211; 19\u00b0<br \/>\n11y\u00b0 = 77\u00b0<br \/>\ny\u00b0 = \\(\\frac{77}{11}\\)<br \/>\ny\u00b0 = 7\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nx\u00b0 = 12\u00b0 and y\u00b0 = 7\u00b0<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38468\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-190.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 190\" width=\"174\" height=\"113\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38468\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-190.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 190\" width=\"174\" height=\"113\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\n42\u00b0 and 6(2y &#8211; 3)\u00b0 are the consecutive interior angles<br \/>\n42\u00b0 and (8x + 2)\u00b0 are the vertical angles<br \/>\nWe know that,<br \/>\nAccording to the &#8220;Consecutive Interior Angles Theorem&#8221;, the sum of the consecutive interior angles is 180\u00b0<br \/>\nAccording to the &#8220;Vertical Angles Theorem&#8221;, the vertical angles are congruent<br \/>\nSo,<br \/>\n42\u00b0 + 6 (2y &#8211; 3)\u00b0 = 180\u00b0<br \/>\n6 (2y\u00b0) &#8211;\u00a0 6(3)\u00b0 = 180\u00b0 &#8211; 42\u00b0<br \/>\n12y\u00b0 &#8211; 18\u00b0 = 138\u00b0<br \/>\n12y\u00b0 = 138\u00b0 + 18\u00b0<br \/>\n12y\u00b0 = 156\u00b0<br \/>\ny\u00b0 = \\(\\frac{156}{12}\\)<br \/>\ny\u00b0 = 13\u00b0<br \/>\nNow,<br \/>\n42\u00b0 = (8x + 2)\u00b0<br \/>\n8x\u00b0 = 42\u00b0 &#8211; 2\u00b0<br \/>\nx\u00b0 = 40\u00b0<br \/>\nx\u00b0 = \\(\\frac{40}{8}\\)<br \/>\nx\u00b0 = 5\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nx\u00b0 = 5\u00b0 and y\u00b0 = 13\u00b0<\/p>\n<p>Find the distance from point A to the given line.<\/p>\n<p>Question 4.<br \/>\nA(3, 4), y = &#8211; x<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = -x &#8212;&#8212;-(1)<br \/>\nThe given point is: A (3, 4)<br \/>\nCompare the given equation with<br \/>\ny = mx + c<br \/>\nWe know that,<br \/>\nThe product of the slopes of the perpendicular lines is equal to -1<br \/>\nSo,<br \/>\nm1m2 = -1<br \/>\n(-1) (m2) = -1<br \/>\nm2 = 1<br \/>\nSo,<br \/>\nThe equation that is perpendicular to the given line equation is:<br \/>\nx = c<br \/>\nSubstitute A (3, 4) in the above equation to find the value of c<br \/>\nSo,<br \/>\nc = 3<br \/>\nHence,<br \/>\nThe equation that is perpendicular to the given line equation is:<br \/>\nx = 3 &#8212;&#8212;(2)<br \/>\nNow,<br \/>\nWe have to find the point of intersection<br \/>\nSo,<br \/>\nEq. (1) = Eq. (2)<br \/>\n-x = x &#8211; 3<br \/>\n-x &#8211; x = -3<br \/>\n2x = 3<br \/>\nx = \\(\\frac{3}{2}\\)<br \/>\nSo,<br \/>\ny = -x<br \/>\ny = &#8211;\\(\\frac{3}{2}\\)<br \/>\nSo,<br \/>\nThe point of intersection = (\\(\\frac{3}{2}\\), &#8211;\\(\\frac{3}{2}\\))<br \/>\nNow,<br \/>\nThe points are: (3, 4), (\\(\\frac{3}{2}\\), &#8211;\\(\\frac{3}{2}\\))<br \/>\nSo,<br \/>\nd = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{30.25 + 2.25}\\)<br \/>\n= 5.70<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance from point A to the given line is: 5.70<\/p>\n<p>Question 5.<br \/>\nA(- 3, 7), y = \\(\\frac{1}{3}\\)x &#8211; 2<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = \\(\\frac{1}{3}\\)x &#8211; 2 &#8212;&#8212;-(1)<br \/>\nThe given point is: A (-3, 7)<br \/>\nCompare the given equation with<br \/>\ny = mx + c<br \/>\nWe know that,<br \/>\nThe product of the slopes of the perpendicular lines is equal to -1<br \/>\nSo,<br \/>\nm1m2 = -1<br \/>\n(\\(\\frac{1}{3}\\)) (m2) = -1<br \/>\nm2 = -3<br \/>\nSo,<br \/>\nThe equation that is perpendicular to the given line equation is:<br \/>\ny = -3x + c<br \/>\nSubstitute A (-3, 7) in the above equation to find the value of c<br \/>\nSo,<br \/>\n7 = -3 (-3) + c<br \/>\nc = 7 &#8211; 9<br \/>\nc = -2<br \/>\nHence,<br \/>\nThe equation that is perpendicular to the given line equation is:<br \/>\ny = -3x &#8211; 2 &#8212;&#8212;(2)<br \/>\nNow,<br \/>\nWe have to find the point of intersection<br \/>\nSo,<br \/>\nEq. (1) = Eq. (2)<br \/>\n\\(\\frac{1}{3}\\)x &#8211; 2 = -3x &#8211; 2<br \/>\n\\(\\frac{1}{3}\\)x + 3x = -2 + 2<br \/>\nx = 0<br \/>\nSo,<br \/>\ny = -3x &#8211; 2<br \/>\ny = -3 (0) &#8211; 2<br \/>\ny = -2<br \/>\nSo,<br \/>\nThe point of intersection = (0, -2)<br \/>\nNow,<br \/>\nThe points are: (-3, 7), (0, -2)<br \/>\nSo,<br \/>\nd = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(-2 &#8211; 7)\u00b2 + (0 + 3)\u00b2}\\)<br \/>\n= 9.48<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance from point A to the given line is: 9.48<\/p>\n<p>Find the value of x that makes m || n.<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38467\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-191.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 191\" width=\"151\" height=\"138\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38467\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-191.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 191\" width=\"151\" height=\"138\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nx\u00b0 and 97\u00b0 are the corresponding angles<br \/>\nWe know that,<br \/>\nAccording to the &#8220;Converse of the Corresponding Angles Theorem&#8221;, m || n is true only when the corresponding angles are congruent<br \/>\nIt is given that m || n<br \/>\nSo,<br \/>\nx\u00b0 = 97\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nx\u00b0 = 97\u00b0<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38466\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-192.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 192\" width=\"190\" height=\"121\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38466\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-192.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 192\" width=\"190\" height=\"121\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\n8x\u00b0 and (4x + 24)\u00b0 are the alternate exterior angles<br \/>\nWe know that,<br \/>\nAccording to the &#8220;Converse of the Alternate Exterior Angles Theorem&#8221;, m || n is true only when the alternate exterior angles are congruent<br \/>\nIt is given that m || n<br \/>\nSo,<br \/>\n8x\u00b0 = (4x + 24)\u00b0<br \/>\n8x\u00b0 &#8211; 4x\u00b0 = 24\u00b0<br \/>\n4x\u00b0 = 24\u00b0<br \/>\nx\u00b0 = \\(\\frac{24}{4}\\)<br \/>\nx\u00b0 = 6\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nx\u00b0 = 6\u00b0<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38465\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-193.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 193\" width=\"170\" height=\"123\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38465\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-193.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 193\" width=\"170\" height=\"123\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\n(11x + 33)\u00b0 and (6x &#8211; 6)\u00b0 are the interior angles<br \/>\nWe know that,<br \/>\nAccording to the &#8220;Converse of the Interior Angles Theory&#8221;, m || n is true only when the sum of the interior angles are supplementary<br \/>\nIt is given that m || n<br \/>\nSo,<br \/>\n(11x + 33)\u00b0+(6x &#8211; 6)\u00b0 = 180\u00b0<br \/>\n17x\u00b0 + 27\u00b0 = 180\u00b0<br \/>\n17x\u00b0 = 180\u00b0 &#8211; 27\u00b0<br \/>\nx\u00b0 = &#8211;\\(\\frac{153}{17}\\)<br \/>\nx\u00b0 = 9\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nx\u00b0 = 9\u00b0<\/p>\n<p>Write an equation of the line that passes through the given point and is<br \/>\n(a) parallel to and<br \/>\n(b) perpendicular to the given line.<\/p>\n<p>Question 9.<br \/>\n(- 5, 2), y = 2x &#8211; 3<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny= 2x &#8211; 3<br \/>\nThe given point is: (-5, 2)<br \/>\na) Parallel to the given line:<br \/>\nWe know that,<br \/>\nThe slopes of the parallel lines are the same<br \/>\nCompare the given equation with<br \/>\ny = mx + c<br \/>\nSo,<br \/>\nThe equation of the line that is parallel to the given line is:<br \/>\ny = 2x + c<br \/>\nTo find the value of c,<br \/>\nSubstitute (-5, 2) in the above equation<br \/>\nSo,<br \/>\n2 = 2 (-5) + c<br \/>\n2 + 10 = c<br \/>\nc = 12<br \/>\nHence,<br \/>\nThe equation of the line that is parallel to the given line equation is:<br \/>\ny = 2x + 12<br \/>\nb) Perpendicular to the given line:<br \/>\nWe know that,<br \/>\nThe product of the slopes of the perpendicular lines is equal to -1<br \/>\nSo,<br \/>\nm1 m2 = -1<br \/>\n2m2 = -1<br \/>\nm2 = &#8211;\\(\\frac{1}{2}\\)<br \/>\nSo,<br \/>\nThe equation of the line that is perpendicular to the given line equation is:<br \/>\ny = &#8211;\\(\\frac{1}{2}\\)x + c<br \/>\nTo find the value of c,<br \/>\nSubstitute (-5, 2) in the given equation<br \/>\n2 = &#8211;\\(\\frac{1}{2}\\) (-5) + c<br \/>\nc = &#8211;\\(\\frac{1}{2}\\)<br \/>\nHence,<br \/>\nThe equation of the line that is perpendicular to the given line equation is:<br \/>\ny = &#8211;\\(\\frac{1}{2}\\)x &#8211; \\(\\frac{1}{2}\\)<\/p>\n<p>Question 10.<br \/>\n(- 1, &#8211; 9), y = &#8211; \\(\\frac{1}{3}\\)x + 4<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny= &#8211;\\(\\frac{1}{3}\\)x + 4<br \/>\nThe given point is: (-1, -9)<br \/>\na) Parallel to the given line:<br \/>\nWe know that,<br \/>\nThe slopes of the parallel lines are the same<br \/>\nCompare the given equation with<br \/>\ny = mx + c<br \/>\nSo,<br \/>\nThe equation of the line that is parallel to the given line is:<br \/>\ny = &#8211;\\(\\frac{1}{3}\\)x + c<br \/>\nTo find the value of c,<br \/>\nSubstitute (-1, -9) in the above equation<br \/>\nSo,<br \/>\n-9 = &#8211;\\(\\frac{1}{3}\\) (-1) + c<br \/>\nc = \\(\\frac{26}{3}\\)<br \/>\nHence,<br \/>\nThe equation of the line that is parallel to the given line equation is:<br \/>\ny = &#8211;\\(\\frac{1}{3}\\)x + \\(\\frac{26}{3}\\)<br \/>\nb) Perpendicular to the given line:<br \/>\nWe know that,<br \/>\nThe product of the slopes of the perpendicular lines is equal to -1<br \/>\nSo,<br \/>\nm1 m2 = -1<br \/>\n&#8211;\\(\\frac{1}{3}\\)m2 = -1<br \/>\nm2 = 3<br \/>\nSo,<br \/>\nThe equation of the line that is perpendicular to the given line equation is:<br \/>\ny = 3x + c<br \/>\nTo find the value of c,<br \/>\nSubstitute (-1, -9) in the given equation<br \/>\n-9 = 3 (-1) + c<br \/>\nc = -6<br \/>\nHence,<br \/>\nThe equation of the line that is perpendicular to the given line equation is:<br \/>\ny = 3x &#8211; 6<\/p>\n<p>Question 11.<br \/>\nA student says. \u201cBecause j \u22a5 K, j \u22a5 l\u2019 What missing information is the student assuming from the diagram? Which theorem is the student trying to use?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38464\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-194.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 194\" width=\"174\" height=\"108\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38464\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-194.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 194\" width=\"174\" height=\"108\" \/><br \/>\nIt is given that a student claimed that j \u22a5 K, j \u22a5 l<br \/>\nWe know that,<br \/>\nAccording to the &#8220;Perpendicular Transversal Theorem&#8221;,<br \/>\nIn a plane, if a line is perpendicular to one of two parallel\u00a0lines, then it is perpendicular to the other line also.<br \/>\nSo,<br \/>\nFrom the above definition,<br \/>\nThe missing information the student assuming from the diagram is:<br \/>\nThe line l is also perpendicular to the line j<br \/>\nHence, from the above,<br \/>\nWe can conclude that the theorem student trying to use is the &#8220;Perpendicular Transversal Theorem&#8221;<\/p>\n<p>Question 12.<br \/>\nYou and your family are visiting some attractions while on vacation. You and your mom visit the shopping mall while your dad and your sister visit the aquarium. You decide to meet at the intersection of lines q and p. Each unit in the coordinate plane corresponds to 50 yards.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38463\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-195.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 195\" width=\"228\" height=\"210\" \/><br \/>\nAnswer:<br \/>\nYou and your family are visiting some attractions while on vacation. You and your mom visit the shopping mall while your dad and your sister visit the aquarium. You decide to meet at the intersection of lines q and p. Each unit in the coordinate plane corresponds to 50 yards.<\/p>\n<p>a. Find an equation of line q.<br \/>\nAnswer:<br \/>\nFrom the figure,<br \/>\nThe coordinates of line q are:<br \/>\n(50, 500), (200, 50)<br \/>\nCompare the given points with<br \/>\n(x1, y1), (x2, y2)<br \/>\nWe know that,<br \/>\nSlope (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{50 &#8211; 500}{200 &#8211; 50}\\)<br \/>\n= \\(\\frac{-450}{150}\\)<br \/>\n= &#8211;\\(\\frac{45}{15}\\)<br \/>\n= -3<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe standard form of the equation is:<br \/>\ny &#8211; y1 = m (x &#8211; x1)<br \/>\nSo,<br \/>\ny &#8211; 500 = -3 (x -50)<br \/>\ny &#8211; 500 = -3x + 150<br \/>\ny = -3x + 150 + 500<br \/>\ny = -3x + 650<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe equation of line q is:<br \/>\ny = -3x + 650<\/p>\n<p>b. Find an equation of line p.<br \/>\nAnswer:<br \/>\nFrom the figure,<br \/>\nThe coordinates of line p are:<br \/>\n(50, 175), (500, 325)<br \/>\nCompare the given points with<br \/>\n(x1, y1), (x2, y2)<br \/>\nWe know that,<br \/>\nSlope (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{325 &#8211;\u00a0 175}{500 &#8211; 50}\\)<br \/>\n= \\(\\frac{15}{45}\\)<br \/>\n= \\(\\frac{1}{3}\\)<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe standard form of the equation is:<br \/>\ny &#8211; y1 = m (x &#8211; x1)<br \/>\nSo,<br \/>\ny &#8211; 175 = \\(\\frac{1}{3}\\) (x -50)<br \/>\n3 (y &#8211; 175) = x &#8211; 50<br \/>\n3y &#8211; 525 = x &#8211; 50<br \/>\n3y = x &#8211; 50 + 525<br \/>\n3y = x + 475<br \/>\ny = \\(\\frac{1}{3}\\)x + \\(\\frac{475}{3}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe equation of line p is:<br \/>\ny = \\(\\frac{1}{3}\\)x + \\(\\frac{475}{3}\\)<\/p>\n<p>c. What are the coordinates of the meeting point?<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can conclue that<br \/>\nThe coordinates of the meeting point are: (150. 200)<\/p>\n<p>d. What is the distance from the meeting point to the subway?<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nThe coordinates of the meeting point are: (150, 200)<br \/>\nThe coordinates of the subway are: (500, 300)<br \/>\nNow,<br \/>\nThe distance between the meeting point and the subway is:<br \/>\nd = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nd = \\(\\sqrt{(300 &#8211; 200)\u00b2 + (500 &#8211; 150)\u00b2}\\)<br \/>\nd = 364.5 yards<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance between the meeting point and the subway is: 364.5 yards<\/p>\n<p>Question 13.<br \/>\nIdentify an example on the puzzle cube of each description. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38462\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-196.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 196\" width=\"239\" height=\"233\" \/><br \/>\na. a pair of skew lines<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe &#8220;Skew lines&#8221; are the lines that are non-intersecting, non-parallel and non-coplanar<br \/>\nHence,<br \/>\nFrom the given figure,<br \/>\nWe can conclude that the pair of skew lines are:<br \/>\n\\(\\overline{A B}\\) and \\(\\overline{G H}\\)<\/p>\n<p>b. a pair of perpendicular lines<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe &#8220;Perpendicular lines&#8221; are the lines that are intersected at the right angles<br \/>\nHence,<br \/>\nFrom the given figure,<br \/>\nWe can conclude that the pair of perpendicular lines are:<br \/>\n\\(\\overline{I J}\\) and \\(\\overline{C D}\\)<\/p>\n<p>c. a pair of paralIeI lines<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe &#8220;parallel lines&#8221; are the lines that do not have any intersection point<br \/>\nHence,<br \/>\nFrom the given figure,<br \/>\nWe can conclude that the pair of parallel lines are:<br \/>\n\\(\\overline{C D}\\) and \\(\\overline{E F}\\)<\/p>\n<p>d. a pair of congruent corresponding angles<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can conclude that<br \/>\n\u22201 and \u22203 are the corresponding angles<\/p>\n<p>e. a pair of congruent alternate interior angles<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can conclude that<br \/>\n\u22202 and \u22203 are the congruent alternate interior angles<\/p>\n<h3><a id=\"Parallel_and_Perpendicular_Lines_Cumulative_Assessment\"><\/a>Parallel and Perpendicular Lines Cumulative Assessment<\/h3>\n<p>Question 1.<br \/>\nUse the steps in the construction to explain how you know that\\(\\overline{C D}\\) is the perpendicular bisector of \\(\\overline{A B}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38487\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-198.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 198\" width=\"593\" height=\"174\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-198.png 593w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-198-300x88.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><br \/>\nAnswer:<br \/>\nStep 1:<br \/>\nDraw a line segment of any length and name that line segment as AB<br \/>\nStep 2:<br \/>\nDraw an arc by using a compass with above half of the length of AB by taking the center at A above AB<br \/>\nStep 3:<br \/>\nDraw another arc by using a compass with above half of the length of AB by taking the center at B above AB<br \/>\nStep 4:<br \/>\nRepeat steps 3 and 4 below AB<br \/>\nStep 5:<br \/>\nDraw a line segment CD by joining the arcs above and below AB<br \/>\nStep 6:<br \/>\nMeasure the lengths of the midpoint of AB i.e., AD and DB.<br \/>\nBy measuring their lengths, we can prove that CD is the perpendicular bisector of AB<\/p>\n<p>Question 2.<br \/>\nThe equation of a line is x + 2y = 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38486\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-199.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 199\" width=\"555\" height=\"136\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-199.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-199-300x74.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><br \/>\na. Use the numbers and symbols to create the equation of a line in slope-intercept form<br \/>\nthat passes through the point (4, &#8211; 5) and is parallel to the given line.<br \/>\nAnswer:<br \/>\nThe given line equation is:<br \/>\nx + 2y = 10<br \/>\nThe given point is: (4, -5)<br \/>\nNow,<br \/>\nThe given equation in the slope-intercept form is:<br \/>\ny = &#8211;\\(\\frac{1}{2}\\)x + 5<br \/>\nWe know that,<br \/>\nThe slopes of the parallel lines are the same<br \/>\nSo,<br \/>\nThe equation of the line that is parallel to the given line equation is:<br \/>\ny = &#8211;\\(\\frac{1}{2}\\)x + c<br \/>\nTo find the value of c,<br \/>\nSubstitute (4, -5) in the above equation<br \/>\nSo,<br \/>\n-5 = &#8211;\\(\\frac{1}{2}\\) (4) + c<br \/>\nc = -5 + 2<br \/>\nc = -3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the line that is parallel to the given line equation is:<br \/>\ny = &#8211;\\(\\frac{1}{2}\\)x &#8211; 3<\/p>\n<p>b. Use the numbers and symbols to create the equation of a line in slope-intercept form<br \/>\nthat passes through the point (2, &#8211; 1) and is perpendicular to the given line.<br \/>\nAnswer:<br \/>\nThe given line equation is:<br \/>\nx + 2y = 10<br \/>\nThe given point is: (4, -5)<br \/>\nNow,<br \/>\nThe given equation in the slope-intercept form is:<br \/>\ny = &#8211;\\(\\frac{1}{2}\\)x + 5<br \/>\nWe know that,<br \/>\nThe product of the slopes of the perpendicular lines is equal to -1<br \/>\nSo,<br \/>\nm1m2 = -1<br \/>\n&#8211;\\(\\frac{1}{2}\\) (m2) = -1<br \/>\nm2 = 2<br \/>\nSo,<br \/>\nThe equation of the line that is perpendicular to the given line equation is:<br \/>\ny = 2x + c<br \/>\nTo find the value of c,<br \/>\nSubstitute (4, -5) in the above equation<br \/>\nSo,<br \/>\n-5 = 2 (4) + c<br \/>\n-5 &#8211; 8 = c<br \/>\nc = -13<br \/>\nHence, from the above,<br \/>\nWe can conclude that a line equation that is perpendicular to the given line equation is:<br \/>\ny = 2x &#8211; 13<\/p>\n<p>Question 3.<br \/>\nClassify each pair of angles whose measurements are given.<br \/>\na.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38485\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-200.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 200\" width=\"220\" height=\"103\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38485\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-200.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 200\" width=\"220\" height=\"103\" \/><br \/>\nFrom the given figure,<br \/>\nWe can conclude that 44\u00b0 and 136\u00b0 are the adjacent angles<\/p>\n<p>b.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38484\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-201.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 201\" width=\"94\" height=\"121\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38484\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-201.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 201\" width=\"94\" height=\"121\" \/><br \/>\nFrom the given figure,<br \/>\nWe can conclude that 18\u00b0 and 23\u00b0 are the adjacent angles<\/p>\n<p>c.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38483\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-202.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 202\" width=\"112\" height=\"110\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38483\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-202.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 202\" width=\"112\" height=\"110\" \/><br \/>\nFrom the given figure,<br \/>\nWe can conclude that 75\u00b0 and 75\u00b0 are alternate interior angles<\/p>\n<p>d.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38482\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-203.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 203\" width=\"142\" height=\"141\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38482\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-203.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 203\" width=\"142\" height=\"141\" \/><br \/>\nFrom the given figure,<br \/>\nWe can conclude that 42\u00b0 and 48\u00b0 are the vertical angles<\/p>\n<p>Question 4.<br \/>\nYour school is installing new turf on the football held. A coordinate plane has been superimposed on a diagram of the football field where 1 unit = 20 feet.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38481\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-204.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 204\" width=\"305\" height=\"143\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-204.png 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-204-300x141.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><br \/>\na. What is the length of the field?<br \/>\nAnswer:<br \/>\nIt is given that a coordinate plane has been superimposed on a diagram of the football field where 1 unit is 20 feet.<br \/>\nSo,<br \/>\nFrom the given figure,<br \/>\nThe length of the field = | 20 &#8211; 340 |<br \/>\n= 320 feet<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of the field is: 320 feet<\/p>\n<p>b. What is the perimeter of the field?<br \/>\nAnswer:<br \/>\nFrom the figure,<br \/>\nThe width of the field is: 140 feet<br \/>\nFrom the figure,<br \/>\nWe can observe that the figure is in the form of a rectangle<br \/>\nWe know that,<br \/>\nThe perimeter of the field = 2 ( Length + Width)<br \/>\n= 2 (320 + 140)<br \/>\n= 2 (460)<br \/>\n= 920 feet<br \/>\nHence, from the above,<br \/>\nWe can conclude that the perimeter of the field is: 920 feet<\/p>\n<p>c. Turf costs $2.69 per square foot. Your school has a $1,50,000 budget. Does the school have enough money to purchase new turf for the entire field?<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe area of the field = Length \u00d7 Width<br \/>\nSo,<br \/>\nThe area of the field = 320 \u00d7 140<br \/>\n= 44,800 square feet<br \/>\nit is given that the turf costs $2.69 per square foot<br \/>\nSo,<br \/>\nThe total cost of the turf = 44,800 \u00d7 2.69<br \/>\n= $1,20,512<br \/>\nIt is given that your school has a budget of $1,50,000 but we only need $1,20,512<br \/>\nHence, from the above,<br \/>\nWe can conclude that the school have enough money to purchase new turf for the entire field<\/p>\n<p>Question 5.<br \/>\nEnter a statement or reason in each blank to complete the two-column proof.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38480\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-205.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 205\" width=\"191\" height=\"120\" \/><br \/>\nGiven \u22201 \u2245\u22203<br \/>\nProve \u22202 \u2245\u22204<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-85090\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-40.png\" alt=\"\" width=\"359\" height=\"130\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-40.png 359w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-40-300x109.png 300w\" sizes=\"(max-width: 359px) 100vw, 359px\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-85090\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-40.png\" alt=\"\" width=\"359\" height=\"130\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-40.png 359w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-40-300x109.png 300w\" sizes=\"(max-width: 359px) 100vw, 359px\" \/><br \/>\nHence,<br \/>\nThe completed table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-85091\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-7.jpg\" alt=\"\" width=\"367\" height=\"131\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-7.jpg 367w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-3-7-300x107.jpg 300w\" sizes=\"(max-width: 367px) 100vw, 367px\" \/><\/p>\n<p>Question 6.<br \/>\nYour friend claims that lines m and n are parallel. Do you support your friend\u2019s claim? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38479\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-206.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 206\" width=\"161\" height=\"123\" \/><br \/>\nAnswer:<br \/>\nYes, I support my friend&#8217;s claim<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38479\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-206.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 206\" width=\"161\" height=\"123\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that 141\u00b0 and 39\u00b0 are the consecutive interior angles<br \/>\nWe know that,<br \/>\nAccording to the consecutive Interior Angles Theorem,<br \/>\nIf the sum of the angles of the consecutive interior angles is 180\u00b0, then the two lines that are cut by a transversal are parallel<br \/>\nHence, from the above,<br \/>\nWe can conclude that the claim of your friend can be supported<\/p>\n<p>Question 7.<br \/>\nWhich of the following is true when <img loading=\"lazy\" class=\"alignnone size-full wp-image-38478\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-207.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 207\" width=\"90\" height=\"26\" \/> are skew?<br \/>\n(A) <img loading=\"lazy\" class=\"alignnone size-full wp-image-38478\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-207.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 207\" width=\"90\" height=\"26\" \/> are parallel.<br \/>\n(B) <img loading=\"lazy\" class=\"alignnone size-full wp-image-38478\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-207.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 207\" width=\"90\" height=\"26\" \/> intersect<br \/>\n(C) <img loading=\"lazy\" class=\"alignnone size-full wp-image-38478\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-207.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 207\" width=\"90\" height=\"26\" \/> are perpendicular<br \/>\n(D) A, B, and C are noncollinear.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe &#8220;Skew lines&#8221; are the lines that are not parallel, non-intersect, and non-coplanar<br \/>\nHene, from the given options,<br \/>\nWe can conclude that option D) is correct because parallel and perpendicular lines have to be lie in the same plane<\/p>\n<p>Question 8.<br \/>\nSelect the angle that makes the statement true.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38477\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-208.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 208\" width=\"163\" height=\"136\" \/><br \/>\n\u22201\u00a0 \u00a0 \u22202\u00a0 \u00a0 \u22203\u00a0 \u00a0 \u22204\u00a0 \u00a0 \u22205\u00a0 \u00a0 \u00a0\u22206\u00a0 \u00a0 \u00a0\u22207\u00a0 \u00a0 \u00a0\u22208<br \/>\na. \u22204 \u2245 ________ b the Alternate Interior Angles Theorem (Thm. 3.2).<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can conclude that<br \/>\nBy using the Alternate interior angles Theorem,<br \/>\n\u22204 \u2245 \u22205<\/p>\n<p>b. \u22202 \u2245 ________ by the Corresponding Angles Theorem (Thm. 3. 1)<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can conclude that<br \/>\nBy using the Corresponding angles Theorem,<br \/>\n\u22202 \u2245 \u22206<\/p>\n<p>c. \u22201 \u2245 ________ by the Alternate Exterior Angles Theorem (Thm. 3.3).<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can conclude that<br \/>\nBy using the Alternate exterior angles Theorem,<br \/>\n\u22201 \u2245 \u22208<\/p>\n<p>d. m\u22206 + m ________ = 180\u00b0 by the Consecutive Interior Angles Theorem (Thm. 3.4).<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can conclude that<br \/>\nBy using the Consecutive interior angles Theorem,<br \/>\n\u22206 + \u22204 = 180\u00b0<\/p>\n<p>Question 9.<br \/>\nYou and your friend walk to school together every day. You meet at the halfway point between your houses first and then walk to school. Each unit in the coordinate plane corresponds to 50 yards.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38476\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-3-Parallel-and-Perpendicular-Lines-209.png\" alt=\"Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 209\" width=\"230\" height=\"220\" \/><br \/>\nAnswer:<br \/>\nIt is given that you and your friend walk to school together every day. You meet at the halfway point between your houses first and then walk to school. Each unit in the coordinate plane corresponds to 50 yards.<br \/>\na. What are the coordinates of the midpoint of the line segment joining the two houses?<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can conclude that the midpoint of the line segment joining the two houses is:<br \/>\nM = (150, 250)<\/p>\n<p>b. What is the distance that the two of you walk together?<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nThe coordinates of the school = (400, 300)<br \/>\nThe coordinates of the midpoint of the line segment joining the two houses = (150, 250)<br \/>\nIt is given that the two friends walk together from the midpoint of the houses to the school<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe distance that the two of you walk together is:<br \/>\nd = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(250 &#8211; 300)\u00b2 + (150 &#8211; 400)\u00b2}\\)<br \/>\n= \\(\\sqrt{2500 + 62,500}\\)<br \/>\n= 255 yards<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance that the two of the friends walk together is: 255 yards<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Seeking help regarding the concepts of Big Ideas Geometry Answer Key Ch 3 Parallel and Perpendicular Lines? 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