{"id":44024,"date":"2022-04-02T17:02:30","date_gmt":"2022-04-02T11:32:30","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=44024"},"modified":"2022-04-07T11:10:51","modified_gmt":"2022-04-07T05:40:51","slug":"big-ideas-math-geometry-answers-chapter-7","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-geometry-answers-chapter-7\/","title":{"rendered":"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons"},"content":{"rendered":"<p>Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Polygons present here will help you get good ideas on the associated lessons in it easily. Utilize the quick resources available here for Big Ideas Math Geometry Ch 7 Solutions and attempt the final exam with confidence. Solving the BIM Book Geometry Ch 7 Quadrilaterals and Polygons will boost up your confidence and improve your speed and accuracy while writing the exam. Download the Chapter 7 Quadrilaterals and Other Polygons <a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-geometry-answers\/\">Big Ideas Math Geometry Answers<\/a> via quick links and ace up your preparation.<\/p>\n<h2>Big Ideas Math Book Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons<\/h2>\n<p>Big Ideas Math Geometry Answers Ch 7 Quadrilaterals and Other Polygons include the topics such as how to measure angles of a polygon, properties of different shapes, finding diagonals on a polygon, etc. If you need any help on the BIM Book Geometry Chapter 7 Quadrilaterals and Other Polygons concepts you can always use this quick reference. With Consistent Practice using the Big Ideas Math Geometry Ch 7 Solutions you will no longer feel any difficulty in understanding the concepts.<\/p>\n<p>&nbsp;<\/p>\n<ul>\n<li><a href=\"#Quadrilaterals_and_Other_Polygons_Maintaining_Mathematical_Proficiency\">Quadrilaterals and Other Polygons Maintaining Mathematical Proficiency &#8211; Page 357<\/a><\/li>\n<li><a href=\"#Quadrilaterals_and_Other_Polygons_Mathematical_Practices\">Quadrilaterals and Other Polygons Mathematical Practices &#8211; Page 358<\/a><\/li>\n<li><a href=\"#7.1_Angles_of_Polygons\">7.1 Angles of Polygons &#8211; Page 359<\/a><\/li>\n<li><a href=\"#Lesson_7.1_Angles_of_Polygons\">Lesson 7.1 Angles of Polygons &#8211; Page(360-366)<\/a><\/li>\n<li><a href=\"#Exercise_7.1_Angles_of_Polygons\">Exercise 7.1 Angles of Polygons &#8211; Page(364-366)<\/a><\/li>\n<li><a href=\"#7.2_Properties_of_Parallelograms\">7.2 Properties of Parallelograms &#8211; Page 367<\/a><\/li>\n<li><a href=\"#Lesson_7.2_Properties_of_Parallelograms\">Lesson 7.2 Properties of Parallelograms &#8211; Page(368-374)<\/a><\/li>\n<li><a href=\"#Exercise_7.2_Properties_of_Parallelograms\">Exercise 7.2 Properties of Parallelograms &#8211; Page(372-374)<\/a><\/li>\n<li><a href=\"#7.3_Proving_That_a_Quadrilateral_is_a_Parallelogram\">7.3 Proving That a Quadrilateral is a Parallelogram &#8211; Page 375<\/a><\/li>\n<li><a href=\"#Lesson_7.3_Proving_that_a_Quadrilateral_is_a_Parallelogram\">Lesson 7.3 Proving that a Quadrilateral is a Parallelogram &#8211; Page(376-384)<\/a><\/li>\n<li><a href=\"#Exercise_7.3_Proving_that_a_Quadrilateral_is_a_Parallelogram\">Exercise 7.3 Proving that a Quadrilateral is a Parallelogram &#8211; Page(381-384)<\/a><\/li>\n<li><a href=\"#7.1_-_7.3_Quiz\">7.1 &#8211; 7.3 Quiz &#8211; Page 386<\/a><\/li>\n<li><a href=\"#7.4_Properties_of_Special_Parallelograms\">7.4 Properties of Special Parallelograms &#8211; Page 387<\/a><\/li>\n<li><a href=\"#Lesson_7.4_Properties_of_Special_Parallelograms\">Lesson 7.4 Properties of Special Parallelograms &#8211; Page (388-396)<\/a><\/li>\n<li><a href=\"#Exercise_7.4_Properties_of_Special_Parallelograms\">Exercise 7.4 Properties of Special Parallelograms &#8211; Page(393-396)<\/a><\/li>\n<li><a href=\"#7.5_Properties_of_Trapezoids_and_Kites\">7.5 Properties of Trapezoids and Kites &#8211; Page 397<\/a><\/li>\n<li><a href=\"#Lesson_7.5_Properties_of_Trapezoids_and_Kites\">Lesson 7.5 Properties of Trapezoids and Kites &#8211; Page(398-406)<\/a><\/li>\n<li><a href=\"#Exercise_7.5_Properties_of_Trapezoids_and_Kites\">Exercise 7.5 Properties of Trapezoids and Kites &#8211; Page(403-406)<\/a><\/li>\n<li><a href=\"#Quadrilaterals_and_Other_Polygons_Review\">Quadrilaterals and Other Polygons Review &#8211; Page(408-410)<\/a><\/li>\n<li><a href=\"#Quadrilaterals_and_Other_Polygons_Test\">Quadrilaterals and Other Polygons Test &#8211; Page 411<\/a><\/li>\n<li><a href=\"#Quadrilaterals_and_Other_Polygons_Cummulative_Assessment\">Quadrilaterals and Other Polygons Cummulative Assessment &#8211; Page(412-413)<\/a><\/li>\n<\/ul>\n<h3><a id=\"Quadrilaterals_and_Other_Polygons_Maintaining_Mathematical_Proficiency\"><\/a>Quadrilaterals and Other Polygons Maintaining Mathematical Proficiency<\/h3>\n<p>Solve the equation by interpreting the expression in parentheses as a single quantity.<\/p>\n<p>Question 1.<br \/>\n4(7 &#8211; x) = 16<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n4 (7 &#8211; x) = 16<br \/>\n7 &#8211; x = \\(\\frac{16}{4}\\)<br \/>\n7 &#8211; x = 4<br \/>\n7 &#8211; 4 = x<br \/>\nx = 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 3<\/p>\n<p>Question 2.<br \/>\n7(1 &#8211; x) + 2 = &#8211; 19<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n7 (1 &#8211; x) + 2 = -19<br \/>\n7 (1 &#8211; x) = -19 &#8211; 2<br \/>\n1 &#8211; x = &#8211;\\(\\frac{21}{7}\\)<br \/>\n1 &#8211; x = -3<br \/>\n1 + 3 = x<br \/>\nx = 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 4<\/p>\n<p>Question 3.<br \/>\n3(x &#8211; 5) + 8(x &#8211; 5) = 22<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n3 (x &#8211; 5) + 8 (x &#8211; 5) = 22<br \/>\n(x &#8211; 5) (3 + 8) = 22<br \/>\nx &#8211; 5 = \\(\\frac{22}{11}\\)<br \/>\nx &#8211; 5 = 2<br \/>\nx = 2 + 5<br \/>\nx = 7<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 7<\/p>\n<p>Determine which lines are parallel and which are perpendicular.<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44102\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 1\" width=\"205\" height=\"203\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-1.png 205w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-1-150x150.png 150w\" sizes=\"(max-width: 205px) 100vw, 205px\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44102\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 1\" width=\"205\" height=\"203\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-1.png 205w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-1-150x150.png 150w\" sizes=\"(max-width: 205px) 100vw, 205px\" \/><br \/>\nFrom the given figure,<br \/>\nThe coordinates of line a are: (-2, 2), (4, -2)<br \/>\nThe coordinates of line b are: (-3, -2), (0, -4)<br \/>\nThe coordinates of line &#8216;c&#8217; are: (-3, 0), (3, -3)<br \/>\nThe coordinates of line &#8216;d&#8217; are: (1, 0), (3, 4)<br \/>\nCompare the given coordinates with (x1, y1), (x2, y2)<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe slope of the line (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\nThe slope of line a = \\(\\frac{-2 &#8211; 2}{4 + 2 }\\)<br \/>\n= \\(\\frac{-4}{6}\\)<br \/>\n= &#8211;\\(\\frac{2}{3}\\)<br \/>\nThe slope of line b = \\(\\frac{-4 + 2}{0 + 3}\\)<br \/>\n= \\(\\frac{-6}{3}\\)<br \/>\n= -2<br \/>\nThe slope of line c = \\(\\frac{-3 &#8211; 0}{3 + 3}\\)<br \/>\n= \\(\\frac{-3}{6}\\)<br \/>\n= &#8211;\\(\\frac{1}{2}\\)<br \/>\nThe slope of line d = \\(\\frac{4 &#8211; 0}{3 &#8211; 1}\\)<br \/>\n= \\(\\frac{4}{2}\\)<br \/>\n= 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that line c and line d are perpendicular lines<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44100\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-2.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 2\" width=\"205\" height=\"205\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-2.png 205w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-2-150x150.png 150w\" sizes=\"(max-width: 205px) 100vw, 205px\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44100\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-2.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 2\" width=\"205\" height=\"205\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-2.png 205w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-2-150x150.png 150w\" sizes=\"(max-width: 205px) 100vw, 205px\" \/><br \/>\nFrom the given figure,<br \/>\nThe coordinates of line a are: (3, 1), (0, -3)<br \/>\nThe coordinates of line b are: (0, 1), (-3, -3)<br \/>\nThe coordinates of line &#8216;c&#8217; are: (2, 1), (-2, 4)<br \/>\nThe coordinates of line &#8216;d&#8217; are: (4, -4), (-4, 2)<br \/>\nCompare the given coordinates with (x1, y1), (x2, y2)<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe slope of the line (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\nThe slope of line a = \\(\\frac{-3 &#8211; 1}{0 &#8211; 3}\\)<br \/>\n= \\(\\frac{-4}{-3}\\)<br \/>\n= \\(\\frac{4}{3}\\)<br \/>\nThe slope of line b = \\(\\frac{-3 &#8211; 1}{-3 &#8211; 0}\\)<br \/>\n= \\(\\frac{-4}{-3}\\)<br \/>\n= \\(\\frac{4}{3}\\)<br \/>\nThe slope of line c = \\(\\frac{2 + 4}{-4 &#8211; 4}\\)<br \/>\n= \\(\\frac{6}{-8}\\)<br \/>\n= &#8211;\\(\\frac{3}{4}\\)<br \/>\nThe slope of line d = \\(\\frac{4 + 2}{-4 &#8211; 4}\\)<br \/>\n= \\(\\frac{6}{-8}\\)<br \/>\n= &#8211;\\(\\frac{3}{4}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nline a and line b are parallel lines<br \/>\nline c and line d are parallel lines<br \/>\nline b and line c and line a and line c are perpendicular lines<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44099\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 3\" width=\"230\" height=\"206\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44099\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 3\" width=\"230\" height=\"206\" \/><br \/>\nFrom the given figure,<br \/>\nThe coordinates of line a are: (4, -4), (-2, -2)<br \/>\nThe coordinates of line b are: (-3, -2), (-2, 2)<br \/>\nThe coordinates of line &#8216;c&#8217; are: (3, 1), (2, -3)<br \/>\nThe coordinates of line &#8216;d&#8217; are: (0, 3), (-4, 4)<br \/>\nCompare the given coordinates with (x1, y1), (x2, y2)<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe slope of the line (m) = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\nThe slope of line a = \\(\\frac{-2 + 4}{-2 &#8211; 4}\\)<br \/>\n= \\(\\frac{2}{-6}\\)<br \/>\n= &#8211;\\(\\frac{1}{3}\\)<br \/>\nThe slope of line b = \\(\\frac{2 + 2}{-2 + 3}\\)<br \/>\n= \\(\\frac{4}{1}\\)<br \/>\n= 4<br \/>\nThe slope of line c = \\(\\frac{-3 &#8211; 1}{2 &#8211; 3}\\)<br \/>\n= \\(\\frac{-4}{-1}\\)<br \/>\n= 4<br \/>\nThe slope of line d = \\(\\frac{4 &#8211; 3}{-4 &#8211; 0}\\)<br \/>\n= \\(\\frac{1}{-4}\\)<br \/>\n= &#8211;\\(\\frac{1}{4}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nline b and line c are parallel lines<br \/>\nline b and line d and line c and line d are perpendicular lines<\/p>\n<p>Question 7.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nExplain why interpreting an expression as a single quantity does not contradict the order of operations.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nIn the order of operations, &#8220;Parenthesis&#8221; occupies the top position according to the BODMAS rule<br \/>\nSo,<br \/>\nThe interpreting of an expression as a single quantity or as different quantities don&#8217;t change the result<br \/>\nHence, from the above,<br \/>\nWe can conclude that the interpreting of an expression as a single quantity does not contradict the order of operations<\/p>\n<h3><a id=\"Quadrilaterals_and_Other_Polygons_Mathematical_Practices\"><\/a>Quadrilaterals and Other Polygons Mathematical Practices<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Use the Venn diagram below to decide whether each statement is true or false. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-85262\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7.png\" alt=\"\" width=\"429\" height=\"206\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7.png 429w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-300x144.png 300w\" sizes=\"(max-width: 429px) 100vw, 429px\" \/><\/p>\n<p>Question 1.<br \/>\nSome trapezoids are kites.<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nSome trapezoids are kites<br \/>\nFrom the given Venn diagram,<br \/>\nWe can observe that there is no relation between trapezoids and kites<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given statement is false<\/p>\n<p>Question 2.<br \/>\nNo kites are parallelograms.<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nNo kites are parallelograms<br \/>\nFrom the given Venn diagram,<br \/>\nWe can observe that there is no relation between kites and parallelograms<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given statement is true<\/p>\n<p>Question 3.<br \/>\nAll parallelograms are rectangles.<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nAll parallelograms are rectangles<br \/>\nFrom the given Venn diagram,<br \/>\nWe can observe that rectangles are a part of parallelograms but not all parallelograms are rectangles because parallelograms contain rhombuses, squares, and rectangles<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given statement is false<\/p>\n<p>Question 4.<br \/>\nSome quadrilaterals are squares.<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nSome quadrilaterals are squares<br \/>\nFrom the given Venn diagram,<br \/>\nWe can observe that squares are a small part of quadrilaterals and quadrilaterals contain other than squares<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given statement is true<\/p>\n<p>Question 5.<br \/>\nExample 1 lists three true statements based on the Venn diagram above. Write six more true statements based on the Venn diagram.<br \/>\nAnswer:<br \/>\nThe given Venn diagram is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-85262\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7.png\" alt=\"\" width=\"429\" height=\"206\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7.png 429w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-300x144.png 300w\" sizes=\"(max-width: 429px) 100vw, 429px\" \/><br \/>\nFrom the above Venn diagram,<br \/>\nThe six more true statements based on the Venn diagram are:<br \/>\na. Some parallelograms are rhombuses<br \/>\nb. Some parallelograms are squares<br \/>\nc. Some parallelograms are rectangles<br \/>\nd. Some quadrilaterals are kites<br \/>\ne. Some quadrilaterals are trapezoids<br \/>\nf. Some quadrilaterals are parallelograms<\/p>\n<p>Question 6.<br \/>\nA cyclic quadrilateral is a quadrilateral that can be circumscribed by a circle so that the circle touches each vertex. Redraw the Venn diagram so that it includes cyclic quadrilaterals.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44098\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-4.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 4\" width=\"280\" height=\"100\" \/><br \/>\nAnswer:<br \/>\nit is given that a cyclic quadrilateral is a quadrilateral that can be circumscribed by a circle so that the circle touches each vertex.<br \/>\nHence,<br \/>\nThe completed Venn diagram that includes cyclic quadrilaterals is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-85349\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-1.png\" alt=\"\" width=\"430\" height=\"259\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-1.png 430w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-1-300x181.png 300w\" sizes=\"(max-width: 430px) 100vw, 430px\" \/><\/p>\n<h3><a id=\"7.1_Angles_of_Polygons\"><\/a>7.1 Angles of Polygons<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>The Sum of the Angle Measures of a Polygon<\/p>\n<p>Work with a partner. Use dynamic geometry software.<\/p>\n<p>a. Draw a quadrilateral and a pentagon. Find the sum of the measures of the interior angles of each polygon.<br \/>\nSample<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44097\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 5\" width=\"305\" height=\"238\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-5.png 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-5-300x234.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><br \/>\nAnswer:<br \/>\nThe representation of the quadrilateral and the pentagon are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-85354\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-3.png\" alt=\"\" width=\"482\" height=\"249\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-3.png 482w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-3-300x155.png 300w\" sizes=\"(max-width: 482px) 100vw, 482px\" \/><br \/>\nFrom the above figures,<br \/>\nThe angle measures of the quadrilateral are 90\u00b0, 90\u00b0, 90\u00b0, 90\u00b0, and 90\u00b0<br \/>\nSo,<br \/>\nThe sum of the angle measures of a quadrilateral = 90\u00b0 + 90\u00b0 + 90\u00b0 + 90\u00b0<br \/>\n= 360\u00b0<br \/>\nNow,<br \/>\nFrom the above figure,<br \/>\nThe angle measures of a pentagon are: 108\u00b0, 108\u00b0, 108\u00b0, 108\u00b0, and 108\u00b0<br \/>\nSo,<br \/>\nThe sum of the angle measures of a pentagon = 108\u00b0 + 108\u00b0 + 108\u00b0 + 108\u00b0 + 108\u00b0<br \/>\n= 540\u00b0<\/p>\n<p>b. Draw other polygons and find the sums of the measures of their interior angles. Record your results in the table below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44096\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-6.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 6\" width=\"534\" height=\"69\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-6.png 534w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-6-300x39.png 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe sum of the angle measures of a polygon = 180\u00b0 (n &#8211; 2)<br \/>\nWhere<br \/>\nn is the number of sides<br \/>\nHence,<br \/>\nThe completed result of the sums of the internal measures of their internal angles is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-85778\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7.jpg\" alt=\"\" width=\"545\" height=\"70\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7.jpg 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-300x39.jpg 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>c. Plot the data from your table in a coordinate plane.<br \/>\nAnswer:<br \/>\nThe table from part (b) is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-85778\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7.jpg\" alt=\"\" width=\"545\" height=\"70\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7.jpg 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-300x39.jpg 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><br \/>\nHence,<br \/>\nThe representation of the data in the table in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-85783\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-4.png\" alt=\"\" width=\"750\" height=\"504\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-4.png 750w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-4-300x202.png 300w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/p>\n<p>d. Write a function that fits the data. Explain what the function represents.<br \/>\n<strong>CONSTRUCTING VIABLE ARGUMENTS<\/strong><br \/>\nTo be proficient in math, you need to reason inductively about data.<br \/>\nAnswer:<br \/>\nFrom part (c),<br \/>\nWhen we observe the coordinate plane,<br \/>\nThe function that fits the data is:<br \/>\ny = 180 (x &#8211; 2)<br \/>\nWhere<br \/>\ny is the sum of the measures of the internal angles<br \/>\nx is the number of sides<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>The measure of one Angle in a Regular Polygon<\/p>\n<p>Work with a partner.<\/p>\n<p>a. Use the function you found in Exploration 1 to write a new function that gives the measure of one interior angle in a regular polygon with n sides.<br \/>\nAnswer:<br \/>\nFrom Exploration 1,<br \/>\nFrom part (d),<br \/>\nThe function that fits the sum of the angle measures of the internal angles of n sides is:<br \/>\ny = 180\u00b0 (n &#8211; 2) &#8212;&#8212;-(1)<br \/>\nNow,<br \/>\nTo find the one interior angle in a regular polygon with n sides,<br \/>\nDivide eq. (1) by n<br \/>\nHence,<br \/>\nThe measure of an interior angle of a polygon = \\(\\frac{180\u00b0 (n &#8211; 2)}{n}\\)<\/p>\n<p>b. Use the function in part (a) to find the measure of one interior angle of a regular pentagon. Use dynamic geometry software are to check your result by constructing a regular pentagon and finding the measure of one of its interior angles.<br \/>\nAnswer:<br \/>\nFrom part (a),<br \/>\nWe know that,<br \/>\nThe measure of an interior angle of a polygon = \\(\\frac{180\u00b0 (n &#8211; 2)}{n}\\)<br \/>\nSo,<br \/>\nThe measure of an interior angle of a regular pentagon = \\(\\frac{180\u00b0 (5 &#8211; 2)}{5}\\)<br \/>\n= \\(\\frac{180\u00b0 (3)}{5}\\)<br \/>\n= 36\u00b0 \u00d7 3<br \/>\n= 108\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the measure of an interior angle of a regular pentagon is: 108\u00b0<\/p>\n<p>c. Copy your table from Exploration 1 and add a row for the measure of one interior angle in a regular polygon with n sides. Complete the table. Use dynamic geometry software to check your results.<br \/>\nAnswer:<br \/>\nThe completed table along with the column of &#8220;Measure of one interior angle in a regular polygon&#8221; is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-85965\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-1.jpg\" alt=\"\" width=\"545\" height=\"99\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-1.jpg 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-1-300x54.jpg 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 3.<br \/>\nWhat is the sum of the measures of the interior angles of a polygon?<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe sum of the measures of the interior angles of a polygon is:<br \/>\nSum = 180\u00b0 (n &#8211; 2)<br \/>\nWhere<br \/>\nn is the number of sides<\/p>\n<p>Question 4.<br \/>\nFind the measure of one interior angle in a regular dodecagon (a polygon with 12 sides).<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe measure of one interior angle in a regular polygon = \\(\\frac{180\u00b0 (n &#8211; 2)}{n}\\)<br \/>\nWhere<br \/>\nn is the number of sides<br \/>\nSo,<br \/>\nFor a regular dodecagon, i.e., a polygon with 12 sides<br \/>\nThe measure of one interior angle in a regular dodecagon = \\(\\frac{180\u00b0 (12 &#8211; 2)}{12}\\)<br \/>\n= \\(\\frac{180\u00b0 (10)}{12}\\)<br \/>\n= 15 \u00d7 10<br \/>\n= 150\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the measure of one interior angle in a regular dodecagon is: 150\u00b0<\/p>\n<h3><a id=\"Lesson_7.1_Angles_of_Polygons\"><\/a>Lesson 7.1 Angles of Polygons<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nThe Coin shown is in the shape of an 11-gon. Find the sum of the measures of the interior angles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44095\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7\" width=\"138\" height=\"138\" \/><br \/>\nAnswer:<br \/>\nIt is given that the coin shown is in the shape of an 11-gon<br \/>\nSo,<br \/>\nThe number of sides in a coin (n) = 11<br \/>\nWe know that,<br \/>\nThe sum pf the measures of the interior angles = 180\u00b0 (n &#8211; 2)<br \/>\n= 180\u00b0 (11 &#8211; 2)<br \/>\n= 180\u00b0 (9)<br \/>\n= 1620\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the sum of the measures of the interior angles in a coin is: 1620\u00b0<\/p>\n<p>Question 2.<br \/>\nThe sum of the measures of the interior angles of a convex polygon is 1440\u00b0. Classify the polygon by the number of sides.<br \/>\nAnswer:<br \/>\nIt is given that the sum of the measures of the interior angles of a convex polygon is 1440\u00b0<br \/>\nWe know that,<br \/>\nThe sum of the measures of the interior angles of a polygon = 180\u00b0 (n &#8211; 2)<br \/>\nWhere<br \/>\nn is the number of sides<br \/>\nSo,<br \/>\n1440\u00b0 = 180\u00b0 (n &#8211; 2)<br \/>\nn &#8211; 2 = \\(\\frac{1440}{180}\\)<br \/>\nn &#8211; 2 = 8<br \/>\nn = 8 + 2<br \/>\nn = 10<br \/>\nHence, from the above,<br \/>\nWe can conclude that the polygon with 10 sides is called &#8220;Decagon&#8221;<\/p>\n<p>Question 3.<br \/>\nThe measures of the interior angles of a quadrilateral are x\u00b0, 3x\u00b0. 5x\u00b0. and 7x\u00b0 Find the measures of all the interior angles.<br \/>\nAnswer:<br \/>\nIt is given that the measures of the interior angles of a quadrilateral are x\u00b0, 3x\u00b0, 5x\u00b0, and 7x\u00b0<br \/>\nWe know that,<br \/>\nThe sum of the measures of the interior angles of a quadrilateral is: 360\u00b0<br \/>\nSo,<br \/>\nx\u00b0 + 3x\u00b0 + 5x\u00b0 + 7x\u00b0 = 360\u00b0<br \/>\n16x\u00b0 = 360\u00b0<br \/>\nx\u00b0 = \\(\\frac{360}{16}\\)<br \/>\nx\u00b0 = 22.5\u00b0<br \/>\nSo,<br \/>\nThe measures of all the interior angles of a quadrilateral are:<br \/>\nx\u00b0 = 22.5\u00b0<br \/>\n3x\u00b0 = 3 (22.5)\u00b0 = 67.5\u00b0<br \/>\n5x\u00b0 = 5 (22.5)\u00b0 = 112.5\u00b0<br \/>\n7x\u00b0 = 7 (22.5)\u00b0 = 157.5\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the measures of the internal angles of a quadrilateral are:<br \/>\n22.5\u00b0, 67.5\u00b0, 112.5\u00b0, and 157.5\u00b0<\/p>\n<p>Question 4.<br \/>\nFind m\u2220S and m\u2220T in the diagram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-86106\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-5.png\" alt=\"\" width=\"117\" height=\"85\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-86106\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-5.png\" alt=\"\" width=\"117\" height=\"85\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that the number of the sides is 5<br \/>\nWe know that,<br \/>\nThe sum of the measures of the interior angles of the pentagon = 540\u00b0<br \/>\nLet<br \/>\n\u2220S = \u2220T = x\u00b0<br \/>\nSo,<br \/>\n93\u00b0 + 156\u00b0 + 85\u00b0 + x\u00b0 + x\u00b0 = 540\u00b0<br \/>\n2x\u00b0 + 334\u00b0 = 540\u00b0<br \/>\n2x\u00b0 = 540\u00b0 &#8211; 334\u00b0<br \/>\n2x\u00b0 = 206\u00b0<br \/>\nx\u00b0 = \\(\\frac{206}{2}\\)<br \/>\nx\u00b0 = 103\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220S = \u2220T = 103\u00b0<\/p>\n<p>Question 5.<br \/>\nSketch a pentagon that is equilateral but not equiangular.<br \/>\nAnswer:<br \/>\ne know that,<br \/>\nThe &#8220;Equilateral&#8221; means all the sides are congruent<br \/>\nThe &#8220;Equiangular&#8221; means all the angles are congruent<br \/>\nHence,<br \/>\nA pentagon that is equilateral but not equiangular is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-86113\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-6.png\" alt=\"\" width=\"183\" height=\"151\" \/><\/p>\n<p>Question 6.<br \/>\nA convex hexagon has exterior angles with measures 34\u00b0, 49\u00b0, 58\u00b0, 67\u00b0, and 75\u00b0. What is the measure of an exterior angle at the sixth vertex?<br \/>\nAnswer:<br \/>\nIt is given that a convex hexagon has exterior angles with measures 34\u00b0, 49\u00b0, 58\u00b0, 67\u00b0, and 75\u00b0<br \/>\nWe know that,<br \/>\nA hexagon has 6 number of sides<br \/>\nWe know that,<br \/>\nThe sum of the measures of the exterior angles of any polygon is: 360\u00b0<br \/>\nLet the exterior angle measure at the sixth vertex of a convex hexagon be: x\u00b0<br \/>\nSo,<br \/>\n34\u00b0 + 49\u00b0 + 58\u00b0 + 67\u00b0 + 75\u00b0 + x\u00b0 = 360\u00b0<br \/>\n283\u00b0 + x\u00b0 = 360\u00b0<br \/>\nx\u00b0 = 360\u00b0 &#8211; 283\u00b0<br \/>\nx\u00b0 = 77\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the measure of the exterior angle at the sixth vertex of the convex hexagon is: 77\u00b0<\/p>\n<p>Question 7.<br \/>\nAn interior angle and an adjacent exterior angle of a polygon form a linear pair. How can you use this fact as another method to find the measure of each exterior angle in Example 6?<br \/>\nAnswer:<br \/>\nIt is given that an interior angle and an adjacent exterior angle of a polygon form a linear pair i.e, it forms a supplementary angle<br \/>\nSo,<br \/>\nInterior angle measure + Adjacent exterior angle measure = 180\u00b0<br \/>\nSo,<br \/>\nBy using the above property,<br \/>\nThe sum of the angle measure of the exterior angle of any polygon = 180\u00b0 \u00d7 4 = 360\u00b0<br \/>\nSo,<br \/>\nThe measure of each exterior angle = \\(\\frac{360}{4}\\)<br \/>\n= 90\u00b0<\/p>\n<h3><a id=\"Exercise_7.1_Angles_of_Polygons\"><\/a>Exercise 7.1 Angles of Polygons<\/h3>\n<p>Question 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nWhy do vertices connected by a diagonal of a polygon have to be nonconsecutive?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49122\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-1.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 1\" width=\"558\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-1.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-1-300x32.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WHICH ONE DOESNT BELONG?<\/strong><br \/>\nWhich sum does not belong with the other three? Explain your reasoning.<\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td width=\"312\">The sum of the measures of the interior\u00a0 angles of a quadrilateral<\/td>\n<td width=\"312\">The sum of the measures of the exterior angles of a quadrilateral<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">The sum of the measures of the interior\u00a0 angles of a pentagon<\/td>\n<td width=\"312\">The sum of the measures of the exterior angles of a pentagon<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Answer:<br \/>\nThe given statements are:<br \/>\na. The sum of the measures of the interior angles of a quadrilateral<br \/>\nb. The sum of the measures of the exterior angles of a quadrilateral<br \/>\nc. The sum of the measures of the interior angles of a pentagon<br \/>\nd. The sum of the measures of the exterior angles of a pentagon<br \/>\nWe know that,<br \/>\nThe sum of the angle measures of the interior angles of a polygon = 180\u00b0 (n &#8211; 2)<br \/>\nThe sum of the angle measures of the exterior angles of any polygon is: 360\u00b0<br \/>\nWe know that,<br \/>\nThe number of sides of a quadrilateral is: 4<br \/>\nThe number of sides of a pentagon is: 5<br \/>\nSo,<br \/>\nThe sum of the angle measures of the interior angles of a quadrilateral = 180\u00b0 ( 4 &#8211; 2)<br \/>\n= 180\u00b0 (2)<br \/>\n= 360\u00b0<\/p>\n<p>The sum of the angle measures of the interior angles of a pentagon = 180\u00b0 ( 5 &#8211; 2)<br \/>\n= 180\u00b0 (3)<br \/>\n= 540\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the statement (c) does not belong with the other three<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3-6, find the sum of the measures of the interior angles of the indicated convex po1gon.<\/p>\n<p>Question 3.<br \/>\nnonagon<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49123\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-3.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 3\" width=\"575\" height=\"89\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-3.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-3-300x46.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 4.<br \/>\n14-gon<br \/>\nAnswer:<br \/>\nThe given convex polygon is: 14-gon<br \/>\nSo,<br \/>\nThe number of sides of 14-gon is: 14<br \/>\nWe know that,<br \/>\nThe sum of the angle measures of the interior angles of a polygon = 180\u00b0 (n &#8211; 2)<br \/>\nSo,<br \/>\nThe sum of the angle measures of the interior angles of 14-gon = 180\u00b0 (14 &#8211; 2)<br \/>\n= 180\u00b0 (12)<br \/>\n= 2160\u00b0<\/p>\n<p>Question 5.<br \/>\n16-gon<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49124\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-5.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 5\" width=\"529\" height=\"91\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-5.png 529w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-5-300x52.png 300w\" sizes=\"(max-width: 529px) 100vw, 529px\" \/><\/p>\n<p>Question 6.<br \/>\n20-gon<br \/>\nAnswer:<br \/>\nThe given convex polygon is: 20-gon<br \/>\nSo,<br \/>\nThe number of sides of 20-gon is: 20<br \/>\nWe know that,<br \/>\nThe sum of the angle measures of the interior angles of a polygon = 180\u00b0 (n &#8211; 2)<br \/>\nSo,<br \/>\nThe sum of the angle measures of the interior angles of 20-gon = 180\u00b0 (20 &#8211; 2)<br \/>\n= 180\u00b0 (18)<br \/>\n= 3240\u00b0<\/p>\n<p>In Exercises 7-10, the sum of the measures of the interior angles of a convex polygon is given. Classify the polygon by the number of sides.<\/p>\n<p>Question 7.<br \/>\n720\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49125\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-7.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 7\" width=\"433\" height=\"199\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-7.png 433w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-7-300x138.png 300w\" sizes=\"(max-width: 433px) 100vw, 433px\" \/><\/p>\n<p>Question 8.<br \/>\n1080\u00b0<br \/>\nAnswer:<br \/>\nIt is given that<br \/>\nThe sum of the angle measures of the interior angles of a convex polygon is: 1080\u00b0<br \/>\nWe know that,<br \/>\nThe sum of the measures of the interior angles of a polygon = 180\u00b0 (n &#8211; 2)<br \/>\nSo,<br \/>\n1080\u00b0 = 180\u00b0 (n &#8211; 2)<br \/>\nn &#8211; 2 = \\(\\frac{1080}{180}\\)<br \/>\nn &#8211; 2 = 6<br \/>\nn = 6 + 2<br \/>\nn = 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of sides is: 8<br \/>\nHence,<br \/>\nThe given polygon is: Octagon<\/p>\n<p>Question 9.<br \/>\n2520\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49126\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-9.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 9\" width=\"403\" height=\"193\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-9.png 403w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-9-300x144.png 300w\" sizes=\"(max-width: 403px) 100vw, 403px\" \/><\/p>\n<p>Question 10.<br \/>\n3240\u00b0<br \/>\nAnswer:<br \/>\nIt is given that<br \/>\nThe sum of the angle measures of the interior angles of a convex polygon is: 3240\u00b0<br \/>\nWe know that,<br \/>\nThe sum of the measures of the interior angles of a polygon = 180\u00b0 (n &#8211; 2)<br \/>\nSo,<br \/>\n3240\u00b0 = 180\u00b0 (n &#8211; 2)<br \/>\nn &#8211; 2 = \\(\\frac{3240}{180}\\)<br \/>\nn &#8211; 2 = 18<br \/>\nn = 18 + 2<br \/>\nn = 20<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of sides is: 20<br \/>\nHence,<br \/>\nThe given polygon is: 20-gon or Icosagon<\/p>\n<p>In Exercises 11-14, find the value of x.<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44094\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-8.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 8\" width=\"189\" height=\"115\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49127\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-11.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 11\" width=\"572\" height=\"158\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-11.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-11-300x83.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44093\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-9.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 9\" width=\"172\" height=\"124\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44093\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-9.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 9\" width=\"172\" height=\"124\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nThe polygon has 4 sides<br \/>\nThe given angle measures of a polygon with 4 sides are:<br \/>\n103\u00b0, 133\u00b0, 58\u00b0, and x\u00b0<br \/>\nSo,<br \/>\nThe sum of the angle measures of the interior angles of a polygon with 4 sides = 180\u00b0 (4 &#8211; 2)<br \/>\n= 180\u00b0 (2)<br \/>\n= 360\u00b0<br \/>\nSo,<br \/>\n103\u00b0 + 133\u00b0 + 58\u00b0 + x\u00b0 = 360\u00b0<br \/>\n294\u00b0 + x\u00b0 = 360\u00b0<br \/>\nx\u00b0 = 360\u00b0 &#8211; 294\u00b0<br \/>\nx\u00b0 = 66\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 66\u00b0<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44092\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-10.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 10\" width=\"192\" height=\"130\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49128\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-13.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 13\" width=\"586\" height=\"155\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-13.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-13-300x79.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44091\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-11.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 11\" width=\"204\" height=\"140\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44091\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-11.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 11\" width=\"204\" height=\"140\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nThe polygon has 4 sides<br \/>\nThe given angle measures of a polygon with 4 sides are:<br \/>\n101\u00b0, 68\u00b0, 92\u00b0, and x\u00b0<br \/>\nSo,<br \/>\nThe sum of the angle measures of the interior angles of a polygon with 4 sides = 180\u00b0 (4 &#8211; 2)<br \/>\n= 180\u00b0 (2)<br \/>\n= 360\u00b0<br \/>\nSo,<br \/>\n101\u00b0 + 68\u00b0 + 92\u00b0 + x\u00b0 = 360\u00b0<br \/>\n261\u00b0 + x\u00b0 = 360\u00b0<br \/>\nx\u00b0 = 360\u00b0 &#8211; 261\u00b0<br \/>\nx\u00b0 = 99\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 99\u00b0<\/p>\n<p>In Exercises 15-18, find the value of x.<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44090\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-12.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 12\" width=\"148\" height=\"118\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49129\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-15.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 15\" width=\"574\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-15.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-15-300x84.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44089\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-13.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 13\" width=\"202\" height=\"108\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44089\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-13.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 13\" width=\"202\" height=\"108\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nThe polygon has 5 sides<br \/>\nThe given angle measures of a polygon with 5 sides are:<br \/>\n140\u00b0, 138\u00b0, 59\u00b0, x\u00b0, and 86\u00b0<br \/>\nSo,<br \/>\nThe sum of the angle measures of the interior angles of a polygon with 5 sides = 180\u00b0 (5 &#8211; 2)<br \/>\n= 180\u00b0 (3)<br \/>\n= 540\u00b0<br \/>\nSo,<br \/>\n140\u00b0 + 138\u00b0 + 59\u00b0 + x\u00b0 + 86\u00b0 = 540\u00b0<br \/>\n423\u00b0 + x\u00b0 = 540\u00b0<br \/>\nx\u00b0 = 540\u00b0 &#8211; 423\u00b0<br \/>\nx\u00b0 = 117\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 117\u00b0<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44088\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-14.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 14\" width=\"177\" height=\"106\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49130\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-17.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 17\" width=\"582\" height=\"163\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-17.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-17-300x84.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44087\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-15.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 15\" width=\"194\" height=\"90\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44087\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-15.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 15\" width=\"194\" height=\"90\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nThe polygon has 8 sides<br \/>\nThe given angle measures of a polygon with 8 sides are:<br \/>\n143\u00b0, 2x\u00b0, 152\u00b0, 116\u00b0, 125\u00b0, 140\u00b0, 139\u00b0, and x\u00b0<br \/>\nSo,<br \/>\nThe sum of the angle measures of the interior angles of a polygon with 8 sides = 180\u00b0 (8 &#8211; 2)<br \/>\n= 180\u00b0 (6)<br \/>\n= 1080\u00b0<br \/>\nSo,<br \/>\n143\u00b0 + 2x\u00b0 + 152\u00b0 + 116\u00b0 + 125\u00b0 + 140\u00b0 + 139\u00b0 + x\u00b0 = 1080\u00b0<br \/>\n815\u00b0 + 3x\u00b0 = 1080\u00b0<br \/>\n3x\u00b0 = 1080\u00b0 &#8211; 815\u00b0<br \/>\n3x\u00b0 = 265\u00b0<br \/>\nx\u00b0 = \\(\\frac{265}{3}\\)<br \/>\nx\u00b0 = 88.6\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 88.6\u00b0<\/p>\n<p>In Exercises 19 &#8211; 22, find the measures of \u2220X and \u2220Y.<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44086\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-16.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 16\" width=\"163\" height=\"133\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49131\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-19.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 19\" width=\"575\" height=\"230\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-19.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-19-300x120.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44085\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-17.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 17\" width=\"190\" height=\"114\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44085\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-17.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 17\" width=\"190\" height=\"114\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nThe polygon has 5 sides<br \/>\nWe know that,<br \/>\nIf the angles are not mentioned in a polygon, the consider that angles as equal angles<br \/>\nNow,<br \/>\nThe given angle measures of a polygon with 5 sides are:<br \/>\n47\u00b0, 119\u00b0, 90\u00b0, x\u00b0, and x\u00b0<br \/>\nSo,<br \/>\nThe sum of the angle measures of the interior angles of a polygon with 5 sides = 180\u00b0 (5 &#8211; 2)<br \/>\n= 180\u00b0 (3)<br \/>\n= 540\u00b0<br \/>\nSo,<br \/>\n47\u00b0 + 119\u00b0 + 90\u00b0 + x\u00b0 + x\u00b0 = 540\u00b0<br \/>\n256\u00b0 + 2x\u00b0 = 540\u00b0<br \/>\n2x\u00b0 = 540\u00b0 &#8211; 256\u00b0<br \/>\n2x\u00b0 = 284\u00b0<br \/>\nx\u00b0 = \\(\\frac{284}{2}\\)<br \/>\nx\u00b0 = 142\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220X = \u2220Y = 142\u00b0<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44084\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-18.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 18\" width=\"200\" height=\"120\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49132\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-21.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 21\" width=\"586\" height=\"227\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-21.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-21-300x116.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44082\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-19.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 19\" width=\"184\" height=\"132\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44082\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-19.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 19\" width=\"184\" height=\"132\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nThe polygon has 6 sides<br \/>\nWe know that,<br \/>\nIf the angles are not mentioned in a polygon, the consider that angles as equal angles<br \/>\nNow,<br \/>\nThe given angle measures of a polygon with 6 sides are:<br \/>\n110\u00b0, 149\u00b0, 91\u00b0, 100\u00b0,\u00a0 x\u00b0, and x\u00b0<br \/>\nSo,<br \/>\nThe sum of the angle measures of the interior angles of a polygon with 6 sides = 180\u00b0 (6 &#8211; 2)<br \/>\n= 180\u00b0 (4)<br \/>\n= 720\u00b0<br \/>\nSo,<br \/>\n110\u00b0 + 149\u00b0 + 91\u00b0 + 100 +\u00a0 x\u00b0 + x\u00b0 = 720\u00b0<br \/>\n440\u00b0 + 2x\u00b0 = 720\u00b0<br \/>\n2x\u00b0 = 720\u00b0 &#8211; 440\u00b0<br \/>\n2x\u00b0 = 280\u00b0<br \/>\nx\u00b0 = \\(\\frac{280}{2}\\)<br \/>\nx\u00b0 = 140\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220X = \u2220Y = 140\u00b0<\/p>\n<p>In Exercises 23-26, find the value of x.<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44081\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-20.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 20\" width=\"175\" height=\"142\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49133\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-23.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 23\" width=\"328\" height=\"98\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-23.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-23-300x90.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44080\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-21.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 21\" width=\"156\" height=\"147\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44080\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-21.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 21\" width=\"156\" height=\"147\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nThe polygon has 7 sides<br \/>\nThe given angle measures of a polygon with 7 sides are:<br \/>\n50\u00b0, 48\u00b0, 59\u00b0, x\u00b0, x\u00b0, 58\u00b0, and 39\u00b0<br \/>\nSo,<br \/>\nThe sum of the angle measures of the exterior angles of any polygon is: 360\u00b0<br \/>\nSo,<br \/>\n50\u00b0 + 48\u00b0 + 59\u00b0 +\u00a0 x\u00b0 + x\u00b0 + 58\u00b0 + 39\u00b0 = 360\u00b0<br \/>\n254\u00b0 + 2x\u00b0 = 360\u00b0<br \/>\n2x\u00b0 = 360\u00b0 &#8211; 254\u00b0<br \/>\n2x\u00b0 = 106\u00b0<br \/>\nx\u00b0 = \\(\\frac{106}{2}\\)<br \/>\nx\u00b0 = 53\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 53\u00b0<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44079\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-22.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 22\" width=\"163\" height=\"153\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49134\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-25.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 25\" width=\"388\" height=\"131\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-25.png 388w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-25-300x101.png 300w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44078\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-23.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 23\" width=\"210\" height=\"138\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44078\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-23.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 23\" width=\"210\" height=\"138\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nThe polygon has 5 sides<br \/>\nThe given angle measures of a polygon with 5 sides are:<br \/>\n45\u00b0, 40\u00b0, x\u00b0, 77\u00b0, and 2x\u00b0<br \/>\nSo,<br \/>\nThe sum of the angle measures of the exterior angles of any polygon is: 360\u00b0<br \/>\nSo,<br \/>\n45\u00b0 + 40\u00b0 +\u00a0 x\u00b0 + 77\u00b0 + 2x\u00b0 = 360\u00b0<br \/>\n162\u00b0 + 3x\u00b0 = 360\u00b0<br \/>\n3x\u00b0 = 360\u00b0 &#8211; 162\u00b0<br \/>\n3x\u00b0 = 198\u00b0<br \/>\nx\u00b0 = \\(\\frac{198}{3}\\)<br \/>\nx\u00b0 = 66\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 66\u00b0<\/p>\n<p>In Exercises 27-30, find the measure of each interior angle and each exterior angle of the indicated regular polygon.<\/p>\n<p>Question 27.<br \/>\npentagon<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49135\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-27.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 27\" width=\"602\" height=\"237\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-27.png 602w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-27-300x118.png 300w\" sizes=\"(max-width: 602px) 100vw, 602px\" \/><\/p>\n<p>Question 28.<br \/>\n18-gon<br \/>\nAnswer:<br \/>\nThe given polygon is: 18-gon<br \/>\nSo,<br \/>\nThe number of sides of 18-gon is: 18<br \/>\nWe know that,<br \/>\nThe measure of each interior angle of a polygon = \\(\\frac{180\u00b0 (n &#8211; 2)}{n}\\)<br \/>\nThe measure of each exterior angle of a polygon = \\(\\frac{360\u00b0}{n}\\)<br \/>\nSo,<br \/>\nThe measure of each interior angle of 18-gon = \\(\\frac{180\u00b0 (18 &#8211; 2)}{18}\\)<br \/>\n= \\(\\frac{180\u00b0 (16)}{18}\\)<br \/>\n= 160\u00b0<br \/>\nThe measure of each exterior angle of 18-gon = \\(\\frac{360\u00b0}{18}\\)<br \/>\n= 20\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe measure of each interior angle of 18-gon is: 160\u00b0<br \/>\nThe measure of each exterior angle of 18-gon is: 20\u00b0<\/p>\n<p>Question 29.<br \/>\n45-gon<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49136\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-29.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 29\" width=\"582\" height=\"249\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-29.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-29-300x128.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 30.<br \/>\n90-gon<br \/>\nAnswer:<br \/>\nThe given polygon is: 90-gon<br \/>\nSo,<br \/>\nThe number of sides of 90-gon is: 90<br \/>\nWe know that,<br \/>\nThe measure of each interior angle of a polygon = \\(\\frac{180\u00b0 (n &#8211; 2)}{n}\\)<br \/>\nThe measure of each exterior angle of a polygon = \\(\\frac{360\u00b0}{n}\\)<br \/>\nSo,<br \/>\nThe measure of each interior angle of 90-gon = \\(\\frac{180\u00b0 (90 &#8211; 2)}{90}\\)<br \/>\n= \\(\\frac{180\u00b0 (88)}{90}\\)<br \/>\n= 176\u00b0<br \/>\nThe measure of each exterior angle of 90-gon = \\(\\frac{360\u00b0}{90}\\)<br \/>\n= 4\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe measure of each interior angle of 90-gon is: 176\u00b0<br \/>\nThe measure of each exterior angle of 90-gon is: 4\u00b0<\/p>\n<p><strong>ERROR ANALYSIS<\/strong><br \/>\nIn Exercises 31 and 32, describe and correct the error in finding the measure of one exterior angle of a regular pentagon.<\/p>\n<p>Question 31.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44077\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-24.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 24\" width=\"325\" height=\"192\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-24.png 325w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-24-300x177.png 300w\" sizes=\"(max-width: 325px) 100vw, 325px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49137\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-31.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 31\" width=\"563\" height=\"140\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-31.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-31-300x75.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 32.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44076\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-25.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 25\" width=\"312\" height=\"103\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-25.png 312w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-25-300x99.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><br \/>\nAnswer:<br \/>\nIt is given that there are 10 exterior angles, two at each vertex<br \/>\nSo,<br \/>\nThe number of sides based on 10 exterior angles is: 10<br \/>\nWe know that,<br \/>\nThe measure of each exterior angle of any polygon = \\(\\frac{360\u00b0}{n}\\)<br \/>\nSo,<br \/>\nThe measure of each exterior angle of a polygon with 10 sides = \\(\\frac{360\u00b0}{10}\\)<br \/>\n= 36\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the measure of each exterior angle in a polygon of 10 sides is: 36\u00b0<\/p>\n<p>Question 33.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe base of a jewelry box is shaped like a regular hexagon. What is the measure of each interior angle of the jewelry box base?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49138\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-33.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 33\" width=\"572\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-33.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-33-300x57.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe floor of the gazebo shown is shaped like a regular decagon. Find the measure of each interior angle of the regular decagon. Then find the measure of each exterior angle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44115\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-33.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 33\" width=\"298\" height=\"202\" \/><br \/>\nAnswer:<br \/>\nIt is given that the floor of the gazebo shown above is shaped like a regular decagon<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe number of sides of a regular decagon is: 10<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe measure of each interior angle of a polygon = \\(\\frac{180\u00b0 (n &#8211; 2)}{n}\\)<br \/>\nThe measure of each exterior angle of a polygon = \\(\\frac{360\u00b0}{n}\\)<br \/>\nSo,<br \/>\nWe know that,<br \/>\nThe measure of each interior angle of a regular decagon = \\(\\frac{180\u00b0 (10 &#8211; 2)}{10}\\)<br \/>\n= \\(\\frac{180\u00b0 (8)}{10}\\)<br \/>\n= 144\u00b0<br \/>\nThe measure of each exterior angle of a regular decagon = \\(\\frac{360\u00b0}{10}\\)<br \/>\n= 36\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe measure of each interior angle of a regular decagon is: 144\u00b0<br \/>\nThe measure of each exterior angle of a regular decagon is: 36\u00b0<\/p>\n<p>Question 35.<br \/>\n<strong>WRITING A FORMULA<\/strong><br \/>\nWrite a formula to find the number of sides n in a regular polygon given that the measure of one interior angle is x\u00b0.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49139\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-35.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 35\" width=\"591\" height=\"495\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-35.png 591w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-35-300x251.png 300w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>WRITING A FORMULA<\/strong><br \/>\nWrite a formula to find the number of sides n in a regular polygon given that the measure of one exterior angle is x\u00b0.<br \/>\nAnswer:<br \/>\nIt is given that the measure of one exterior angle is: x\u00b0<br \/>\nWe know that,<br \/>\nThe measure of each exterior angle of a polygon = \\(\\frac{360\u00b0}{n}\\)<br \/>\nWhere<br \/>\nn is the number of sides<br \/>\nSo,<br \/>\nx\u00b0 = \\(\\frac{360\u00b0}{n}\\)<br \/>\nn = \\(\\frac{360\u00b0}{x\u00b0}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe formula to find the number of sides n in a regular polygon given that the measure of one exterior angle is:<br \/>\nn = \\(\\frac{360\u00b0}{x\u00b0}\\)<\/p>\n<p><strong>REASONING<\/strong><br \/>\nIn Exercises 37-40, find the number of sides for the regular polygon described.<\/p>\n<p>Question 37.<br \/>\nEach interior angle has a measure of 156\u00b0.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49140\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-37.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 37\" width=\"560\" height=\"117\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-37.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-37-300x63.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 38.<br \/>\nEach interior angle has a measure of 165\u00b0.<br \/>\nAnswer:<br \/>\nIt is given that each interior angle has a measure of 165\u00b0<br \/>\nWe know that,<br \/>\nThe measure of each interior angle of a polygon = \\(\\frac{180\u00b0 (n &#8211; 2)}{n}\\)<br \/>\nSo,<br \/>\n165\u00b0 = \\(\\frac{180\u00b0 (n &#8211; 2)}{n}\\)<br \/>\n165n = 180 (n &#8211; 2)<br \/>\n165n = 180n &#8211; 360<br \/>\n180n &#8211; 165n = 360<br \/>\n15n = 360<br \/>\nn = \\(\\frac{360}{15}\\)<br \/>\nn = 24<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of sides with each interior angle 165\u00b0 is: 24<\/p>\n<p>Question 39.<br \/>\nEach exterior angle has a measure of 9\u00b0.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49141\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-39.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 39\" width=\"557\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-39.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-39-300x60.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 40.<br \/>\nEach exterior angle has a measure of 6\u00b0.<br \/>\nAnswer:<br \/>\nIt is given that each exterior angle has a measure of 6\u00b0<br \/>\nWe know that,<br \/>\nThe measure of each exterior angle of a polygon = \\(\\frac{360\u00b0}{n}\\)<br \/>\nSo,<br \/>\n6\u00b0 = \\(\\frac{360\u00b0}{n}\\)<br \/>\n6n = 360<br \/>\nn = \\(\\frac{360}{6}\\)<br \/>\nn = 60<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of sides with each exterior angle 6\u00b0 is: 60<\/p>\n<p>Question 41.<br \/>\n<strong>DRAWING CONCLUSIONS<\/strong><br \/>\nWhich of the following angle measures are possible interior angle measures of a regular polygon? Explain your reasoning. Select all that apply.<br \/>\n(A) 162\u00b0<br \/>\n(B) 171\u00b0<br \/>\n(C) 75\u00b0<br \/>\n(D) 40\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49142\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-41.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 41\" width=\"560\" height=\"383\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-41.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-41-300x205.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nThe Polygon Interior Angles Theorem (Theorem 7.1) states that the sum of the measures of the interior angles of a convex n-gon is (n &#8211; 2) \u2022 180\u00b0. Write a paragraph proof of this theorem for the case when n = 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44075\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-26.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 26\" width=\"160\" height=\"121\" \/><br \/>\nAnswer:<br \/>\nPolygon Interior Angles Theorem:<br \/>\nStatement:<br \/>\nThe sum of the measures of the interior angles of a convex n-gon is: 180\u00b0 (n &#8211; 2)<\/p>\n<p>Proof of the Polygon Interior Angles Theorem:<br \/>\n<img title=\"Interior Angles of a Polygon\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2019\/09\/interior-angles-of-a-polygon.png\" alt=\"Interior Angles of a Polygon\" \/><br \/>\nABCDE is an \u201cn\u201d sided polygon. Take any point O inside the polygon. Join OA, OB, OC.<br \/>\nFor \u201cn\u201d sided polygon, the polygon forms \u201cn\u201d triangles.<br \/>\nWe know that the sum of the angles of a triangle is equal to 180 degrees<br \/>\nTherefore,<br \/>\nThe sum of the angles of n triangles = n \u00d7 180\u00b0<br \/>\nFrom the above statement, we can say that<br \/>\nSum of interior angles + Sum of the angles at O = 2n \u00d7 90\u00b0 \u2014\u2014(1)<br \/>\nBut, the sum of the angles at O = 360\u00b0<br \/>\nSubstitute the above value in (1), we get<br \/>\nSum of interior angles + 360\u00b0= 2n \u00d7 90\u00b0<br \/>\nSo, the sum of the interior angles = (2n \u00d7 90\u00b0) \u2013 360\u00b0<br \/>\nTake 90 as common, then it becomes<br \/>\nThe sum of the interior angles = (2n \u2013 4) \u00d7 90\u00b0<br \/>\nTherefore,<br \/>\nThe sum of \u201cn\u201d interior angles is (2n \u2013 4) \u00d7 90\u00b0<br \/>\nHence,<br \/>\nWhen n= 5,<br \/>\nThe sum of interior angles = ([2 \u00d7 5] &#8211; 4) \u00d7 90\u00b0<br \/>\n= (10 &#8211; 4) \u00d7 90\u00b0<br \/>\n= 6 \u00d7 90\u00b0<br \/>\n= 540\u00b0<\/p>\n<p>Question 43.<br \/>\n<strong>PROVING A COROLLARY<\/strong><br \/>\nWrite a paragraph proof of the Corollary to the Polygon Interior Angles Theorem (Corollary 7. 1).<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49143\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-43.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 43\" width=\"578\" height=\"144\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-43.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-43-300x75.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims that to find the interior angle measures of a regular polygon. you do not have to use the Polygon Interior Angles Theorem (Theorem 7. 1). You instead can use the Polygon Exterior Angles Theorem (Theorem 7.2) and then the Linear Pair Postulate (Postulate 2.8). Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\nYes, your friend is correct<\/p>\n<p>Explanation:<br \/>\nIt is given that your friend claims that to find the interior angle measures of a regular polygon. you do not have to use the Polygon Interior Angles Theorem. You instead can use the Polygon Exterior Angles Theorem and then the Linear Pair Postulate.<br \/>\nWe know that<br \/>\nIn a polygon,<br \/>\nThe sum of the angle measures of exterior angles + The sum of the angle measures of interior angles = 180\u00b0<br \/>\nSo,<br \/>\nThe sum of the angle measures of interior angles = 180\u00b0 &#8211; (The sum of the angle measures of exterior angles)<br \/>\nSo,<br \/>\nFrom the above,<br \/>\nWe know that<br \/>\nAccording to Linear Pair Postulate<br \/>\nThe sum of the exterior angle and interior angle measures is: 180\u00b0<br \/>\nThe angle measures of the exterior angles can be found out by using the &#8220;Polygon Exterior Angles Theorem&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that the claim of your friend is correct<\/p>\n<p>Question 45.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nIn an equilateral hexagon. four of the exterior angles each have a measure of x\u00b0. The other two exterior angles each have a measure of twice the sum of x and 48. Find the measure of each exterior angle.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49144\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-45.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 45\" width=\"571\" height=\"391\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-45.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-45-300x205.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nFor a concave polygon, is it true that at least one of the interior angle measures must be greater than 180\u00b0? If not, give an example. If so, explain your reasoning.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nFor a concave polygon,<br \/>\nThe angle measure of at least one interior angle should be greater than 180\u00b0<br \/>\nNow,<br \/>\nThe word &#8220;Concave&#8221; implies that at least 1 interior angle is folding in and so this &#8220;Folding in&#8221; should be greater than 180\u00b0 to produce the required shape<br \/>\nHence, from the above,<br \/>\nWe can conclude that it is true that at least one of the interior angle measures must be greater than 180\u00b0<\/p>\n<p>Question 47.<br \/>\n<strong>WRITING EXPRESSIONS<\/strong><br \/>\nWrite an expression to find the sum of the measures of the interior angles for a concave polygon. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44074\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-27.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 27\" width=\"248\" height=\"169\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49145\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-47.1.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 47.1\" width=\"599\" height=\"627\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-47.1.png 599w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-47.1-287x300.png 287w\" sizes=\"(max-width: 599px) 100vw, 599px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49146\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-47.2.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 47.2\" width=\"621\" height=\"555\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-47.2.png 621w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-47.2-300x268.png 300w\" sizes=\"(max-width: 621px) 100vw, 621px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nPolygon ABCDEFGH is a regular octagon. Suppose sides \\(\\overline{A B}\\) and \\(\\overline{C D}\\) are extended to meet at a point P. Find m\u2220BPC. Explain your reasoning. Include a diagram with your answer.<br \/>\nAnswer:<br \/>\nIt is given that polygon ABCDEFGH is a regular polygon and \\(\\overline{A B}\\) and \\(\\overline{C D}\\) are extended to meet at a point P.<br \/>\nSo,<br \/>\nThe representation of the regular octagon is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-86395\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-7.png\" alt=\"\" width=\"340\" height=\"354\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-7.png 340w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-7-288x300.png 288w\" sizes=\"(max-width: 340px) 100vw, 340px\" \/><br \/>\nWe know that,<br \/>\nThe angle measure of each exterior angle = \\(\\frac{360\u00b0}{n}\\)<br \/>\nWhere<br \/>\nn is the number of sides<br \/>\nIt is given that a polygon is: Octagon<br \/>\nSo,<br \/>\nThe number of sides of the Octagon is: 8<br \/>\nSo,<br \/>\nThe angle measure of each exterior angle = \\(\\frac{360\u00b0}{8}\\)<br \/>\n= 45\u00b0<br \/>\nWe know that,<br \/>\nAll the angles in the Octagon are equal<br \/>\nSo,<br \/>\nFrom the given figure,<br \/>\nWe can observe that \u0394BPC is an Isosceles triangle<br \/>\nSo,<br \/>\nFrom \u0394BPC,<br \/>\n\u2220B = \u2220C = 45\u00b0, \u2220P = x\u00b0<br \/>\nWe know that,<br \/>\nthe sum of the angle measures of a given triangle is: 180\u00b0<br \/>\nSo,<br \/>\n45\u00b0 + x\u00b0 + 45\u00b0 = 180\u00b0<br \/>\nx\u00b0 + 90\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 90\u00b0<br \/>\nx\u00b0 = 90\u00b0<br \/>\nHence, from the above,<br \/>\n\u2220BPC = 90\u00b0<\/p>\n<p>Question 49.<br \/>\n<strong>MULTIPLE REPRESENTATIONS<\/strong><br \/>\nThe formula for the measure of each interior angle in a regular polygon can be written in function notation.<\/p>\n<p>a. Write a junction h(n). where n is the number of sides in a regular polygon and h(n) is the measure of any interior angle in the regular polygon.<br \/>\nb. Use the function to find h(9).<br \/>\nc. Use the function to find n when h(n) = 150\u00b0.<br \/>\nd. Plot the points for n = 3, 4, 5, 6, 7, and 8. What happens to the value of h(n) as n gets larger?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49147\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-49.1.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 49.1\" width=\"578\" height=\"500\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-49.1.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-49.1-300x260.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49148\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-49.2.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 49.2\" width=\"592\" height=\"637\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-49.2.png 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-49.2-279x300.png 279w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p>Question 50.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nIs the hexagon a regular hexagon? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44073\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-28.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 28\" width=\"187\" height=\"172\" \/><br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nWrite a paragraph proof of the Polygon Exterior Angles Theorem (Theorem 7.2). (Hint: In a convex n-gon. the sum of the measures of an interior angle and an adjacent exterior angle at any vertex is 180\u00b0.)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49149\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-51.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 51\" width=\"547\" height=\"226\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-51.png 547w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-51-300x124.png 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><\/p>\n<p>Question 52.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nYou are given a convex polygon. You are asked to draw a new polygon by increasing the sum of the interior angle measures by 540\u00b0. How many more sides does our new polygon have? Explain your reasoning.<br \/>\nAnswer:<br \/>\nIt is given that you are given a convex polygon and you are asked to draw a new polygon by increasing the sum of the interior angle measures by 540\u00b0<br \/>\nSo,<br \/>\nWe know that<br \/>\nThe sum of the angle measures of the interior angles in a polygon = 180\u00b0 (n &#8211; 2)<br \/>\nLet the number of sides of a new polygon be x<br \/>\nSo,<br \/>\n180\u00b0 (x &#8211; 2) + 540\u00b0 = 180\u00b0 (n &#8211; 2)<br \/>\n180x &#8211; 360\u00b0 + 540\u00b0 = 180n &#8211; 360\u00b0<br \/>\n180x &#8211; 180n = -540\u00b0<br \/>\n180 (x &#8211; n) = -540\u00b0<br \/>\nx &#8211; n = \\(\\frac{540}{180}\\)<br \/>\nx &#8211; n = -3<br \/>\nn &#8211; x = 3<br \/>\nn = x + 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nWe have to add 3 more sides to the original convex polygon<\/p>\n<p>Maintaining Mathematical Proficiency<\/p>\n<p>Find the value of x.<\/p>\n<p>Question 53.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44072\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-29.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 29\" width=\"156\" height=\"145\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49150\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-53.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 53\" width=\"232\" height=\"94\" \/><\/p>\n<p>Question 54.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44071\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-30.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 30\" width=\"155\" height=\"146\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44071\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-30.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 30\" width=\"155\" height=\"146\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\n113\u00b0 and x\u00b0 are the corresponding angles<br \/>\nWe know that,<br \/>\nAccording to the &#8220;Corresponding Angles Theorem&#8221;, the corresponding angles are congruent i.e., equal<br \/>\nSo,<br \/>\nx\u00b0 = 113\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 113\u00b0<\/p>\n<p>Question 55.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44070\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-31.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 31\" width=\"153\" height=\"137\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49151\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-55.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 7.1 a 55\" width=\"336\" height=\"132\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-55.png 336w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.1-a-55-300x118.png 300w\" sizes=\"(max-width: 336px) 100vw, 336px\" \/><\/p>\n<p>Question 56.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44069\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-32.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 32\" width=\"196\" height=\"133\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44069\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-32.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 32\" width=\"196\" height=\"133\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\n(3x + 10)\u00b0 and (6x &#8211; 19)\u00b0 are the corresponding angles<br \/>\nWe know that,<br \/>\nAccording to the &#8220;Corresponding angles Theorem&#8221;, the corresponding angles are congruent i.e., equal<br \/>\nSo,<br \/>\n(3x + 10)\u00b0 = (6x &#8211; 19)\u00b0<br \/>\n6x &#8211; 3x = 19\u00b0 + 10\u00b0<br \/>\n3x\u00b0 = 29\u00b0<br \/>\nx\u00b0 = \\(\\frac{29}{3}\\)<br \/>\nx\u00b0 = 9.6\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 9.6\u00b0<\/p>\n<h3><a id=\"7.2_Properties_of_Parallelograms\"><\/a>7.2 Properties of Parallelograms<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Discovering Properties of Parallelograms<\/p>\n<p>Work with a partner: Use dynamic geometry software.<\/p>\n<p>a. Construct any parallelogram and label it ABCD. Explain your process.<br \/>\nSample<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44571\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-34.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 34\" width=\"308\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-34.png 308w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-34-300x233.png 300w\" sizes=\"(max-width: 308px) 100vw, 308px\" \/><br \/>\nAnswer:<br \/>\nThe representation of parallelogram ABCD is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-87114\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-8.png\" alt=\"\" width=\"311\" height=\"192\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-8.png 311w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-8-300x185.png 300w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><\/p>\n<p>b. Find the angle measures of the parallelogram. What do you observe?<br \/>\nAnswer:<br \/>\nThe representation of parallelogram ABCD with the angles is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-87121\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-9.png\" alt=\"\" width=\"334\" height=\"191\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-9.png 334w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-9-300x172.png 300w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><br \/>\nHence,<br \/>\nFrom the parallelogram ABCD,<br \/>\nWe can observe that<br \/>\n\u2220A = 105\u00b0, \u2220B = 75\u00b0, \u2220D = 105\u00b0, and \u2220C = 75\u00b0<\/p>\n<p>c. Find the side lengths of the parallelogram. What do you observe?<br \/>\nAnswer:<br \/>\nThe representation of the parallelogram ABCD along with the side lengths is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-87153\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-10.png\" alt=\"\" width=\"361\" height=\"207\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-10.png 361w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-10-300x172.png 300w\" sizes=\"(max-width: 361px) 100vw, 361px\" \/><br \/>\nHence,<br \/>\nFrom the parallelogram ABCD,<br \/>\nWe can observe that<br \/>\nAB = CD = 5cm, and AC = BD = 2.8cm<\/p>\n<p>d. Repeat parts (a)-(c) for several other parallelograms. Use your results to write conjectures about the angle measures and side lengths of a parallelogram.<br \/>\nAnswer:<br \/>\nThe representation of parallelogram ABCD along with its angles and the side lengths is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-87153\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-10.png\" alt=\"\" width=\"361\" height=\"207\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-10.png 361w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-10-300x172.png 300w\" sizes=\"(max-width: 361px) 100vw, 361px\" \/><br \/>\nHence,<br \/>\nFrom the parallelogram ABCD,<br \/>\nWe can conclude that<br \/>\na. The opposite sides (i.e., AB and CD; AC and BD) are congruent i.e., equal<br \/>\nb. The opposite angles (i.e., A and C; B and D) are congruent i.e, equal<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Discovering a Property of Parallelograms<\/p>\n<p>Work with a partner: Use dynamic geometry software.<\/p>\n<p>a. Construct any parallelogram and label it ABCD.<br \/>\nAnswer:<br \/>\nThe representation of the parallelogram ABCD is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-87161\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-11.png\" alt=\"\" width=\"280\" height=\"176\" \/><\/p>\n<p>b. Draw the two diagonals of the parallelogram. Label the point of intersection E.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44570\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-35.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 35\" width=\"304\" height=\"235\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-35.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-35-300x232.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><br \/>\nAnswer:<br \/>\nThe representation of the parallelogram ABCD along with its diagonals is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-87164\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-12.png\" alt=\"\" width=\"303\" height=\"184\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-12.png 303w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-12-300x182.png 300w\" sizes=\"(max-width: 303px) 100vw, 303px\" \/><br \/>\nFrom the parallelogram ABCD,<br \/>\nWe can observe that<br \/>\nThe diagonals of parallelogram ABCD are: AC and BD<br \/>\nThe intersection point of AC and BD is: E<\/p>\n<p>c. Find the segment lengths AE, BE, CE, and DE. What do you observe?<br \/>\nAnswer:<br \/>\nThe representation of the parallelogram ABCD along the segment lengths is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-87168\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-13.png\" alt=\"\" width=\"285\" height=\"186\" \/><br \/>\nHence,<br \/>\nFrom the parallelogram ABCD,<br \/>\nWe can observe that<br \/>\nAE = DE = 1.9 cm<br \/>\nCE = BE = 2.7 cm<\/p>\n<p>d. Repeat parts (a)-(c) for several other parallelograms. Use your results to write a conjecture about the diagonals of a parallelogram.<br \/>\n<strong>MAKING SENSE OF PROBLEMS<\/strong><br \/>\nTo be proficient in math, you need to analyze givens, constraints, relationships, and goals.<br \/>\nAnswer:<br \/>\nThe representation of the parallelogram ABCD along with the length of the diagonals is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-87168\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-13.png\" alt=\"\" width=\"285\" height=\"186\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe diagonals bisect each other<br \/>\nThe lengths of the diagonals are:<br \/>\nAD = 3.8 cm and BC = 5.4 cm<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 3.<br \/>\nWhat are the properties of parallelograms?<br \/>\nAnswer:<br \/>\nThe properties of parallelograms are:<br \/>\na. The opposite sides are parallel.<br \/>\nb. The opposite sides are congruent.<br \/>\nc. The opposite angles\u00a0are\u00a0congruent.<br \/>\nd. Consecutive angles are supplementary.<br \/>\ne. The diagonals bisect each other.<\/p>\n<h3><a id=\"Lesson_7.2_Properties_of_Parallelograms\"><\/a>Lesson 7.2 Properties of Parallelograms<\/h3>\n<p><strong>Monitoring progress<\/strong><\/p>\n<p>Question 1.<br \/>\nFind FG and m\u2220G.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44569\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-36.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 36\" width=\"177\" height=\"97\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44569\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-36.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 36\" width=\"177\" height=\"97\" \/><br \/>\nIt is given that<br \/>\nEH = 8 and \u2220E = 60\u00b0<br \/>\nWe know that,<br \/>\nIn a parallelogram,<br \/>\na. The opposite sides are congruent<br \/>\nb. The opposite angles are congruent<br \/>\nSo,<br \/>\nFrom the given figure,<br \/>\nWe can say that<br \/>\nFG = HE and GH = FE<br \/>\n\u2220G = \u2220E and \u2220H = \u2220F<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nFG = 8 and \u2220G = 60\u00b0<\/p>\n<p>Question 2.<br \/>\nFind the values of x and y.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44568\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-37.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 37\" width=\"194\" height=\"97\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44568\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-37.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 37\" width=\"194\" height=\"97\" \/><br \/>\nFrom the given parallelogram,<br \/>\nWe can observe that<br \/>\nJK = 18 and LM = y + 3<br \/>\n\u2220J = 2x\u00b0 and \u2220L = 50\u00b0<br \/>\nWe know that,<br \/>\nIn a parallelogram,<br \/>\na. The opposite sides are congruent<br \/>\nb. The opposite angles are congruent<br \/>\nSo,<br \/>\nJK = LM and \u2220J = \u2220L<br \/>\nSo,<br \/>\ny + 3 =18<br \/>\ny = 18 &#8211; 3<br \/>\ny = 15<br \/>\n2x\u00b0 = 50\u00b0<br \/>\nx\u00b0 = \\(\\frac{50}{2}\\)<br \/>\nx\u00b0 = 25\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the values of x and y are: 25\u00b0 and 15<\/p>\n<p>Question 3.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nIn Example 2, find in m\u2220BCD when m\u2220ADC is twice the measure of \u2220BCD.<br \/>\nAnswer:<br \/>\nFrom Example 2,<br \/>\nIt is given that ABCD is a parallelogram<br \/>\nIn the parallelogram ABCD,<br \/>\nIt is given that<br \/>\n\u2220ADC = 110\u00b0<br \/>\nWe know that,<br \/>\nIn a parallelogram,<br \/>\nThe sum of the angle measure of the consecutive angles is supplementary<br \/>\nSo,<br \/>\nFrom Example 2,<br \/>\nWe can observe that<br \/>\n\u2220ADC + \u2220BCD = 180\u00b0<br \/>\nSo,<br \/>\n\u2220BCD = 180\u00b0 &#8211; 110\u00b0<br \/>\n= 70\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220BCD = 70\u00b0<\/p>\n<p>Question 4.<br \/>\nUsing the figure and the given statement in Example 3, prove that \u2220C and \u2220F are supplementary angles.<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nFind the coordinates of the intersection of the diagonals of <img loading=\"lazy\" class=\"alignnone size-full wp-image-44554\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-51.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 51\" width=\"18\" height=\"18\" \/>STUV with vertices S(- 2, 3), T(1, 5), U(6, 3), and V(3, 1).<br \/>\nAnswer:<br \/>\nThe given coordinates of the parallelogram STUV are:<br \/>\nS (-2, 3), T (1, 5), U (6, 3), and V (3, 1)<br \/>\nCompare the given points with (x1, y1), (x2, y2)<br \/>\nWe know that,<br \/>\nThe opposite vertices form a diagonal<br \/>\nSo,<br \/>\nIn the parallelogram STUV,<br \/>\nSU and TV are the diagonals<br \/>\nSo,<br \/>\nWe know that,<br \/>\nThe intersection of the diagonals means the midpoint of the vertices of the diagonals because diagonals bisect each other<br \/>\nSo,<br \/>\nThe midpoint of SU = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\n= (\\(\\frac{6 &#8211; 2}{2}\\), \\(\\frac{3 + 3}{2}\\))<br \/>\n= (\\(\\frac{4}{2}\\), \\(\\frac{6}{2}\\))<br \/>\n= (2, 3)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the coordinates of the intersection of the diagonals of parallelogram STUV is: (2, 3)<\/p>\n<p>Question 6.<br \/>\nThree vertices of <img loading=\"lazy\" class=\"alignnone size-full wp-image-44554\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-51.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 51\" width=\"18\" height=\"18\" \/>ABCD are A(2, 4), B(5, 2), and C(3, &#8211; 1). Find the coordinates of vertex D.<br \/>\nAnswer:<br \/>\nThe given vertices of parallelogram ABCD are:<br \/>\nA (2, 4), B (5, 2), and C (3, -1)<br \/>\nLet the fourth vertex of the parallelogram ABCD be: (x, y)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-87351\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-15.png\" alt=\"\" width=\"324\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-15.png 324w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-15-300x149.png 300w\" sizes=\"(max-width: 324px) 100vw, 324px\" \/><br \/>\nWe know that,<br \/>\nIn a parallelogram,<br \/>\nThe diagonals bisect each other i.e., the angle between the diagonals is 90\u00b0<br \/>\nSo,<br \/>\nWe can say that the diagonals are the perpendicular lines<br \/>\nSo,<br \/>\nIn the given parallelogram,<br \/>\nAC and BD are the diagonals<br \/>\nNow,<br \/>\nSlope of AC = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{-1 &#8211; 4}{3 &#8211; 2}\\)<br \/>\n= \\(\\frac{-5}{1}\\)<br \/>\n= -5<br \/>\nSlope of BD = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{y &#8211; 2}{x &#8211; 5}\\)<br \/>\nWe know that,<br \/>\nAC and BD are the perpendicular lines<br \/>\nSO,<br \/>\nThe product of the slopes of the perpendicular lines is equal to -1<br \/>\nSo,<br \/>\n(Slope of AC) \u00d7 (Slope of BD) = -1<br \/>\n-5 \u00d7 \\(\\frac{y &#8211; 2}{x &#8211; 5}\\) = -1<br \/>\n\\(\\frac{y &#8211; 2}{x &#8211; 5}\\) = \\(\\frac{1}{5}\\)<br \/>\nEquate the numerator and denominator of both expreesions<br \/>\nWe get,<br \/>\ny &#8211; 2 = 1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 x &#8211; 5 = 5<br \/>\ny = 1 + 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0x = 5 + 5<br \/>\ny = 3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 x = 10<br \/>\nHence, from the above,<br \/>\nWe can conclude that the coordinates of the vertex D are: (10, 3)<\/p>\n<p>Exercise 7.2 Properties of Parallelograms<\/p>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nWhy is a parallelogram always a quadrilateral, but a quadrilateral is only sometimes a parallelogram?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49152\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-1.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 1\" width=\"588\" height=\"143\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-1.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-1-300x73.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nYou are given one angle measure of a parallelogram. Explain how you can find the other angle measures of the parallelogram.<br \/>\nAnswer:<br \/>\nThe parallelogram is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-87351\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-15.png\" alt=\"\" width=\"324\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-15.png 324w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-15-300x149.png 300w\" sizes=\"(max-width: 324px) 100vw, 324px\" \/><br \/>\nIt is given that you have one angle measure of a polygon<br \/>\nLet the one angle measure of the given parallelogram be \u2220A<br \/>\nWe know that,<br \/>\nIn a parallelogram,<br \/>\nThe opposite angles are congruent i.e., equal<br \/>\nThe consecutive angles have the sum 180\u00b0<br \/>\nSo,<br \/>\nFrom the given figure,<br \/>\nWe can say that<br \/>\n\u2220A = \u2220C and \u2220B = \u2220D<br \/>\nHence, from the above,<br \/>\nWe can measure the other angles of the parallelogram by using the property of &#8220;The opposite angles are congruent&#8221;<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3-6, find the value of each variable in the parallelogram.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44567\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-38.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 38\" width=\"141\" height=\"83\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49153\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-3.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 3\" width=\"580\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-3.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-3-300x31.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44566\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-39.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 39\" width=\"130\" height=\"101\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44566\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-39.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 39\" width=\"130\" height=\"101\" \/><br \/>\nWe know that,<br \/>\nAccording to the Parallelogram Opposite sides Theorem,<br \/>\nAB = CD and AD = BC<br \/>\nSo,<br \/>\nFrom the given figure,<br \/>\nWe can say that<br \/>\nn = 12\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 m + 1 = 6<br \/>\nn = 12\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 m = 6 &#8211; 1<br \/>\nn = 12\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 m = 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the values of m and n are: 5 and 12<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44565\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-40.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 40\" width=\"162\" height=\"71\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49154\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-5.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 5\" width=\"512\" height=\"242\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-5.png 512w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-5-300x142.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44564\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-41.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 41\" width=\"177\" height=\"66\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44564\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-41.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 41\" width=\"177\" height=\"66\" \/><\/p>\n<p>We know that,<br \/>\nAccording to the parallelogram Opposite sides Theorem,<br \/>\nAB = CD and AD = BC<br \/>\nAccording to the parallelogram Opposite Angles Theorem,<br \/>\n\u2220A = \u2220C and \u2220B = \u2220D<br \/>\nHence, from the figure,<br \/>\n(g + 4)\u00b0 = 65\u00b0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a016 &#8211; h = 7<br \/>\ng\u00b0 = 65\u00b0 &#8211; 4\u00b0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 h = 16 &#8211; 7<br \/>\ng\u00b0 = 61\u00b0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0h = 9<br \/>\nHence, from he above,<br \/>\nWe can conclude that the values of g and h are: 61\u00b0 and 9<\/p>\n<p>In Exercises 7 and 8. find the measure of the indicated angle in the parallelogram.<\/p>\n<p>Question 7.<br \/>\nFind m\u2220B.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49155\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-7.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 7\" width=\"227\" height=\"100\" \/><\/p>\n<p>Question 8.<br \/>\nFind m \u2220 N.<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-87464\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-16.png\" alt=\"\" width=\"103\" height=\"69\" \/><br \/>\nWe know that,<br \/>\nAccording to the parallelogram Consecutive angles Theorem,<br \/>\nThe sum of the consecutive angle measures is equal to: 180\u00b0<br \/>\nSo,<br \/>\nFrom the given figure,<br \/>\n\u2220M + \u2220N = 180\u00b0<br \/>\n95\u00b0 + \u2220N = 180\u00b0<br \/>\n\u2220N = 180\u00b0 &#8211; 95\u00b0<br \/>\n\u2220N = 85\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of \u2220N is: 85\u00b0<\/p>\n<p>In Exercises 9-16. find the indicated measure in <img loading=\"lazy\" class=\"alignnone size-full wp-image-44554\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-51.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 51\" width=\"18\" height=\"18\" \/>LMNQ. Explain your reasoning.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-44563\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-42.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 42\" width=\"178\" height=\"111\" \/><\/p>\n<p>Question 9.<br \/>\nLM<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49156\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-9.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 9\" width=\"522\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-9.png 522w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-9-300x33.png 300w\" sizes=\"(max-width: 522px) 100vw, 522px\" \/><\/p>\n<p>Question 10.<br \/>\nLP<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44563\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-42.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 42\" width=\"178\" height=\"111\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nLN = 7<br \/>\nWe know that,<br \/>\nIn the parallelogram,<br \/>\nThe diagonals bisect each other. So, the length of each diagonal will be divided into half of the value of the diagonal length<br \/>\nSo,<br \/>\nLN can be divided into LP and PN<br \/>\nSo,<br \/>\nLP = \\(\\frac{LN}{2}\\)<br \/>\nLP = \\(\\frac{7}{2}\\)<br \/>\nLP = 3.5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of LP is: 3.5<\/p>\n<p>Question 11.<br \/>\nLQ<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49157\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-11.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 11\" width=\"634\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-11.png 634w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-11-300x27.png 300w\" sizes=\"(max-width: 634px) 100vw, 634px\" \/><\/p>\n<p>Question 12.<br \/>\nMQ<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44563\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-42.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 42\" width=\"178\" height=\"111\" \/><br \/>\nHence,<br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nMQ = 8.2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of MQ is: 8.2<\/p>\n<p>Question 13.<br \/>\nm\u2220LMN<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49158\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-13.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 13\" width=\"513\" height=\"125\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-13.png 513w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-13-300x73.png 300w\" sizes=\"(max-width: 513px) 100vw, 513px\" \/><\/p>\n<p>Question 14.<br \/>\nm\u2220NQL<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44563\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-42.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 42\" width=\"178\" height=\"111\" \/><br \/>\nWe know that,<br \/>\nAccording to the parallelogram Consecutive angles Theorem,<br \/>\nThe sum of the consecutive angle measures is: 180\u00b0<br \/>\nSo,<br \/>\nFrom the figure,<br \/>\n\u2220L + \u2220M = 180\u00b0<br \/>\n100\u00b0 + \u2220M = 180\u00b0<br \/>\n\u2220M = 180\u00b0 &#8211; 100\u00b0<br \/>\n\u2220M = 80\u00b0<br \/>\nWe know that,<br \/>\nAccording to the parallelogram Opposite angles Theorem,<br \/>\nThe opposite angles are congruent i.e., equal<br \/>\nSo,<br \/>\nFrom the figure,<br \/>\n\u2220M = \u2220Q<br \/>\nSo,<br \/>\n\u2220Q = 80\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of \u2220NQL is: 80\u00b0<\/p>\n<p>Question 15.<br \/>\nm\u2220MNQ<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49159\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-15.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 15\" width=\"499\" height=\"92\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-15.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-15-300x55.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><\/p>\n<p>Question 16.<br \/>\nm\u2220LMQ<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44563\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-42.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 42\" width=\"178\" height=\"111\" \/><br \/>\nWe know that,<br \/>\nAccording to the parallelogram Consecutive angles Theorem,<br \/>\nThe sum of the consecutive angle measures is: 180\u00b0<br \/>\nSo,<br \/>\nFrom the figure,<br \/>\n\u2220L + \u2220M = 180\u00b0<br \/>\n100\u00b0 + \u2220M = 180\u00b0<br \/>\n\u2220M = 180\u00b0 &#8211; 100\u00b0<br \/>\n\u2220M = 80\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of \u2220LMQ is: 80\u00b0<\/p>\n<p>In Exercises 17-20. find the value of each variable in the parallelogram.<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44562\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-43.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 43\" width=\"104\" height=\"87\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49160\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-17.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 17\" width=\"254\" height=\"166\" \/><\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44561\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-44.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 44\" width=\"169\" height=\"84\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44561\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-44.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 44\" width=\"169\" height=\"84\" \/><br \/>\nWe know that,<br \/>\nAccording to the parallelogram Opposite Angles Theorem,<br \/>\n\u2220A = \u2220C and \u2220B = \u2220D<br \/>\nAccording to the parallelogram Consecutive angles Theorem,<br \/>\n\u2220A + \u2220B = 180\u00b0 and \u2220C + \u2220D = 180\u00b0 and \u2220A + \u2220D = 180\u00b0 and \u2220B + \u2220C = 180\u00b0<br \/>\nSo,<br \/>\nFrom the given figure,<br \/>\n(b &#8211; 10)\u00b0 + (b + 10)\u00b0 = 180\u00b0<br \/>\n2b\u00b0 = 180\u00b0<br \/>\nb\u00b0 = \\(\\frac{180}{2}\\)<br \/>\nb\u00b0 = 90\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of b is: 90\u00b0<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44560\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-45.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 45\" width=\"173\" height=\"89\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49161\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-19.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 19\" width=\"213\" height=\"117\" \/><\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44559\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-46.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 46\" width=\"168\" height=\"99\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44559\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-46.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 46\" width=\"168\" height=\"99\" \/><br \/>\nWe know that,<br \/>\nIn the parallelogram,<br \/>\nThe diagonals bisect each other<br \/>\nSo,<br \/>\nFrom the given figure,<br \/>\nWe can say that<br \/>\n\\(\\frac{v}{3}\\) = 6\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a02u + 2 = 5u &#8211; 10<br \/>\nv = 6 (3)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a05u &#8211; 2u = 10 + 2<br \/>\nv = 18\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 3u = 18<br \/>\nv = 18\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0u = \\(\\frac{18}{3}\\)<br \/>\nv = 18\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 u = 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the values of u and v are: 6 and 18<\/p>\n<p><strong>ERROR ANALYSIS<\/strong><br \/>\nIn Exercises 21 and 22, describe and correct the error in using properties of parallelograms.<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44558\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-47.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 47\" width=\"309\" height=\"147\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-47.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-47-300x143.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49162\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-21.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 21\" width=\"568\" height=\"81\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-21.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-21-300x43.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44557\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-48.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 48\" width=\"303\" height=\"175\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-48.png 303w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-48-300x173.png 300w\" sizes=\"(max-width: 303px) 100vw, 303px\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nAccording to the properties of the parallelogram,<br \/>\nGJ and HK are the diagonals of the parallelogram and F is the perpendicular bisector of the diagonals<br \/>\nSo,<br \/>\nSnce F is the perpendicular bisector,<br \/>\nWe know that,<br \/>\nGF = FJ and KF = FH<br \/>\nHence, from the baove,<br \/>\nWe can conclude that because quadrilateral GHJK is a parallelogram,<br \/>\n\\(\\overline{G F}\\) = \\(\\overline{F J}\\)<\/p>\n<p><strong>PROOF<\/strong><br \/>\nIn Exercises 23 and 24, write a two-column proof.<\/p>\n<p>Question 23.<br \/>\nGiven ABCD and CEFD are parallelograms.<br \/>\nProve \\(\\overline{A B} \\cong \\overline{F E}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44556\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-49.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 49\" width=\"166\" height=\"127\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49163\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-23.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 23\" width=\"587\" height=\"420\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-23.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-23-300x215.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 24.<br \/>\nGiven ABCD, EBGF, and HJKD are parallelograms.<br \/>\nProve \u22202 \u2245\u22203<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44555\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-50.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 50\" width=\"181\" height=\"131\" \/><br \/>\nAnswer:<br \/>\nGiven:<br \/>\nABCD, EBGF, and HJKD are parallelograms<br \/>\nProve:<br \/>\n\u22202 \u2245 \u22203<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-94035\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-2.jpg\" alt=\"\" width=\"533\" height=\"272\" \/><\/p>\n<p>In Exercises 25 and 26, find the coordinates of the intersection of the diagonals of the parallelogram with the given vertices.<\/p>\n<p>Question 25.<br \/>\nW(- 2, 5), X(2, 5), Y(4, 0), Z(0, 0)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49164\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-25.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 25\" width=\"565\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-25.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-25-300x112.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 26.<br \/>\nQ(- 1, 3), R(5, 2), S(1, &#8211; 2), T(- 5, &#8211; 1)<br \/>\nAnswer:<br \/>\nThe given coordinates of the parallelogram are:<br \/>\nQ (-1, 3), R (5, 2), S (1, -2), and T (-5, -1)<br \/>\nCompare the given coordinates with (x1, y1), and (x2, y2)<br \/>\nWe know that,<br \/>\nBy the parallelogram Diagonals Theorem, the diagonals of a parallelogram bisect each other<br \/>\nSo,<br \/>\nFrom the given coordinates,<br \/>\nThe diagonals of the parallelogram are: QS and RT<br \/>\nSo,<br \/>\nThe midpoint of QS = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\n= (\\(\\frac{1 &#8211; 1}{2}\\), \\(\\frac{3 &#8211; 2}{2}\\))<br \/>\n= (0, \\(\\frac{1}{2}\\))<br \/>\nThe midpoint of RT = (\\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\))<br \/>\n= (\\(\\frac{5 &#8211; 5}{2}\\), \\(\\frac{2 &#8211; 1}{2}\\))<br \/>\n= (0, \\(\\frac{1}{2}\\))<br \/>\nHence from the above,<br \/>\nWe can conclude that the coordinates of the intersection of the diagonals of the given parallelogram are:<br \/>\n(0, \\(\\frac{1}{2}\\))<\/p>\n<p>In Exercises 27-30, three vertices of <img loading=\"lazy\" class=\"alignnone size-full wp-image-44554\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-51.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 51\" width=\"18\" height=\"18\" \/>DEFG are given. Find the coordinates of the remaining vertex.<\/p>\n<p>Question 27.<br \/>\nD(0, 2), E(- 1, 5), G(4, 0)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49165\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-27.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 27\" width=\"568\" height=\"348\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-27.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-27-300x184.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 28.<br \/>\nD(- 2, &#8211; 4), F(0, 7), G(1, 0)<br \/>\nAnswer:<br \/>\nThe given vertices of parallelogram are:<br \/>\nD (-2, -4), F (0, 7), and G (1, 0)<br \/>\nLet the fourth vertex of the parallelogram be: (x, y)<br \/>\nWe know that,<br \/>\nIn a parallelogram,<br \/>\nThe diagonals bisect each other i.e., the angle between the diagonals is 90\u00b0<br \/>\nSo,<br \/>\nWe can say that the diagonals are the perpendicular lines<br \/>\nSo,<br \/>\nIn the given parallelogram,<br \/>\nDF and EG are the diagonals<br \/>\nNow,<br \/>\nSlope of DF = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{7 + 4}{0 + 2}\\)<br \/>\n= \\(\\frac{11}{2}\\)<br \/>\nSlope of EG = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{y &#8211; 0}{x &#8211; 1}\\)<br \/>\n= \\(\\frac{y}{x &#8211; 1}\\)<br \/>\nWe know that,<br \/>\nDF and EG are the perpendicular lines<br \/>\nSo,<br \/>\nThe product of the slopes of the perpendicular lines is equal to -1<br \/>\nSo,<br \/>\n(Slope of DF) \u00d7 (Slope of EG) = -1<br \/>\n\\(\\frac{11}{2}\\) \u00d7 \\(\\frac{y}{x &#8211; 1}\\) = -1<br \/>\n\\(\\frac{y}{x &#8211; 1}\\) = &#8211;\\(\\frac{2}{11}\\)<br \/>\nEquate the numerator and denominator of both expreesions<br \/>\nWe get,<br \/>\ny = -2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 x &#8211; 1 = 11<br \/>\ny = -2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 x = 11 + 1<br \/>\ny = -2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 x = 12<br \/>\nHence, from the above,<br \/>\nWe can conclude that the coordinates of the fourth vertex are: (12, -2)<\/p>\n<p>Question 29.<br \/>\nD(- 4, &#8211; 2), E(- 3, 1), F(3, 3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49166\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-29.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 29\" width=\"490\" height=\"350\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-29.png 490w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-29-300x214.png 300w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><\/p>\n<p>Question 30.<br \/>\nE (1, 4), f(5, 6), G(8, 0)<br \/>\nAnswer:<br \/>\nThe given vertices of a parallelogram are:<br \/>\nE (1, 4), F (5, 6), and G (8, 0)<br \/>\nLet the fourth vertex of the parallelogram be: (x, y)<br \/>\nWe know that,<br \/>\nIn a parallelogram,<br \/>\nThe diagonals bisect each other i.e., the angle between the diagonals is 90\u00b0<br \/>\nSo,<br \/>\nWe can say that the diagonals are the perpendicular lines<br \/>\nSo,<br \/>\nIn the given parallelogram,<br \/>\nFH and EG are the diagonals<br \/>\nNow,<br \/>\nSlope of FH = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{y &#8211; 6}{x &#8211; 5}\\)<br \/>\nSlope of EG = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{0 &#8211; 4}{8 &#8211; 1}\\)<br \/>\n= \\(\\frac{-4}{7}\\)<br \/>\n= &#8211;\\(\\frac{4}{7}\\)<br \/>\nWe know that,<br \/>\nFH and EG are the perpendicular lines<br \/>\nSo,<br \/>\nThe product of the slopes of the perpendicular lines is equal to -1<br \/>\nSo,<br \/>\n(Slope of FH) \u00d7 (Slope of EG) = -1<br \/>\n&#8211;\\(\\frac{4}{7}\\) \u00d7 \\(\\frac{y &#8211; 6}{x &#8211; 5}\\) = -1<br \/>\n\\(\\frac{y &#8211; 6}{x &#8211; 4}\\) = \\(\\frac{7}{4}\\)<br \/>\nEquate the numerator and denominator of both expreesions<br \/>\nWe get,<br \/>\ny &#8211; 6 = 7\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 x &#8211; 4 = 4<br \/>\ny = 7 + 6\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0x = 4 + 4<br \/>\ny = 13\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 x = 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the coordinates of the fourth vertex are: (8, 13)<\/p>\n<p><strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nIn Exercises 31 and 32. find the measure of each angle.<\/p>\n<p>Question 31.<br \/>\nThe measure of one interior angle of a parallelogram is 0.25 times the measure of another angle.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49167\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-31.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 31\" width=\"359\" height=\"181\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-31.png 359w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-31-300x151.png 300w\" sizes=\"(max-width: 359px) 100vw, 359px\" \/><\/p>\n<p>Question 32.<br \/>\nThe measure of one interior angle of a parallelogram is 50 degrees more than 4 times the measure of another angle.<br \/>\nAnswer:<br \/>\nIt is given that the measure of one interior angle of a parallelogram is 50 degrees more than 4 times the measure of another angle.<br \/>\nSo,<br \/>\nThe measure of one interior angle is: x\u00b0<br \/>\nThe measure of another interior angle is: 50\u00b0 + 4x\u00b0<br \/>\nWe know that,<br \/>\nThe opposite angles of the parallelogram are equal<br \/>\nThe sum of the angles of the parallelogram is: 360\u00b0<br \/>\nSo,<br \/>\nx\u00b0 + 4x + 50\u00b0 + x\u00b0 + 4x + 50\u00b0 = 360\u00b0<br \/>\n10x\u00b0 + 100\u00b0 = 360\u00b0<br \/>\n10x\u00b0 = 360\u00b0 &#8211; 100\u00b0<br \/>\n10x\u00b0 = 260\u00b0<br \/>\nx\u00b0 = \\(\\frac{260}{10}\\)<br \/>\nx\u00b0 = 26\u00b0<br \/>\nSo,<br \/>\nThe angle measures of the parallelogram are:<br \/>\nx\u00b0 = 26\u00b0<br \/>\n4x\u00b0 + 50\u00b0 = 4 (26\u00b0) + 50\u00b0<br \/>\n= 104\u00b0 + 50\u00b0<br \/>\n= 154\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the angle measures are: 26\u00b0 and 154\u00b0<\/p>\n<p>Question 33.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nIn quadrilateral ABCD.<br \/>\nm\u2220B = 124\u00b0, m\u2220A = 56\u00b0, and m\u2220C = 124\u00b0.<br \/>\nYour friend claims quadrilateral ABCD could be a parallelogram. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49168\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-33.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 33\" width=\"593\" height=\"68\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-33.png 593w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-33-300x34.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>ATTENDING TO PRECISION<\/strong><br \/>\n\u2220J and \u2220K are Consecutive angles in a parallelogram. m\u2220J = (3t + 7)\u00b0. and m\u2220K = (5t &#8211; 11)\u00b0. Find the measure of each angle.<br \/>\nAnswer:<br \/>\nIt is given that \u2220J and \u2220K are the consecutive angles in a parallelogram<br \/>\nSo,<br \/>\n\u2220J + \u2220K = 180\u00b0<br \/>\nNow,<br \/>\nIt is given that<br \/>\n\u2220J = (3t + 7)\u00b0 and \u2220K = (5t &#8211; 11)\u00b0<br \/>\nSo,<br \/>\n(3t + 7)\u00b0 + (5t &#8211; 11)\u00b0 = 180\u00b0<br \/>\n8t\u00b0 &#8211; 4 = 180\u00b0<br \/>\n8t\u00b0 = 180\u00b0 + 4\u00b0<br \/>\n8t\u00b0 = 184\u00b0<br \/>\nt\u00b0 = \\(\\frac{184}{8}\\)<br \/>\nt\u00b0 = 23\u00b0<br \/>\nSo,<br \/>\n\u2220J = (3t + 7)\u00b0<br \/>\n= 3 (23)\u00b0 + 7<br \/>\n= 69\u00b0 + 7\u00b0<br \/>\n= 76\u00b0<br \/>\n\u2220K = (5t &#8211; 11)\u00b0<br \/>\n= 5 (23)\u00b0 &#8211; 11<br \/>\n= 115\u00b0 &#8211; 11\u00b0<br \/>\n= 104\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the measure of each angle is: 76\u00b0 and 104\u00b0<\/p>\n<p>Question 35.<br \/>\n<strong>CONSTRUCTION<\/strong><br \/>\nConstruct any parallelogram and label it ABCD. Draw diagonals \\(\\overline{A C}\\) and \\(\\overline{B D}\\). Explain how to use paper folding to verify the Parallelogram Diagonals Theorem (Theorem 7.6) for\u00a0<img loading=\"lazy\" class=\"alignnone size-full wp-image-44554\" style=\"font-weight: inherit;\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-51.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 51\" width=\"18\" height=\"18\" \/><span style=\"font-size: 16px;\">ABCD.<br \/>\n<\/span>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49169\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-35.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 35\" width=\"605\" height=\"397\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-35.png 605w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-35-300x197.png 300w\" sizes=\"(max-width: 605px) 100vw, 605px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe feathers on an arrow from two congruent parallelograms. The parallelograms are reflections of each other over the line that contains their shared side. Show that m \u2220 2 = 2m \u2220 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44553\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-52.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 52\" width=\"335\" height=\"38\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-52.png 335w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-52-300x34.png 300w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nUse the diagram to write a two-column proof of the Parallelogram Opposite Angles Theorem (Theorem 7.4).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44552\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-53.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 53\" width=\"150\" height=\"88\" \/><br \/>\nGiven ABCD is a parallelogram.<br \/>\nProve \u2220A \u2245 \u2220C, \u2220B \u2245 \u2220D<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49170\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-37.1.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 37.1\" width=\"580\" height=\"636\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-37.1.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-37.1-274x300.png 274w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49171\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-37.2.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 37.2\" width=\"609\" height=\"406\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-37.2.png 609w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-37.2-300x200.png 300w\" sizes=\"(max-width: 609px) 100vw, 609px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nUse the diagram to write a two-column proof of the Parallelogram Consecutive Angles Theorem (Theorem 7.5).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44551\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-54.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 54\" width=\"178\" height=\"96\" \/><br \/>\nGiven PQRS is a parallelogram.<br \/>\nProve x\u00b0 + y\u00b0 = 180\u00b0<br \/>\nAnswer:<br \/>\nGiven:<br \/>\nPQRS is a parallelogram<br \/>\nProve:<br \/>\nx\u00b0 + y\u00b0 = 180\u00b0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-94181\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-3.jpg\" alt=\"\" width=\"594\" height=\"179\" \/><\/p>\n<p>Question 39.<br \/>\n<strong>PROBLEM-SOLVING<\/strong><br \/>\nThe sides of <img loading=\"lazy\" class=\"alignnone size-full wp-image-44554\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-51.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 51\" width=\"18\" height=\"18\" \/>MNPQ are represented by the expressions below. Sketch <img loading=\"lazy\" class=\"alignnone size-full wp-image-44554\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-51.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 51\" width=\"18\" height=\"18\" \/>MNPQ and find its perimeter.<br \/>\nMQ = &#8211; 2x + 37 QP = y + 14<br \/>\nNP= x &#8211; 5 MN = 4y + 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49172\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-39.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 39\" width=\"587\" height=\"751\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-39.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-39-234x300.png 234w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nIn <img loading=\"lazy\" class=\"alignnone size-full wp-image-44554\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-51.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 51\" width=\"18\" height=\"18\" \/>LMNP, the ratio of LM to MN is 4 : 3. Find LM when the perimeter of <img loading=\"lazy\" class=\"alignnone size-full wp-image-44554\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-51.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 51\" width=\"18\" height=\"18\" \/>LMNP is 28.<br \/>\nAnswer:<br \/>\nIt is given that<br \/>\nIn the parallelogram LMNP,<br \/>\nThe ratio of LM to MN is: 4 : 3<br \/>\nIt is also given that<br \/>\nThe perimeter of the parallelogram LMNP is: 28<br \/>\nSo,<br \/>\nLet the length of LM be 4x<br \/>\nLet the length of MN be 3x<br \/>\nWe know that,<br \/>\nThe opposite sides of the parallelogram are equal<br \/>\nThe perimeter is the sum of all the sides<br \/>\nSo,<br \/>\n4x + 3x + 4x + 3x = 28<br \/>\n8x + 6x = 28<br \/>\n14x = 28<br \/>\nx = \\(\\frac{28}{14}\\)<br \/>\nx = 2<br \/>\nSo,<br \/>\nThe length of LM = 4 x<br \/>\n= 4 (2)<br \/>\n= 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of LM is: 8<\/p>\n<p>Question 41.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nCan you prove that two parallelograms are congruent by proving that all their corresponding sides are congruent? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49173\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-41.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 41\" width=\"577\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-41.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-41-300x30.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe mirror shown is attached to the wall by an arm that can extend away from the wall. In the figure. points P, Q, R, and S are the vertices of a parallelogram. This parallelogram is one of several that change shape as the mirror is extended.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44550\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-55.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 55\" width=\"213\" height=\"187\" \/><br \/>\na. What happens to m\u2220P as m\u2220Q increases? Explain.<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\n\u2220P and \u2220Q are the consecutive angles<br \/>\nSo,<br \/>\n\u2220P + \u2220Q = 180\u00b0<br \/>\nNow,<br \/>\nTo make the sum 180\u00b0, if one angle measure increases, then the other angle measure has to decrease<br \/>\nHence, from the above,<br \/>\nWe can conclude that when \u2220Q increases, \u2220P has to decrease<\/p>\n<p>b. What happens to QS as m\u2220Q decreases? Explain.<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nQS is a diagonal of the parallelogram<br \/>\nQ and S are the opposite angles<br \/>\nWe know that,<br \/>\nThe opposite angles are equal<br \/>\nSo,<br \/>\nAs \u2220Q decreases, the length of QS may also decrease or may also increase<\/p>\n<p>c. What happens to the overall distance between the mirror and the wall when m\u2220Q decreases? Explain.<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can observe that,<br \/>\nAs the angle between Q and the wall increases,<br \/>\nThe overall distance between the mirror and the wall increase<\/p>\n<p>Question 43.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nIn <img loading=\"lazy\" class=\"alignnone size-full wp-image-44554\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-51.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 51\" width=\"18\" height=\"18\" \/>STUV m\u2220TSU = 32\u00b0, m\u2220USV = (x<sup>2<\/sup>)\u00b0, m\u2220TUV = 12x\u00b0, and \u2220TUV is an acute angle. Find m\u2220USV.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44549\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-56.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 56\" width=\"206\" height=\"86\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49174\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-43.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 43\" width=\"313\" height=\"361\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-43.png 313w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-43-260x300.png 260w\" sizes=\"(max-width: 313px) 100vw, 313px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nIs it possible that any triangle can be partitioned into four congruent triangles that can be rearranged to form a parallelogram? Explain your reasoning.<br \/>\nAnswer:<br \/>\nYes, it is possible that any triangle can be partitioned into four congruent triangles that can be rearranged to form a parallelogram<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nIn any quadrilateral,<br \/>\nThe diagonals bisect each other and the angles may or may not be 90\u00b0 in the diagonals<br \/>\nSo,<br \/>\nAfter the bisecting with the diagonals in a quadrilateral,<br \/>\nWe can observe that the quadrilateral is divided into four triangles<br \/>\nHence, from the above,<br \/>\nWe can conclude that it is possible that any triangle can be partitioned into four congruent triangles that can be rearranged to form a parallelogram<\/p>\n<p>Question 45.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nPoints W(1. 2), X(3, 6), and Y(6, 4) are three vertices of a parallelogram. How many parallelograms can be created using these three vertices? Find the coordinates of each point that could be the fourth vertex.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49175\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-45.1.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 45.1\" width=\"527\" height=\"596\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-45.1.png 527w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-45.1-265x300.png 265w\" sizes=\"(max-width: 527px) 100vw, 527px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49176\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-45.2.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 45.2\" width=\"495\" height=\"652\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-45.2.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-45.2-228x300.png 228w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>PROOF<\/strong><br \/>\nIn the diagram. \\(\\overline{E K}\\) bisects \u2220FEH, and \\(\\overline{F J}\\) bisects \u2220EFG. Prove that \\(\\overline{E K}\\) \u22a5 \\(\\overline{F J}\\). (Hint: Write equations using the angle measures of the triangles and quadrilaterals formed.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44548\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-57.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 57\" width=\"190\" height=\"112\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-94212\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-4.jpg\" alt=\"\" width=\"327\" height=\"205\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-94213\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-5.jpg\" alt=\"\" width=\"677\" height=\"521\" \/><\/p>\n<p>Question 47.<br \/>\n<strong>PROOF<\/strong><br \/>\nProve the congruent Parts of Parallel Lines Corollary: If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44547\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-58.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 58\" width=\"140\" height=\"141\" \/><br \/>\nGiven <img loading=\"lazy\" class=\"alignnone size-full wp-image-44546\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-59.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 59\" width=\"176\" height=\"30\" \/><br \/>\nProve \\(\\overline{H K}\\) \u2245 \\(\\overline{K M}\\)<br \/>\n(Hint: Draw \\(\\overline{K P}\\) and \\(\\overline{M Q}\\) such that quadrilatcral GPKJ and quadrilateral JQML are parallelorams.)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49177\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-47.1.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 47.1\" width=\"565\" height=\"555\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-47.1.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-47.1-300x295.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49178\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-47.2.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 47.2\" width=\"571\" height=\"586\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-47.2.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-47.2-292x300.png 292w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Maintaining Mathematical Proficiency<\/p>\n<p>Determine whether lines l and m are parallel. Explain your reasoning.<\/p>\n<p>Question 48.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44545\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-60.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 60\" width=\"129\" height=\"155\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44545\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-60.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 60\" width=\"129\" height=\"155\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that the given angles are the corresponding angles i.e., an interior angle and an exterior angle<br \/>\nHence,<br \/>\nAccording to the Corresponding Angles Theorem,<br \/>\nWe can conclude that l and m are parallel lines<\/p>\n<p>Question 49.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44544\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-61.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 61\" width=\"200\" height=\"128\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49179\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-49.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 7.2 a 49\" width=\"520\" height=\"68\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-49.png 520w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-7.2-a-49-300x39.png 300w\" sizes=\"(max-width: 520px) 100vw, 520px\" \/><\/p>\n<p>Question 50.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44543\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-62.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 62\" width=\"197\" height=\"133\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44543\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-62.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 62\" width=\"197\" height=\"133\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that the given angles are the consecutive interior angles<br \/>\nWe know that,<br \/>\nThe sum of the angle measures of the consecutive interior angles is: 180\u00b0<br \/>\nBut, from the given figure,<br \/>\nThe sum of the angle measures is not 180\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that l is not parallel to m<\/p>\n<h3><a id=\"7.3_Proving_That_a_Quadrilateral_is_a_Parallelogram\"><\/a>7.3 Proving That a Quadrilateral is a Parallelogram<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Proving That a Quadrilateral is a Parallelogram<\/p>\n<p>Work with a partner: Use dynamic geometry software.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45039\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-63.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 63\" width=\"393\" height=\"242\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-63.png 393w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-63-300x185.png 300w\" sizes=\"(max-width: 393px) 100vw, 393px\" \/><br \/>\na. Construct a quadrilateral ABCD whose opposite sides are congruent.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-94271\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-18.png\" alt=\"\" width=\"255\" height=\"182\" \/><\/p>\n<p>b. Is the quadrilateral a parallelogram? Justify your answer.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nIf a quadrilateral which has opposite sides congruent and each angle measure not equal to 90\u00b0 and the diagonals bisected each other, then that quadrilateral is called the &#8220;Parallelogram&#8221;<br \/>\nHence,<br \/>\nThe representation of the quadrilateral ABCD as a parallelogram is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-94272\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-19.png\" alt=\"\" width=\"272\" height=\"175\" \/><\/p>\n<p>c. Repeat parts (a) and (b) for several other quadrilaterals. Then write a conjecture based on your results.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-94272\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-19.png\" alt=\"\" width=\"272\" height=\"175\" \/><br \/>\nFrom the above quadrilateral,<br \/>\nThe conjecture about the quadrilaterals is:<br \/>\nIf the opposite sides of a quadrilateral are equal, then the opposite angles of a quadrilateral are equal<\/p>\n<p><span style=\"font-size: 16px;\">d. Write the converse of your conjecture. Is the Converse true? Explain.<\/span><\/p>\n<p><strong>REASONING ABSTRACTLY<\/strong><br \/>\nTo be proficient in math, you need to know and flexibly use different properties of objects.<br \/>\nAnswer:<br \/>\nFrom part (c),<br \/>\nThe conjecture about quadrilaterals is:<br \/>\nIf the opposite sides of a quadrilateral are equal, then the opposite angles of a quadrilateral are equal<br \/>\nThe converse of your conjecture is:<br \/>\nIf the opposite angles of a quadrilateral are equal, then the opposite sides of a quadrilateral are equal<br \/>\nNow,<br \/>\nFrom the below figure,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-94273\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-20.png\" alt=\"\" width=\"329\" height=\"195\" \/><br \/>\nWe can observe that<br \/>\nWhen \u2220B and \u2220D are 90\u00b0,<br \/>\nAD = BC = 2.9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the converse of the conjecture from part (c) is true<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Proving That a Quadrilateral Is a Parallelogram<\/p>\n<p>Work with a partner: Use dynamic geometry software.<\/p>\n<p>a. Construct any quadrilateral ABCD whose opposite angles are congruent.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-94274\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-21.png\" alt=\"\" width=\"291\" height=\"203\" \/><\/p>\n<p>b. Is the quadrilateral a parallelogram? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45038\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-64.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 64\" width=\"437\" height=\"240\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-64.png 437w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-64-300x165.png 300w\" sizes=\"(max-width: 437px) 100vw, 437px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-94274\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-21.png\" alt=\"\" width=\"291\" height=\"203\" \/><br \/>\nWe know that,<br \/>\nFor a quadrilateral to be a parallelogram,<br \/>\nThe opposite sides are equal and the opposite angles are equal<br \/>\nHence, from the above figure,<br \/>\nWe can conclude that the given quadrilateral ABCD is a parallelogram<\/p>\n<p>c. Repeat parts (a) and (b) for several other quadrilaterals. Then write a conjecture based on your results.<br \/>\nAnswer:<br \/>\nFrom parts (a) and (b),<br \/>\nThe conjecture about the quadrilaterals is given as:<br \/>\nIf the opposite angles of a quadrilateral are equal, then the opposite sides of a quadrilateral are equal<\/p>\n<p>d. Write the converse of your conjecture. Is the converse true? Explain.<br \/>\nAnswer:<br \/>\nFrom part (c),<br \/>\nThe conjecture about quadrilaterals is given as:<br \/>\nIf the opposite angles of a quadrilateral are equal, then the opposite sides of a quadrilateral are equal<br \/>\nHence,<br \/>\nThe converse of the conjecture of the quadrilaterals is given as:<br \/>\nIf the opposite sides of a quadrilateral are equal, then the opposite angles of a quadrilateral are equal<\/p>\n<p>Communicate Your Answer<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-45037\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-65.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 65\" width=\"164\" height=\"141\" \/><\/p>\n<p>Question 3.<br \/>\nHow can you prove that a quadrilateral is a parallelogram?<br \/>\nAnswer:<br \/>\nThe number of ways to prove that a quadrilateral is a parallelogram are:<br \/>\na. The opposite sides are congruent<br \/>\nb. The opposite angles are congruent<br \/>\nc. The opposite sides are parallel<br \/>\nd. The consecutive angles are supplementary<br \/>\ne. An angle is supplementary to both its consecutive angles<\/p>\n<p>Question 4.<br \/>\nIs the quadrilateral at the left a parallelogram? Explain your reasoning<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can observe that the opposite angles are equal<br \/>\nSo,<br \/>\nFrom the conjecture of the quadrilateral,<br \/>\nIf the opposite angles of the quadrilateral are equal, then the opposite sides of the quadrilateral are equal<br \/>\nWe know that,<br \/>\nif the opposite angles are equal and the angles are not 90\u00b0, then the quadrilateral is called the &#8220;parallelogram&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that the quadrilateral ate the left is the &#8220;Parallelogram&#8221;<\/p>\n<h3><a id=\"Lesson_7.3_Proving_that_a_Quadrilateral_is_a_Parallelogram\"><\/a>Lesson 7.3 Proving that a Quadrilateral is a Parallelogram<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nIn quadrilateral WXYZ, m\u2220W = 42\u00b0, m\u2220X = 138\u00b0, and m\u2220Y = 42\u00b0. Find m\u2220Z. Is WXYZ a parallelogram\u2019? Explain your reasoning.<br \/>\nAnswer:<br \/>\nIt is given that<br \/>\nIn quadrilateral WXYZ,<br \/>\n\u2220W = 42\u00b0, \u2220X = 138\u00b0, and \u2220Y = 42\u00b0<br \/>\nLet<br \/>\n\u2220Z = x\u00b0<br \/>\nWe know that,<br \/>\nThe sum of the angles of a quadrilateral is 360\u00b0<br \/>\nSo,<br \/>\n\u2220W + \u2220X + \u2220Y + \u2220Z = 360\u00b0<br \/>\n42\u00b0 + 138\u00b0 + 42\u00b0 + x\u00b0 = 360\u00b0<br \/>\n84\u00b0 + 138\u00b0 + x\u00b0 = 360\u00b0<br \/>\nx\u00b0 = 360\u00b0 &#8211; 222\u00b0<br \/>\nx\u00b0 = 138\u00b0<br \/>\nSo,<br \/>\n\u2220Z = 138\u00b0<br \/>\nNow,<br \/>\nWe know that,<br \/>\nIf the opposite angles of a quadrilateral are equal and the angle is not equal to 90\u00b0, then that quadrilateral is called the &#8220;Parallelogram&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that WXYZ is a parallelogram<\/p>\n<p>Question 2.<br \/>\nFor what values of x and y is quadrilateral ABCD a parallelogram? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45036\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-66.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 66\" width=\"197\" height=\"120\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45036\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-66.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 66\" width=\"197\" height=\"120\" \/><br \/>\nWe know that,<br \/>\nFor a quadrilateral to be a parallelogram,<br \/>\nThe opposite angles are equal<br \/>\nSo,<br \/>\nFrom the given figure,<br \/>\n4y\u00b0 = (y + 87)\u00b0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 2x\u00b0 = (3x &#8211; 32)\u00b0<br \/>\n4y\u00b0 &#8211; y\u00b0 = 87\u00b0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 3x\u00b0 &#8211; 2x\u00b0 = 32\u00b0<br \/>\n3y\u00b0 = 87\u00b0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 x\u00b0 = 32\u00b0<br \/>\ny\u00b0 = 87 \/ 3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 x\u00b0 = 32\u00b0<br \/>\ny\u00b0 = 29\u00b0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 x\u00b0 = 32\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that for<br \/>\nx\u00b0 = 32\u00b0 and y\u00b0 = 29\u00b0<br \/>\nThe quadrilateral ABCD is a parallelogram<\/p>\n<p>State the theorem you can use to show that the quadrilateral is a parallelogram.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45035\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-67.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 67\" width=\"155\" height=\"87\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45035\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-67.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 67\" width=\"155\" height=\"87\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that the opposite sides are equal and are parallel<br \/>\nHence,<br \/>\nAccording to the &#8220;Opposite sides parallel and congruent Theorem&#8221;,<br \/>\nThe given quadrilateral is a parallelogram<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45034\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-68.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 68\" width=\"160\" height=\"84\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45034\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-68.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 68\" width=\"160\" height=\"84\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that the opposite sides are congruent and are parallel<br \/>\nHence,<br \/>\nAccording to the &#8220;Opposite sides parallel and congruent Theorem&#8221;,<br \/>\nThe given quadrilateral is a parallelogram<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45033\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-69.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 69\" width=\"141\" height=\"89\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45033\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-69.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 69\" width=\"141\" height=\"89\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that the opposite angles are equal and are parallel<br \/>\nHence,<br \/>\nAccording to the &#8220;Opposite angles parallel and congruent Theorem&#8221;,<br \/>\nThe given quadrilateral is a parallelogram<\/p>\n<p>Question 6.<br \/>\nFor what value of x is quadrilateral MNPQ a parallelogram? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45032\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-70.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 70\" width=\"207\" height=\"96\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45032\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-70.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 70\" width=\"207\" height=\"96\" \/><br \/>\nFrom the &#8220;Parallelogram Diagonals Converse Theorem&#8221;,<br \/>\nMP and NQ bisect each other<br \/>\nSo,<br \/>\nMP = NQ<br \/>\nFrom the given figure,<br \/>\nIt is given that<br \/>\nMP = 10 &#8211; 3x<br \/>\nNQ = 2x<br \/>\nSo,<br \/>\n2x = 10 &#8211; 3x<br \/>\n2x + 3x = 10<br \/>\n5x = 10<br \/>\nx = \\(\\frac{10}{5}\\)<br \/>\nx = 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that for x = 2, the quadrilateral MNPQ is a parallelogram<\/p>\n<p>Question 7.<br \/>\nShow that quadrilateral JKLM is a parallelogram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45031\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-71.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 71\" width=\"209\" height=\"206\" \/><br \/>\nAnswer:<br \/>\nFrom the given coordinate plane,<br \/>\nThe coordinates of the quadrilateral JKLM are:<br \/>\nJ (-5, 3), K (-3, -1), L (2, -3), and M (2, -3)<br \/>\nNow,<br \/>\nFor the quadrilateral JKLM to be a parallelogram,<br \/>\nThe opposite sides of the quadrilateral JKLM must be equal<br \/>\nSo,<br \/>\nJL = KM<br \/>\nWe know that,<br \/>\nThe distance between the 2 points = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nSo,<br \/>\nJL = \\(\\sqrt{(5 + 2)\u00b2 + (3 + 3)\u00b2}\\)<br \/>\n= \\(\\sqrt{(7)\u00b2 + (6)\u00b2}\\)<br \/>\n= \\(\\sqrt{49 + 36}\\)<br \/>\n= \\(\\sqrt{85}\\)<br \/>\n= 9.21<br \/>\nKM = \\(\\sqrt{(5 + 2)\u00b2 + (3 + 3)\u00b2}\\)<br \/>\n= \\(\\sqrt{(7)\u00b2 + (6)\u00b2}\\)<br \/>\n= \\(\\sqrt{49 + 36}\\)<br \/>\n= \\(\\sqrt{85}\\)<br \/>\n= 9.21<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe quadrilateral JKLM is a parallelogram according to the &#8220;Opposite sides parallel and congruent Theorem&#8221;<\/p>\n<p>Question 8.<br \/>\nRefer to the Concept Summary. Explain two other methods you can use to show that quadrilateral ABCD in Example 5 is a parallelogram.<br \/>\nConcept Summary<br \/>\nWays to Prove a Quadrilateral is a Parallelogram<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45030\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-72.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 72\" width=\"718\" height=\"394\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-72.png 718w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-72-300x165.png 300w\" sizes=\"(max-width: 718px) 100vw, 718px\" \/><br \/>\nAnswer:<br \/>\nThe other ways to prove a quadrilateral parallelogram are:<br \/>\na. Prove that the sum of the consecutive angles is supplementary<br \/>\nb. Prove that an angle is supplementary to both the consecutive angles<\/p>\n<h3><a id=\"Exercise_7.3_Proving_that_a_Quadrilateral_is_a_Parallelogram\"><\/a>Exercise 7.3 Proving that a Quadrilateral is a Parallelogram<\/h3>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nA quadrilateral has four congruent sides. Is the quadrilateral a parallelogram? Justify your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49180\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-1.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 1\" width=\"564\" height=\"83\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-1.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-1-300x44.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find \u201cboth&#8221; answers.<\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td width=\"312\">Construct a quadrilateral with opposite sides congruent.<\/td>\n<td width=\"312\">Construct a quadrilateral with one pair of parallel sides.<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">Construct a quadrilateral with opposite angles congruent,<\/td>\n<td width=\"312\">Construct a quadrilateral with one pair of opposite sides congruent and parallel.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Answer:<br \/>\nThe given statements are:<br \/>\na. Construct a quadrilateral with opposite sides congruent<br \/>\nb. Construct a quadrilateral with opposite angles congruent<br \/>\nc. Construct a quadrilateral with one pair of parallel sides<br \/>\nd. Construct a quadrilateral with one pair of opposite sides congruent and parallel<br \/>\nNow,<br \/>\nWe know that,<br \/>\nFor constructing a parallelogram,<br \/>\nWe need<br \/>\na. 2 pairs of opposite sides congruent and parallel<br \/>\nb. 2 pairs of opposite angles congruent and parallel<br \/>\nNow,<br \/>\nFrom the given sattements,<br \/>\nStatements a., b., and d are needed for onstructing a parallelogram whereas statement c. is unnecessary<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3-8, state which theorem you can use to show that the quadrilateral is a parallelogram.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45029\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-73.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 73\" width=\"151\" height=\"78\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49181\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-3.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 3\" width=\"500\" height=\"37\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-3.png 500w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-3-300x22.png 300w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45028\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-74.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 74\" width=\"137\" height=\"98\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45028\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-74.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 74\" width=\"137\" height=\"98\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that the opposite sides are congruent and parallel<br \/>\nHence,<br \/>\nBy using the &#8220;Parallelogram Opposite sides Congruent and Parallel Theorem&#8221;,<br \/>\nWe can say that the given quadrilateral is a parallelogram<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45027\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-75.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 75\" width=\"138\" height=\"92\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49182\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-5.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 5\" width=\"459\" height=\"32\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-5.png 459w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-5-300x21.png 300w\" sizes=\"(max-width: 459px) 100vw, 459px\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45026\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-76.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 76\" width=\"127\" height=\"109\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45026\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-76.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 76\" width=\"127\" height=\"109\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that the opposite sides are congruent and parallel<br \/>\nHence,<br \/>\nBy using the &#8220;Parallelogram Opposite sides Congruent and Parallel Theorem&#8221;,<br \/>\nWe can say that the given quadrilateral is a parallelogram<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45025\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-77.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 77\" width=\"139\" height=\"100\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49183\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-7.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 7\" width=\"549\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-7.png 549w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-7-300x18.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45024\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-78.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 78\" width=\"163\" height=\"78\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45024\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-78.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 78\" width=\"163\" height=\"78\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that the diagonals of the quadrilateral bisected each other<br \/>\nHence,<br \/>\nBy using the &#8220;Parallelogram Diagonals Converse Theorem&#8221;,<br \/>\nWe can say that the given quadrilateral is a parallelogram<\/p>\n<p>In Exercises 9-12, find the values of x and y that make the quadrilateral a parallelogram.<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45023\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-79.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 79\" width=\"145\" height=\"140\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49184\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-9.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 9\" width=\"549\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-9.png 549w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-9-300x33.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45022\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-80.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 80\" width=\"135\" height=\"161\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45022\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-80.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 80\" width=\"135\" height=\"161\" \/><br \/>\nIt is given that the given quadrilateral is a parallelogram<br \/>\nSo,<br \/>\nWe know that,<br \/>\nAccording to the &#8220;Parallelogram Opposite sides congruent and parallel Theorem&#8221;,<br \/>\nThe lengths of the opposite sides of the given quadrilateral are equal<br \/>\nSo,<br \/>\nx = 16 and y = 9<br \/>\nHence, from the above,<br \/>\nWe can conclude that for the given quadrilateral to be a parallelogram,<br \/>\nThe alues of x and y are:<br \/>\nx = 16 and y = 9<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45021\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-81.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 81\" width=\"163\" height=\"142\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49185\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-11.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 11\" width=\"551\" height=\"315\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-11.png 551w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-11-300x172.png 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45020\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-82.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 82\" width=\"173\" height=\"148\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45020\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-82.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 82\" width=\"173\" height=\"148\" \/><br \/>\nIt is given that the given quadrilateral is a parallelogram<br \/>\nNow,<br \/>\nWe know that,<br \/>\nAccording to the &#8220;Opposite angles Theorem&#8221;,<br \/>\nThe opposite angles of the parallelogram are equal<br \/>\nSo,<br \/>\n(4x + 13)\u00b0 = (5x &#8211; 12)\u00b0<br \/>\n4x\u00b0 &#8211; 5x\u00b0 = -12\u00b0 &#8211; 13\u00b0<br \/>\nx\u00b0 = -25\u00b0<br \/>\nx\u00b0 = 25\u00b0<br \/>\n(3x &#8211; 8)\u00b0 = (4y + 7)\u00b0<br \/>\n3x &#8211; 8 &#8211; 7 = 4y\u00b0<br \/>\n4y\u00b0 = 3 (25\u00b0)\u00a0 15<br \/>\n4y\u00b0 = 75 &#8211; 15<br \/>\n4y\u00b0 = 60\u00b0<br \/>\ny\u00b0 = \\(\\frac{60}{4}\\)<br \/>\ny\u00b0 = 15\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that for a given quadrilateral to be a parallelogram,<br \/>\nThe values of x and y are:<br \/>\nx = 25\u00b0 and y = 15\u00b0<\/p>\n<p>In Exercises 13-16, find the value of x that makes the quadrilateral a parallelogram.<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45019\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-83.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 83\" width=\"176\" height=\"84\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49186\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-13.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 13\" width=\"517\" height=\"173\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-13.png 517w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-13-300x100.png 300w\" sizes=\"(max-width: 517px) 100vw, 517px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45018\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-84.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 84\" width=\"144\" height=\"110\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45018\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-84.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 84\" width=\"144\" height=\"110\" \/><br \/>\nIt is given that the given quadrilateral is a parallelogram<br \/>\nNow,<br \/>\nWe know that,<br \/>\nAccording to the &#8220;Parallelogram Opposite angles parallel and congruent Theorem&#8221;,<br \/>\nThe lengths of the opposite sides of the parallelogram are equal<br \/>\nSo,<br \/>\n2x + 3 = x + 7<br \/>\n2x &#8211; x = 7 &#8211; 3<br \/>\nx = 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that for a given quadrilateral to be a parallelogram,<br \/>\nThe value of x is:<br \/>\nx = 4<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45017\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-85.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 85\" width=\"167\" height=\"105\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49187\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-15.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 15\" width=\"635\" height=\"204\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-15.png 635w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-15-300x96.png 300w\" sizes=\"(max-width: 635px) 100vw, 635px\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45016\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-86.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 86\" width=\"170\" height=\"90\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45016\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-86.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 86\" width=\"170\" height=\"90\" \/><br \/>\nIt is given that the given quadrilateral is a parallelogram<br \/>\nNow,<br \/>\nWe know that,<br \/>\nAccording to the &#8220;Parallelogram Diagonals Converse Theorem&#8221;,<br \/>\nThe diagonals bisect each other<br \/>\nSo,<br \/>\n6x = 3x + 2<br \/>\n6x &#8211; 3x = 2<br \/>\n3x = 2<br \/>\nx = \\(\\frac{2}{3}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that for a given quadrilateral to be a parallelogram,<br \/>\nThe value of x is:<br \/>\nx = \\(\\frac{2}{3}\\)<\/p>\n<p>In Exercises 17-20, graph the quadrilateral with the given vertices in a coordinate plane. Then show that the quadrilateral is a parallelogram.<\/p>\n<p>Question 17.<br \/>\nA(0, 1), B(4, 4), C(12, 4), D(8, 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49188\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-17.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 17\" width=\"582\" height=\"589\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-17.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-17-296x300.png 296w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 18.<br \/>\nE(- 3, 0), F(- 3, 4), G(3, &#8211; 1), H(3, &#8211; 5)<br \/>\nAnswer:<br \/>\nThe given vertices of the quadrilateral are:<br \/>\nE (-3, 0), F (-3, 4), G (3, -1), and H (3, -5)<br \/>\nSo,<br \/>\nThe representation of the vertices of a quadrilateral in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-94655\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-22.png\" alt=\"\" width=\"334\" height=\"444\" \/><br \/>\nNow,<br \/>\nWe know that,<br \/>\nFor a quadrilateral to be a parallelogram,<br \/>\nThe length of the opposite sides of a parallelogram are congruent and parallel<br \/>\nWe know that,<br \/>\nThe distance between 2 points = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nSo,<br \/>\nEF = \\(\\sqrt{(4 + 0)\u00b2 + (3 &#8211; 3)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4)\u00b2 + (0)\u00b2}\\)<br \/>\n= \\(\\sqrt{16 + 0}\\)<br \/>\n= 4<\/p>\n<p>GH = \\(\\sqrt{(5 &#8211; 1)\u00b2 + (3 &#8211; 3)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4)\u00b2 + (0)\u00b2}\\)<br \/>\n= 4<br \/>\nHence,<br \/>\nAccording to the &#8220;Parallelogram opposite sides parallel and congruent Theorem&#8221;,<br \/>\nWe can conclude that the quadrilateral with the given vertices is a parallelogram<\/p>\n<p>Question 19.<br \/>\nJ(- 2, 3), K(- 5, 7), L(3, 6), M(6, 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49189\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-19.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 19\" width=\"585\" height=\"684\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-19.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-19-257x300.png 257w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 20.<br \/>\nN(- 5, 0), P(0, 4), Q(3, 0), R(- 2, &#8211; 4)<br \/>\nAnswer:<br \/>\nThe given vertices of the quadrilateral are:<br \/>\nN (-5, 0), P (0, 4), Q (3, 0), R (-2, -4)<br \/>\nSo,<br \/>\nThe representation of the vertices of the quadrilateral in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-94690\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-23.png\" alt=\"\" width=\"494\" height=\"424\" \/><br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe distance between 2 points = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nSo,<br \/>\nNP = \\(\\sqrt{(4 &#8211; 0)\u00b2 + (0 + 5)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4)\u00b2 + (5)\u00b2}\\)<br \/>\n= \\(\\sqrt{16 + 25}\\)<br \/>\n= 6.40<\/p>\n<p>QR = \\(\\sqrt{(4 + 0)\u00b2 + (3 + 2)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4)\u00b2 + (5)\u00b2}\\)<br \/>\n= \\(\\sqrt{16 + 25}\\)<br \/>\n= 6.40<br \/>\nHence,<br \/>\nAccording to the &#8220;Parallelograms Opposite sides parallel and congruent Theorem&#8221;,<br \/>\nWe can conclude that the quadrilateral with the given vertices is a parallelogram<\/p>\n<p><strong>ERROR ANALYSIS<\/strong><br \/>\nIn Exercises 21 and 22, describe and correct the error in identifying a parallelogram.<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45015\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-87.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 87\" width=\"314\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-87.png 314w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-87-300x129.png 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49190\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-21.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 21\" width=\"579\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-21.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-21-300x46.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45014\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-88.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 88\" width=\"320\" height=\"172\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-88.png 320w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-88-300x161.png 300w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><br \/>\nAnswer:<br \/>\nIn the given quadrilateral JKLM,<br \/>\nThe lengths of the 2 sides are given and the given 2 lengths are congruent and are parallel to each other<br \/>\nHence,<br \/>\nThe quadrilateral JKLM is said to be a parallelogram by the &#8220;Parallelogram Opposite sides parallel and congruent Theorem&#8221;<\/p>\n<p>Question 23.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nWhat value of x makes the quadrilateral a parallelogram? Explain how you found your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45013\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-89.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 89\" width=\"271\" height=\"137\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49191\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-23.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 23\" width=\"574\" height=\"598\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-23.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-23-288x300.png 288w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 24.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend says you can show that quadrilateral WXYZ is a parallelogram by using the Consecutive Interior Angles Converse (Theorem 3.8) and the Opposite Sides Parallel and Congruent Theorem (Theorem 7.9). Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45012\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-90.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 90\" width=\"195\" height=\"109\" \/><br \/>\nAnswer:<br \/>\nYes, your friend is correct<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45012\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-90.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 90\" width=\"195\" height=\"109\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that the given angles are the consecutive angles and the sum of the angles are supplementary<br \/>\nWe know that,<br \/>\nFor the quadrilateral WXYZ to be a parallelogram, any one of the be low condition has to be satisfied:<br \/>\na. The opposite sides are congruent<br \/>\nb. The sum of the consecutive interior angles are supplementary<br \/>\nSo,<br \/>\nFrom the given figure,<br \/>\nWe can observe that the sum of the consecutive interior angles is supplementary<br \/>\nNow,<br \/>\nYour friend says you can show that quadrilateral WXYZ is a parallelogram by using the Consecutive Interior Angles Converse and the Opposite Sides Parallel and Congruent Theorem.<br \/>\nHence, from the above,<br \/>\nWe can conclude that your friend is correct<\/p>\n<p><strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nIn Exercises 25-27, write the indicated theorems as a biconditional statement.<\/p>\n<p>Question 25.<br \/>\nParallelogram Opposite Sides Theorem (Theorem 7.3) and Parallelogram Opposite Sides Converse (Theorem 7.7)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49192\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-25.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 25\" width=\"577\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-25.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-25-300x33.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 26.<br \/>\nParallelogram Opposite Angles Theorem (Theorem 7.4) and Parallelogram Opposite Angles Converse (Theorem 7.8)<br \/>\nAnswer:<br \/>\nThe given Theorems are:<br \/>\nParallelograms Opposite angles Theorem and Parallelogram Opposite Angles Converse<br \/>\nHence,<br \/>\nThe representation of Theorems as a biconditional statement is:<br \/>\nA quadrilateral is a parallelogram if and only if both pairs of opposite angles are congruent<\/p>\n<p>Question 27.<br \/>\nParallclorarn Diagonals Theorem (Theorem 7.6) and<br \/>\nParallelogram Diagonals Converse (Theorem 7.10)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49193\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-27.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 27\" width=\"574\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-27.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-27-300x29.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>CONSTRUCTION<\/strong><br \/>\nDescribe a method that uses the Opposite Sides Parallel and Congruent Theorem (Theorem 7.9) to construct a parallelogram. Then construct a parallelogram using your method.<br \/>\nAnswer:<br \/>\nThe steps to construct a parallelogram using the Opposite Sides parallel and Congruent Theorem are:<br \/>\na.<br \/>\nDraw a segment of length x cm (Say) and name the segment as AB<br \/>\nb.<br \/>\nTake one endpoint as B and draw another segment of length y cm (Say) and name the segment as BC<br \/>\nc.<br \/>\nBy using the Opposite sides parallel and congruent Theorem,<br \/>\nThe lengths of AB and CD must be equal<br \/>\nSo,<br \/>\nAB = CD = x cm<br \/>\nd.<br \/>\nBy using the Opposite sides parallel and congruent Theorem,<br \/>\nThe lengths of BC and DA must be equal<br \/>\nSo,<br \/>\nBC = DA = y cm<br \/>\nHence,<br \/>\nThe representation of the parallelogram by using the above steps is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-94743\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-24.png\" alt=\"\" width=\"242\" height=\"201\" \/><\/p>\n<p>Question 29.<br \/>\n<strong>REASONING<\/strong><br \/>\nFollow the steps below to construct a parallelogram. Explain why this method works. State a theorem to support your answer.<br \/>\nStep 1: Use a ruler to draw two segments that intersect at their midpoints.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45011\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-91.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 91\" width=\"191\" height=\"115\" \/><\/p>\n<p>Step 2: Connect the endpoints of the segments to form a parallelogram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45010\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-92.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 92\" width=\"195\" height=\"116\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49194\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-29.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 29\" width=\"593\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-29.png 593w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-29-300x47.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour brother says to show that quadrilateral QRST is a parallelogram. you must show that \\(\\overline{Q R}\\) || \\(\\overline{T S}\\) and \\(\\overline{Q T}\\) || \\(\\overline{R S}\\). Your sister says that you must show that \\(\\overline{Q R} \\cong \\overline{T S}\\) and \\(\\overline{Q T} \\cong \\overline{R S}\\). Who is correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45009\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-93.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 93\" width=\"205\" height=\"207\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-93.png 205w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-93-150x150.png 150w\" sizes=\"(max-width: 205px) 100vw, 205px\" \/><br \/>\nAnswer:<br \/>\nIt is given that the quadrilateral QRST is a parallelogram<br \/>\nSo,<br \/>\nAccording to the Opposite Sides Parallel and Congruent Theorem,<br \/>\nIn the quadrilateral QRST,<br \/>\nQR \u2245TS and QT \u2245 RS<br \/>\nQR || TS and QT || RS<br \/>\nNow,<br \/>\nAccording to your brother,<br \/>\nYou have to show that<br \/>\nQR || TS and QT || RS<br \/>\nAccording t your sisiter,<br \/>\nYou have to show that<br \/>\nQR \u2245TS and QT \u2245 RS<br \/>\nHence, from the above,<br \/>\nWe can conclude that to make the quadrilateral QRSt a parallelogram,<br \/>\nYour brother and sister both are correct<\/p>\n<p><strong>REASONING<\/strong><br \/>\nIn Exercises 31 and 32, our classmate incorrectly claims that the marked information can be used to show that the figure is a parallelogram. Draw a quadrilateral with the same marked properties that are clearly not a parallelogram.<\/p>\n<p>Question 31.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45008\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-94.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 94\" width=\"164\" height=\"79\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49195\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-31.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 31\" width=\"361\" height=\"213\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-31.png 361w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-31-300x177.png 300w\" sizes=\"(max-width: 361px) 100vw, 361px\" \/><\/p>\n<p>Question 32.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45007\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-95.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 95\" width=\"165\" height=\"86\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45007\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-95.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 95\" width=\"165\" height=\"86\" \/><br \/>\nIt is given that the given quadrilateral is a parallelogram<br \/>\nHence,<br \/>\nThe representation of the given quadrilateral that is not a parallelogram is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-95197\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-25.png\" alt=\"\" width=\"464\" height=\"412\" \/><\/p>\n<p>Question 33.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou shoot a pool ball, and it rolls back to where it started, as shown in the diagram. The ball bounces off each wall at the same angle at which it hits the wall.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45006\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-96.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 96\" width=\"283\" height=\"169\" \/><br \/>\na. The ball hits the first wall at an angle of 63\u00b0. So m\u2220AEF = m\u2220BEH = 63\u00b0. What is m\u2220AFE? Explain your reasoning.<br \/>\nb. Explain why m\u2220FGD = 63\u00b0.<br \/>\nc. What is m\u2220GHC? m\u2220EHB?<br \/>\nd. Is quadrilateral EFGH a parallelogram? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49196\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-33.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 33\" width=\"590\" height=\"343\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-33.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-33-300x174.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nIn the diagram of the parking lot shown, m\u2220JKL = 60\u00b0, JK = LM = 21 feet, and KL = JM = 9 feet.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45005\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-97.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 97\" width=\"409\" height=\"149\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-97.png 409w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-97-300x109.png 300w\" sizes=\"(max-width: 409px) 100vw, 409px\" \/><br \/>\na. Explain how to show that parking space JKLM is a parallelogram.<br \/>\nAnswer:<br \/>\nIt is given that<br \/>\nJK = LM = 21 feet<br \/>\nKL = JM = 9 feet<br \/>\nFrom the parking lot JKLM,<br \/>\nWe can observe that the shape of the parking lot is a quadrilateral<br \/>\nWe can also observe that<br \/>\nJK and LM are the opposite sides<br \/>\nJM and KL are the opposite sides<br \/>\nIt is given that<br \/>\nJK = LM and JM = KL<br \/>\nWe know that,<br \/>\nIf the opposite sides are congruent and parallel, then according to the Opposite sides congruent and parallel Theorem,<br \/>\nWe can say that the quadrilateral is a parallelogram<br \/>\nHence, from the above,<br \/>\nWe can conclude that the parking space JKLM is a parallelogram<\/p>\n<p>b. Find m\u2220JML, m\u2220KJM, and m\u2220KLM.<br \/>\nAnswer:<br \/>\nIt is given that<br \/>\n\u2220JKL = 60\u00b0<br \/>\nWe know that,<br \/>\nThe parking space JKLM is a parallelogram<br \/>\nSo,<br \/>\n\u2220K = \u2220M and \u2220J = \u2220L<br \/>\nSo,<br \/>\n\u2220K = \u2220M = 60\u00b0<br \/>\nWe know that,<br \/>\nIn a parallelogram,<br \/>\nThe sum of the consecutive interior angles is 180\u00b0<br \/>\nSo,<br \/>\n\u2220K + \u2220L = 180\u00b0<br \/>\n\u2220L = 180\u00b0 &#8211; \u2220K<br \/>\n\u2220L = 180\u00b0 &#8211; 60\u00b0<br \/>\n\u2220L = 120\u00b0<br \/>\nSo,<br \/>\n\u2220J = \u2220L = 120\u00b0<br \/>\nHence, from the above,<br \/>\nWe can coclude that<br \/>\n\u2220K = \u2220M = 60\u00b0<br \/>\n\u2220J = \u2220L = 120\u00b0<\/p>\n<p>c. \\(\\overline{L M}\\)||\\(\\overline{N O}\\) and \\(\\overline{N O}\\) || \\(\\overline{P Q}\\) which theorem could you use to show that \\(\\overline{J K}\\) || \\(\\overline{P Q}\\)?<br \/>\nAnswer:<br \/>\nIt is given that<br \/>\nLM || NO and NO || PQ<br \/>\nSo,<br \/>\nFrom the given data,<br \/>\nWe can say that JKPQ is a parallelogram<br \/>\nHence,<br \/>\nWe can conclude that<br \/>\nAccording to the Opposite sides parallel and Congruent Theorem,<br \/>\nJK || PQ<\/p>\n<p><strong>REASONING<\/strong><br \/>\nIn Exercises 35-37. describe how to prove that ABCD is a parallelogram.<\/p>\n<p>Question 35.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45004\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-98.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 98\" width=\"202\" height=\"115\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49197\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-35.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 35\" width=\"573\" height=\"115\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-35.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-35-300x60.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 36.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45003\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-99.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 99\" width=\"167\" height=\"96\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45003\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-99.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 99\" width=\"167\" height=\"96\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that the opposite angles are congruent<br \/>\nSo,<br \/>\n\u2220B = \u2220D<br \/>\nHence,<br \/>\nWe can conclude that<br \/>\nAccording to the Opposite Angles Converse Theorem,<br \/>\nThe given quadrilateral ABCD is a parallelogram<\/p>\n<p>Question 37.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45002\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-100.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 100\" width=\"185\" height=\"105\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49198\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-37.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 37\" width=\"585\" height=\"95\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-37.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-37-300x49.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>REASONING<\/strong><br \/>\nQuadrilateral JKLM is a parallelogram. Describe how to prove that \u2206MGJ \u2245 \u2206KHL.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45001\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-101.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 101\" width=\"217\" height=\"121\" \/><br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nProve the Parallelogram Opposite Angles Converse (Theorem 7.8). (Hint: Let x\u00b0 represent m\u2220A and m\u2220C. Let y\u00b0 represent m\u2220B and m\u2220D. Write and simplify an equation involving x and y)<br \/>\nGien \u2220A \u2245 \u2220C, \u2220B \u2245\u2220D<br \/>\nProve ABCD is a parallelogram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45000\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-102.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 102\" width=\"181\" height=\"94\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49199\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-39.1.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 39.1\" width=\"611\" height=\"585\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-39.1.png 611w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-39.1-300x287.png 300w\" sizes=\"(max-width: 611px) 100vw, 611px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49200\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-39.2.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 39.2\" width=\"588\" height=\"244\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-39.2.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-39.2-300x124.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nUse the diagram of PQRS with the auxiliary line segment drawn to prove the Opposite Sides Parallel and Congruent Theorem (Theorem 7.9).<br \/>\nGiven \\(\\overline{Q R}\\) || \\(\\overline{P S}\\). \\(\\overline{Q R} \\cong \\overline{P S}\\)<br \/>\nProve PQRS is a parallelogram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44999\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-103.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 103\" width=\"176\" height=\"96\" \/><br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nProve the Parallelogram Diagonals Converse (Theorem 7.10).<br \/>\nGiven Diagonals \\(\\overline{J L}\\) and \\(\\overline{K M}\\) bisect each other.<br \/>\nProve JKLM is a parallelogram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44998\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-104.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 104\" width=\"175\" height=\"96\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49201\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-41.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 41\" width=\"605\" height=\"727\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-41.png 605w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-41-250x300.png 250w\" sizes=\"(max-width: 605px) 100vw, 605px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>PROOF<\/strong><br \/>\nWrite the proof.<br \/>\nGiven DEBF is a parallelogram.<br \/>\nAE = CF<br \/>\nProve ABCD is a parallelogram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44997\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-105.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 105\" width=\"250\" height=\"94\" \/><br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<strong>REASONING<\/strong><br \/>\nThree interior angle measures of a quadrilateral are 67\u00b0, 67\u00b0, and 113\u00b0, Is this enough information to conclude that the quadrilateral is a parallelogram? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49202\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-43.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 43\" width=\"593\" height=\"114\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-43.png 593w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-43-300x58.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nA music stand can be folded up, as shown. In the diagrams. AEFD and EBCF are parallelograms. Which labeled segments remain parallel as the stand is folded?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44996\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-106.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 106\" width=\"366\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-106.png 366w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-106-300x111.png 300w\" sizes=\"(max-width: 366px) 100vw, 366px\" \/><br \/>\nAnswer:<br \/>\nThe given music stand when folded and not folded is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44996\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-106.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 106\" width=\"366\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-106.png 366w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-106-300x111.png 300w\" sizes=\"(max-width: 366px) 100vw, 366px\" \/><br \/>\nIt is given that AEFD and EBCF are the parallelograms<br \/>\nHence,<br \/>\nThe segments that remain parallel as the music stand folded are:<br \/>\nIn the parallelogram AEFD,<br \/>\nAE || FD and AD || EF<br \/>\nIn the parallelogram EBCF,<br \/>\nEB || CF and EF || BC<\/p>\n<p>Question 45.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nIn the diagram, ABCD is a parallelogram, BF = DE = 12, and CF = 8. Find AE. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44995\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-107.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 107\" width=\"190\" height=\"117\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49203\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-45.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 45\" width=\"685\" height=\"230\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-45.png 685w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-45-300x101.png 300w\" sizes=\"(max-width: 685px) 100vw, 685px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nCreate a regular hexagon using congruent parallelograms.<br \/>\nAnswer:<br \/>\nThe representation of a regular hexagon using congruent parallelograms are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-95198\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-26.png\" alt=\"\" width=\"374\" height=\"345\" \/><br \/>\nHence, from the above regular hexagon,<br \/>\nABCF and CDEF are the consecutive parallelograms<\/p>\n<p>Question 47.<br \/>\n<strong>WRITING<\/strong><br \/>\nThe Parallelogram Consecutive Angles Theorem (Theorem 7.5) says that if a quadrilateral is a parallelogram, then its consecutive angles are supplementary. Write the converse of this theorem. Then write a plan for proving the converse. Include a diagram.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49204\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-47.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 47\" width=\"597\" height=\"377\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-47.png 597w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-47-300x189.png 300w\" sizes=\"(max-width: 597px) 100vw, 597px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>PROOF<\/strong><br \/>\nWrite the proof.<br \/>\nGiven ABCD is a parallelogram.<br \/>\n\u2220A is a right angle.<br \/>\nProve \u2220B, \u2220C, and \u2220D are right angles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44994\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-108.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 108\" width=\"131\" height=\"100\" \/><br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nThe midpoints of the sides of a quadrilateral have been joined to turn what looks like a parallelogram. Show that a quadrilateral formed by connecting the midpoints of the sides of any quadrilateral is always a parallelogram. (Hint: Draw a diagram. Include a diagonal of the larger quadrilateral. Show how two sides of the smaller quadrilateral relate to the diagonal.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44993\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-109.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 109\" width=\"122\" height=\"78\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49205\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-49.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 49\" width=\"736\" height=\"383\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-49.png 736w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-49-300x156.png 300w\" sizes=\"(max-width: 736px) 100vw, 736px\" \/><\/p>\n<p>Question 50.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nShow that if ABCD is a parallelogram with its diagonals intersecting at E, then you can connect the midpoints F, G, H, and J of \\(\\overline{A E}\\), \\(\\overline{B E}\\), \\(\\overline{C E}\\), and \\(\\overline{D E}\\), respcetively, to form another parallelogram, FGHJ.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44992\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-110.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 110\" width=\"249\" height=\"112\" \/><br \/>\nAnswer:<\/p>\n<p>Maintaining Mathematical proficiency<\/p>\n<p>Classify the quadrilateral.<\/p>\n<p>Question 51.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44991\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-111.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 111\" width=\"169\" height=\"103\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49206\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-51.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 51\" width=\"586\" height=\"89\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-51.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-51-300x46.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 52.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44990\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-112.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 112\" width=\"189\" height=\"82\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44990\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-112.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 112\" width=\"189\" height=\"82\" \/><br \/>\nFrom the given quadrilateral,<br \/>\nWe can observe that the opposite sides are congruent and parallel and the angles are 90\u00b0<br \/>\nWe know that,<br \/>\nA quadrilateral that has congruent and parallel opposite sides and an angle 90\u00b0 is called a &#8220;Rectangle&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given quadrilateral is a rectangle<\/p>\n<p>Question 53.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44989\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-113.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 113\" width=\"97\" height=\"104\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49207\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-53.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 7.3 a 53\" width=\"568\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-53.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-7.3-a-53-300x30.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 54.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44988\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-114.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 114\" width=\"136\" height=\"93\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44988\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-114.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 114\" width=\"136\" height=\"93\" \/><br \/>\nFrom the given quadrilateral,<br \/>\nWe can observe that all the sides are congruent but the angle measures are not 90\u00b0<br \/>\nWe know that,<br \/>\nA quadrilateral that has 4 congruent sides but not an angle equal to 90\u00b0 is called a &#8220;Rhombus&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given quadrilateral is a rhombus<\/p>\n<h3><a id=\"7.1_-_7.3_Quiz\"><\/a>7.1 &#8211; 7.3 Quiz<\/h3>\n<p>Find the value of x.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45063\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-115.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 115\" width=\"120\" height=\"125\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45063\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-115.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 115\" width=\"120\" height=\"125\" \/><br \/>\nWe know that,<br \/>\nThe sum of the angle measures of a polygon = 180\u00b0 (n &#8211; 2)<br \/>\nWhere,<br \/>\nn is the number of sides<br \/>\nSo,<br \/>\nThe sum of the angle measures of a polygon = 180\u00b0 (4 &#8211; 2)<br \/>\n= 180\u00b0 (2)<br \/>\n= 360\u00b0<br \/>\nSo,<br \/>\n115\u00b0 + 95\u00b0 + 70\u00b0 + x\u00b0 = 360\u00b0<br \/>\n280\u00b0 + x\u00b0 = 360\u00b0<br \/>\nx\u00b0 = 360\u00b0 &#8211; 280\u00b0<br \/>\nx\u00b0 = 80\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 80\u00b0<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45062\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-116.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 116\" width=\"103\" height=\"138\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45062\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-116.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 116\" width=\"103\" height=\"138\" \/><br \/>\nWe know that,<br \/>\nThe sum of the angle measures of a polygon = 180\u00b0 (n &#8211; 2)<br \/>\nWhere,<br \/>\nn is the number of sides<br \/>\nSo,<br \/>\nThe sum of the angle measures of a polygon = 180\u00b0 (5 &#8211; 2)<br \/>\n= 180\u00b0 (3)<br \/>\n= 540\u00b0<br \/>\nSo,<br \/>\n150\u00b0 + 120\u00b0 + 60\u00b0 + x\u00b0 + 75\u00b0 = 540\u00b0<br \/>\n405\u00b0 + x\u00b0 = 540\u00b0<br \/>\nx\u00b0 = 540\u00b0 &#8211; 405\u00b0<br \/>\nx\u00b0 = 135\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 135\u00b0<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45061\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-117.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 117\" width=\"190\" height=\"162\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45061\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-117.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 117\" width=\"190\" height=\"162\" \/><br \/>\nWe know that,<br \/>\nThe sum of the exterior angles of any polygon is: 360\u00b0<br \/>\nSo,<br \/>\n60\u00b0 + 30\u00b0 + 72\u00b0 + 46\u00b0 + 55\u00b0 + x\u00b0 = 360\u00b0<br \/>\n263\u00b0 + x\u00b0 = 360\u00b0<br \/>\nx\u00b0 = 360\u00b0 &#8211; 263\u00b0<br \/>\nx\u00b0 = 97\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 97\u00b0<\/p>\n<p>Find the measure of each interior angle and each exterior angle of the indicated regular polygon.<\/p>\n<p>Question 4.<br \/>\ndecagon<br \/>\nAnswer:<br \/>\nThe given polygon is: Decagon<br \/>\nWe know that,<br \/>\nThe number of sides of Decagon is: 10<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe measure of each interior angle of a polygon = \\(\\frac{180\u00b0 (n &#8211; 2)}{n}\\)<br \/>\nThe measure of each exterior angle of a polygon = \\(\\frac{360\u00b0}{n}\\)<br \/>\nWhere,<br \/>\nn is the number of sides<br \/>\nSo,<br \/>\nThe measure of each interior angle of Decagon = \\(\\frac{180\u00b0 (10 &#8211; 2)}{10}\\)<br \/>\n= \\(\\frac{180\u00b0 (8)}{10}\\)<br \/>\n= 144\u00b0<br \/>\nThe measure of each exterior angle of a Decagon = \\(\\frac{360\u00b0}{10}\\)<br \/>\n= 36\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe measure of each interior angle of Decagon is: 144\u00b0<br \/>\nThe measure of each exterior angle of Decagon is:36\u00b0<\/p>\n<p>Question 5.<br \/>\n15-gon<br \/>\nAnswer:<br \/>\nThe given polygon is: 15-gon<br \/>\nWe know that,<br \/>\nThe number of sides of 15-gon is: 15<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe measure of each interior angle of a polygon = \\(\\frac{180\u00b0 (n &#8211; 2)}{n}\\)<br \/>\nThe measure of each exterior angle of a polygon = \\(\\frac{360\u00b0}{n}\\)<br \/>\nWhere,<br \/>\nn is the number of sides<br \/>\nSo,<br \/>\nThe measure of each interior angle of 15-gon = \\(\\frac{180\u00b0 (15 &#8211; 2)}{15}\\)<br \/>\n= \\(\\frac{180\u00b0 (13)}{15}\\)<br \/>\n= 156\u00b0<br \/>\nThe measure of each exterior angle of a 15-gon = \\(\\frac{360\u00b0}{15}\\)<br \/>\n= 24\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe measure of each interior angle of 15-gon is: 156\u00b0<br \/>\nThe measure of each exterior angle of 15-gon is: 24\u00b0<\/p>\n<p>Question 6.<br \/>\n24-gon<br \/>\nAnswer:<br \/>\nThe given polygon is: 24-gon<br \/>\nWe know that,<br \/>\nThe number of sides of 24-gon is: 24<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe measure of each interior angle of a polygon = \\(\\frac{180\u00b0 (n &#8211; 2)}{n}\\)<br \/>\nThe measure of each exterior angle of a polygon = \\(\\frac{360\u00b0}{n}\\)<br \/>\nWhere,<br \/>\nn is the number of sides<br \/>\nSo,<br \/>\nThe measure of each interior angle of 24-gon = \\(\\frac{180\u00b0 (24 &#8211; 2)}{24}\\)<br \/>\n= \\(\\frac{180\u00b0 (22)}{24}\\)<br \/>\n= 165\u00b0<br \/>\nThe measure of each exterior angle of a 24-gon = \\(\\frac{360\u00b0}{24}\\)<br \/>\n= 15\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe measure of each interior angle of 24-gon is: 165\u00b0<br \/>\nThe measure of each exterior angle of 24-gon is: 15\u00b0<\/p>\n<p>Question 7.<br \/>\n60-gon<br \/>\nAnswer:<br \/>\nThe given polygon is: 60-gon<br \/>\nWe know that,<br \/>\nThe number of sides of 60-gon is: 60<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe measure of each interior angle of a polygon = \\(\\frac{180\u00b0 (n &#8211; 2)}{n}\\)<br \/>\nThe measure of each exterior angle of a polygon = \\(\\frac{360\u00b0}{n}\\)<br \/>\nWhere,<br \/>\nn is the number of sides<br \/>\nSo,<br \/>\nThe measure of each interior angle of 60-gon = \\(\\frac{180\u00b0 (60 &#8211; 2)}{60}\\)<br \/>\n= \\(\\frac{180\u00b0 (58)}{60}\\)<br \/>\n= 174\u00b0<br \/>\nThe measure of each exterior angle of a 60-gon = \\(\\frac{360\u00b0}{60}\\)<br \/>\n= 6\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe measure of each interior angle of 60-gon is: 174\u00b0<br \/>\nThe measure of each exterior angle of 60-gon is: 6\u00b0<\/p>\n<p>Find the indicated measure in <img loading=\"lazy\" class=\"alignnone size-full wp-image-44554\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-51.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 51\" width=\"18\" height=\"18\" \/>ABCD. Explain your reasoning.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-45060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-118.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 118\" width=\"291\" height=\"118\" \/><\/p>\n<p>Question 8.<br \/>\nCD<br \/>\nAnswer:<br \/>\nThe given parallelogram is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-118.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 118\" width=\"291\" height=\"118\" \/><br \/>\nWe know that,<br \/>\nThe lengths of the opposite sides of the parallelogram are equal<br \/>\nSo,<br \/>\nIn parallelogram ABCD,<br \/>\nAB = CD<br \/>\nIn the given figure,<br \/>\nIt is given that<br \/>\nAB = 16<br \/>\nSo,<br \/>\nCD = 16<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of the CD is: 16<\/p>\n<p>Question 9.<br \/>\nAD<br \/>\nAnswer:<br \/>\nThe given parallelogram is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-118.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 118\" width=\"291\" height=\"118\" \/><br \/>\nWe know that,<br \/>\nThe lengths of the opposite sides of the parallelogram are equal<br \/>\nSo,<br \/>\nIn parallelogram ABCD,<br \/>\nAD = BC<br \/>\nIn the given figure,<br \/>\nIt is given that<br \/>\nBC = 7<br \/>\nSo,<br \/>\nAD = 7<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of the AD is: 7<\/p>\n<p>Question 10.<br \/>\nAE<br \/>\nAnswer:<br \/>\nThe given parallelogram is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-118.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 118\" width=\"291\" height=\"118\" \/><br \/>\nWe know that,<br \/>\nThe diagonals of the parallelogram bisect each other<br \/>\nSo,<br \/>\nIn parallelogram ABCD,<br \/>\nAE = EC<br \/>\nIn the given figure,<br \/>\nIt is given that<br \/>\nEC = 7<br \/>\nSo,<br \/>\nAE = 7<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of the AE is: 7<\/p>\n<p>Question 11.<br \/>\nBD<br \/>\nAnswer:<br \/>\nThe given parallelogram is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-118.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 118\" width=\"291\" height=\"118\" \/><br \/>\nWe know that,<br \/>\nThe diagonals of the parallelogram bisect each other<br \/>\nSo,<br \/>\nIn parallelogram ABCD,<br \/>\nAC \u22a5 BD<br \/>\nIn the given figure,<br \/>\nIt is given that<br \/>\nED = 10.2<br \/>\nWe know that,<br \/>\nBD = BE + ED<br \/>\nBE = ED<br \/>\nSo,<br \/>\nBD = 20.4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of the BD is: 20.4<\/p>\n<p>Question 12.<br \/>\nm\u2220BCD<br \/>\nAnswer:<br \/>\nThe given parallelogram is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-118.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 118\" width=\"291\" height=\"118\" \/><br \/>\nWe know that,<br \/>\nThe opposite angles of the parallelogram are equal<br \/>\nSo,<br \/>\nIn parallelogram ABCD,<br \/>\n\u2220A = \u2220C<br \/>\nIn the given figure,<br \/>\n\u2220A = 120\u00b0<br \/>\nSo,<br \/>\n\u2220C = 120\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of \u2220BCD is: 120\u00b0<\/p>\n<p>Question 13.<br \/>\nm\u2220ABC<br \/>\nAnswer:<br \/>\nThe given parallelogram is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-118.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 118\" width=\"291\" height=\"118\" \/><br \/>\nWe know that,<br \/>\nThe sum of the consecutive angles of the parallelogram are supplementary<br \/>\nSo,<br \/>\nIn parallelogram ABCD,<br \/>\n\u2220A + \u2220B = 180\u00b0<br \/>\nIn the given figure,<br \/>\n\u2220A = 120\u00b0<br \/>\nSo,<br \/>\n\u2220B = 180\u00b0 &#8211; 120\u00b0<br \/>\n= 60\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of \u2220ABC is: 60\u00b0<\/p>\n<p>Question 14.<br \/>\nm\u2220ADC<br \/>\nAnswer:<br \/>\nThe given parallelogram is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-118.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 118\" width=\"291\" height=\"118\" \/><br \/>\nWe know that,<br \/>\nThe opposite angles of the parallelogram are equal<br \/>\nSo,<br \/>\nIn parallelogram ABCD,<br \/>\n\u2220B = \u2220D<br \/>\nFrom Exercise 13,<br \/>\n\u2220B = 60\u00b0<br \/>\nSo,<br \/>\n\u2220D = 60\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of \u2220ADC is: 60\u00b0<\/p>\n<p>Question 15.<br \/>\nm\u2220DBC<br \/>\nAnswer:<br \/>\nThe given parallelogram is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-118.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 118\" width=\"291\" height=\"118\" \/><br \/>\nWe know that,<br \/>\nThe opposite angles of the parallelogram are equal<br \/>\nSo,<br \/>\nIn parallelogram ABCD,<br \/>\n\u2220B = \u2220D<br \/>\nIn the given figure,<br \/>\n\u2220D = 60\u00b0<br \/>\nSo,<br \/>\n\u2220B = 60\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of \u2220DBC is: 60\u00b0<\/p>\n<p>State which theorem you can use to show that the quadrilateral is a parallelogram.<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45059\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-119.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 119\" width=\"199\" height=\"98\" \/><br \/>\nAnswer:<br \/>\nThe given quadrilateral is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45059\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-119.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 119\" width=\"199\" height=\"98\" \/><br \/>\nFrom the given quadrilateral,<br \/>\nWe can observe that the length of the opposite sides are equal and parallel<br \/>\nHence,<br \/>\nAccording to the Parallelograms Opposite sides congruent and parallel Theorem,<br \/>\nWe can conclude that the given quadrilateral is a parallelogram<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45058\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-120.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 120\" width=\"174\" height=\"98\" \/><br \/>\nAnswer:<br \/>\nThe given quadrilateral is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45058\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-120.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 120\" width=\"174\" height=\"98\" \/><br \/>\nFrom the given quadrilateral,<br \/>\nWe can observe that the diagonals bisect each other<br \/>\nHence,<br \/>\nAccording to the Diagonals Congruent Converse Theorem,<br \/>\nWe can conclude that the given quadrilateral is a parallelogram<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45057\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-121.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 121\" width=\"199\" height=\"101\" \/><br \/>\nAnswer:<br \/>\nThe given quadrilateral is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45057\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-121.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 121\" width=\"199\" height=\"101\" \/><br \/>\nFrom the given quadrilateral,<br \/>\nWe can observe that,<br \/>\nThe opposite angles of the given quadrilateral are congruent and the angle measures are not 90\u00b0<br \/>\nHence,<br \/>\nAccording to the Parallelograms Opposite Angles Theorem,<br \/>\nWe can conclude that the given quadrilateral is a parallelogram<\/p>\n<p>Graph the quadrilateral with the given vertices in a coordinate plane. Then show that the quadrilateral is a parallelogram.<\/p>\n<p>Question 19.<br \/>\nQ(- 5, &#8211; 2) R(3, &#8211; 2), S(1, &#8211; 6), T(- 7, &#8211; 6)<br \/>\nAnswer:<br \/>\nThe given vertices of a quadrilateral are:<br \/>\nQ (-5, -2), R (3, -2), S (1, -6), and T (-7, -6)<br \/>\nFrom the given vertices of a quadrilateral,<br \/>\nQS and RT are the opposite vertices<br \/>\nNow,<br \/>\nThe representation of the quadrilateral in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-95303\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-27.png\" alt=\"\" width=\"530\" height=\"248\" \/><br \/>\nWe know that,<br \/>\nFor the given quadrilateral to be a parallelogram,<br \/>\nThe lengths of the opposite sides must be equal<br \/>\nThe opposite sides must be parallel<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe slope between 2 points = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nThe distance between 2 points = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nSo,<br \/>\nQS = \\(\\sqrt{(6 &#8211; 2)\u00b2 + (1 + 5)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4)\u00b2 + (6)\u00b2}\\)<br \/>\n= \\(\\sqrt{16 + 36}\\)<br \/>\n= 7.2<br \/>\nRT = \\(\\sqrt{(6 &#8211; 2)\u00b2 + (3 + 7)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4)\u00b2 + (10)\u00b2}\\)<br \/>\n= \\(\\sqrt{16 + 100}\\)<br \/>\n= 10.77<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given vertices of a quadrilateral are not parallelogram since the lengths of the opposite sides are not equal<\/p>\n<p>Question 20.<br \/>\nW(- 3, 7), X(3, 3), Y(1, &#8211; 3), Z(- 5, 1)<br \/>\nAnswer:<br \/>\nThe given vertices of a quadrilateral are:<br \/>\nW (-3, 7), X (3, 3), Y (1, -3), Z (-5, 1)<br \/>\nFrom the given vertices of a quadrilateral,<br \/>\nWY and XZ are the opposite vertices<br \/>\nNow,<br \/>\nThe representation of the quadrilateral in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-95307\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-28.png\" alt=\"\" width=\"485\" height=\"439\" \/><br \/>\nWe know that,<br \/>\nFor the given quadrilateral to be a parallelogram,<br \/>\nThe lengths of the opposite sides must be equal<br \/>\nThe opposite sides must be parallel<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe slope between 2 points = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nThe distance between 2 points = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nSo,<br \/>\nWY = \\(\\sqrt{(1 + 3)\u00b2 + (7 + 3)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4)\u00b2 + (10)\u00b2}\\)<br \/>\n= \\(\\sqrt{16 + 100}\\)<br \/>\n= 10.77<br \/>\nXZ = \\(\\sqrt{(3 &#8211; 1)\u00b2 + (3 + 5)\u00b2}\\)<br \/>\n= \\(\\sqrt{(2)\u00b2 + (8)\u00b2}\\)<br \/>\n= \\(\\sqrt{4 + 64}\\)<br \/>\n= 8.24<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given vertices of a quadrilateral are not parallelogram since the lengths of the opposite<br \/>\nsides are not equal<\/p>\n<p>Question 21.<br \/>\nA stop sign is a regular polygon. (Section 7.1)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45056\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-122.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 122\" width=\"114\" height=\"119\" \/><br \/>\na. Classify the stop sign by its number of sides.<br \/>\nAnswer:<br \/>\nThe given stop sign is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45056\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-122.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 122\" width=\"114\" height=\"119\" \/><br \/>\nIt is given that the sign is a regular polygon<br \/>\nFrom the given stop sign,<br \/>\nWe can observe that the number of sides is: 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the stop sign is in the shape of a &#8220;Hexagon&#8221;<\/p>\n<p>b. Find the measure of each interior angle and each exterior angle of the stop sign.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe measure of each interior angle of a polygon = \\(\\frac{180\u00b0 (n &#8211; 2)}{n}\\)<br \/>\nThe measure of each exterior angle of any polygon = \\(\\frac{360\u00b0}{n}\\)<br \/>\nNow,<br \/>\nFrom part (a),<br \/>\nThe stop sign is in the shape of a regular hexagon<br \/>\nWe know that,<br \/>\nThe number of sides of a regular hexagon is: 6<br \/>\nSo,<br \/>\nThe measure of each interior angle of a hexagon = \\(\\frac{180\u00b0 (6 &#8211; 2)}{6}\\)<br \/>\n= 120\u00b0<br \/>\nThe measure of each exterior angle of a hexagon = \\(\\frac{360\u00b0}{6}\\)<br \/>\n= 60\u00b0<\/p>\n<p>Question 22.<br \/>\nIn the diagram of the staircase shown, JKLM is a parallelogram, \\(\\overline{Q T}\\) || \\(\\overline{R S}\\), QT = RS = 9 feet, QR = 3 feet, and m\u2220QRS = 123\u00b0.<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-45055\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-7-Quadrilaterals-and-Other-Polygons-123.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 7 Quadrilaterals and Other Polygons 123\" width=\"255\" height=\"264\" \/><\/p>\n<p>a. List all congruent sides and angles in <img loading=\"lazy\" class=\"alignnone size-full wp-image-44554\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-51.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 51\" width=\"18\" height=\"18\" \/>JKLM. Explain your reasoning.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nIn a parallelogram,<br \/>\nThe opposite sides and the angles are congruent<br \/>\nHence,<br \/>\nIn the parallelogram JKLM,<br \/>\nThe congruent sides are:<br \/>\nJK || LM and JM || KL<br \/>\nThe congruent angles are:<br \/>\n\u2220J = \u2220L and \u2220K = \u2220M<\/p>\n<p>b. Which theorem could you use to show that QRST is a parallelogram?<br \/>\nAnswer:<br \/>\nIt is given that<br \/>\nQT = RS = 9 feet<br \/>\nQR = 3 feet<br \/>\nHence,<br \/>\nAccording to the &#8220;Parallelograms Opposite sides congruent and parallel Theorem&#8221;,<br \/>\nWe can conclude that QRST is a parallelogram<\/p>\n<p>c. Find ST, m\u2220QTS, m\u2220TQR, and m\u2220TSR. Explain your reasoning.<br \/>\nAnswer:<br \/>\nIt is given that<br \/>\nQT = RS = 9 feet<br \/>\nQR = 3 feet<br \/>\nm\u2220QRS = 123\u00b0<br \/>\nFrom part (b),<br \/>\nWe know that,<br \/>\nQRST is a parallelogram<br \/>\nSo,<br \/>\nFrom the parallelogram QRST,<br \/>\nQR = ST<br \/>\nSo,<br \/>\nST = 3 feet<br \/>\nNow,<br \/>\nFrom the parallelogram QRST,<br \/>\nBy using the opposite angles Theorem,<br \/>\n\u2220T = \u2220R and \u2220Q = \u2220S<br \/>\nIt is given that<br \/>\n\u2220R = 123\u00b0<br \/>\nSo,<br \/>\n\u2220T = 123\u00b0<br \/>\nFrom the parallelogram QRST,<br \/>\n\u2220Q + \u2220R = 180\u00b0<br \/>\nSo,<br \/>\n\u2220Q = 180\u00b0 &#8211; 123\u00b0<br \/>\n\u2220Q = 57\u00b0<br \/>\nSo,<br \/>\n\u2220S = 57\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nST = 3 feet<br \/>\nm\u2220QTS = 123\u00b0<br \/>\nm\u2220TQR = 57\u00b0<br \/>\nm\u2220TSR = 57\u00b0<\/p>\n<h3><a id=\"7.4_Properties_of_Special_Parallelograms\"><\/a>7.4 Properties of Special Parallelograms<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Identifying Special Quadrilaterals<\/p>\n<p>Work with a partner: Use dynamic geometry software.<\/p>\n<p>Sample<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45845\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-124.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 124\" width=\"302\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-124.png 302w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-124-300x237.png 300w\" sizes=\"(max-width: 302px) 100vw, 302px\" \/><\/p>\n<p>a. Draw a circle with center A.<br \/>\nAnswer:<br \/>\nThe representation of a circle with center A is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-96249\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-29.png\" alt=\"\" width=\"276\" height=\"216\" \/><\/p>\n<p>b. Draw two diameters of the circle. Label the endpoints B, C, D, and E.<br \/>\nAnswer:<br \/>\nThe representation of the two diameters of the circle is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-96253\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-30.png\" alt=\"\" width=\"287\" height=\"221\" \/><\/p>\n<p>c. Draw quadrilateral BDCE.<br \/>\nAnswer:<br \/>\nThe representation of quadrilateral BDCE is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-96288\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-31.png\" alt=\"\" width=\"263\" height=\"229\" \/><\/p>\n<p>d. Is BDCE a parallelogram? rectangle? rhombus? square? Explain your reasoning.<br \/>\nAnswer:<br \/>\nThe representation of quadrilateral BDCE is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-96288\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-31.png\" alt=\"\" width=\"263\" height=\"229\" \/><br \/>\nFrom the above quadrilateral,<br \/>\nWe can observe that the opposite sides and the opposite angles are equal<br \/>\nHence, from the above,<br \/>\nWe can conclude that the quadrilateral BDCE is a rhombus<\/p>\n<p>e. Repeat parts (a)-(d) for several other circles. Write a conjecture based on your results.<br \/>\nAnswer:<br \/>\nFrom parts (a) &#8211; (d) of the circles,<br \/>\nWe can observe that the quadrilaterals formed will be either a rhombus,a parallelogram, or a\u00a0 square<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Identifying Special Quadrilaterals<\/p>\n<p>Work with a partner: Use dynamic geometry software.<\/p>\n<p>Sample<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45844\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-125.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 125\" width=\"305\" height=\"243\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-125.png 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-125-300x239.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><\/p>\n<p>a. Construct two segments that are perpendicular bisectors of each other. Label the endpoints A, B, D, and E. Label the intersection C.<br \/>\nAnswer:<br \/>\nThe representation of a line segment and its perpendicular bisector is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-96360\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-32.png\" alt=\"\" width=\"423\" height=\"250\" \/><\/p>\n<p>b. Draw quadrilateral AEBD.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-96365\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-33.png\" alt=\"\" width=\"465\" height=\"261\" \/><\/p>\n<p>c. Is AEBD a parallelogram? rectangle? rhombus? square? Explain your reasoning.<br \/>\nAnswer:<br \/>\nThe representation of the quadrilateral AEBD is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-96365\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-33.png\" alt=\"\" width=\"465\" height=\"261\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that the quadrilateral AEBD is a rhombus because all the sides are equal and the angles bisect each other at 90\u00b0<\/p>\n<p>d. Repeat parts (a)-(c) for several other segments. Write a conjecture based on your results.<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 \/>\nFrom parts (a) &#8211; (c),<br \/>\nWe can conclude that the quadrilaterals formed from the perpendicular bisectors will be only a &#8220;Rhombus&#8221;<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 3.<br \/>\nWhat are the properties of the diagonals of rectangles, rhombuses, and squares?<br \/>\nAnswer:<br \/>\nThe properties of diagonals of rectangles, rhombuses, and squares are:<br \/>\nRhombuses:<br \/>\nThe two diagonals of the rhombus are perpendicular<br \/>\nRectangles:<br \/>\nThe diagonals are congruent and bisect each other<br \/>\nSquares:<br \/>\nThe diagonals bisect each other and the angle is 90\u00b0<\/p>\n<p>Question 4.<br \/>\nIs RSTU a parallelogram? rectangle? rhombus? square? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45843\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-126.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 126\" width=\"153\" height=\"138\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45843\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-126.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 126\" width=\"153\" height=\"138\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that the diagonals bisect each other at 90 degrees and the diagonals are congruent to each other<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given quadrilateral is a rhombus<\/p>\n<p>Question 5.<br \/>\nWhat type of quadrilateral has congruent diagonals that bisect each other?<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe quadrilateral that has congruent diagonals that bisect each other is called a &#8220;Rectangle&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that the quadrilateral that has congruent diagonals that bisect each other is called a &#8220;Rectangle&#8221;<\/p>\n<h3><a id=\"Lesson_7.4_Properties_of_Special_Parallelograms\"><\/a>Lesson 7.4 Properties of Special Parallelograms<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nFor any square JKLM, is it always or sometimes true that \\(\\overline{J K}\\) \u22a5 \\(\\overline{K L}\\)? Explain your reasoning.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe diagonals of a square bisect each other at 90\u00b0<br \/>\nAll 4 angles of a square are equal i.e., 90\u00b0<br \/>\nSo,<br \/>\nThe angles between any 2 adjacent sides in a square is also 90\u00b0 i.e., the two adjacent sides are perpendicular<br \/>\nHence, from the above,<br \/>\nWe can conclude that for any square JKLM, it is always true that<br \/>\n\\(\\overline{j K}\\) \u22a5 \\(\\overline{K L}\\)<\/p>\n<p>Question 2.<br \/>\nFor any rectangle EFGH, is it always or sometimes true that \\(\\overline{F G} \\cong \\overline{G H}\\)? Explain your reasoning.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe opposite sides of a rectangle are congruent<br \/>\nSo,<br \/>\nIn rectangle EFGH,<br \/>\nEF and GH are the parallel sides<br \/>\nFG and EH are the parallel sides<br \/>\nSo,<br \/>\nEF \u2245GH<br \/>\nFG \u2245 EH<br \/>\nHence, from the above,<br \/>\nWe can conclude that for a rectangle EFGH, it is always false that \\(\\overline{F G} \\cong \\overline{G H}\\)<\/p>\n<p>Question 3.<br \/>\nA quadrilateral has four congruent sides and four congruent angles. Sketch the quadrilateral and classily it.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nA quadrilateral that has 4 congruent sides and 4 congruent angles is called a &#8220;Square&#8221;<br \/>\nHence,<br \/>\nThe representation of a square is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-97400\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-34.png\" alt=\"\" width=\"240\" height=\"192\" \/><\/p>\n<p>Question 4.<br \/>\nIn Example 3, what are m\u2220ADC and m\u2220BCD?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-97404\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-35.png\" alt=\"\" width=\"158\" height=\"111\" \/><br \/>\nFrom the given figure,<br \/>\nWe know that,<br \/>\nThe sum of the angle measures of a triangle is: 180\u00b0<br \/>\nSo,<br \/>\nFrom \u0394BCD,<br \/>\n\u2220B + \u2220C + \u2220D = 180\u00b0<br \/>\nNow,<br \/>\nBy using the Vertical Angles Theorem,<br \/>\n\u2220D = \u22204<br \/>\nBy using the Corresponding Angles Theorem,<br \/>\n\u22204 = \u2220C<br \/>\nSo,<br \/>\n\u22204 = \u2220D = 61\u00b0<br \/>\n\u2220C = 61\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220ADC = \u2220BCD = 61\u00b0<\/p>\n<p>Question 5.<br \/>\nFind the measures of the numbered angles in rhombus DEFG.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45842\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-127.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 127\" width=\"138\" height=\"110\" \/><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nSuppose you measure only the diagonals of the window opening in Example 4 and they have the same measure. Can you conclude that the opening is a rectangle? Explain.<br \/>\nAnswer:<br \/>\nThe representation of the window opening as mentioned in Example 4 is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-98088\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-36.png\" alt=\"\" width=\"169\" height=\"194\" \/><br \/>\nFrom the given figure,<br \/>\nWe observe that the opposite sides of the opening window are equal<br \/>\nIt is given that the diagonals of the opening window have the same measure<br \/>\nWe know that,<br \/>\nBy the Rectangle Diagonals measure Theorem,<br \/>\nA parallelogram is said to be a rectangle only when the length of the diagonals are congruent<br \/>\nHence, from the above,<br \/>\nWe can conclude that the opening window is a rectangle<\/p>\n<p>Question 7.<br \/>\nWHAT IF?<br \/>\nIn Example 5. QS = 4x &#8211; 15 and RT = 3x + 8. Find the lengths of the diagonals of QRST.<br \/>\nAnswer:<br \/>\nThe given lengths of the diagonals of the rectangle QRST are:<br \/>\nQS = 4x &#8211; 15 and RT = 3x + 8<br \/>\nWe know that,<br \/>\nBy Rectangle Diagonal Measure Theorem,<br \/>\nThe diagonals of a rectangle are congruent<br \/>\nSo,<br \/>\nIn a rectangle QRST,<br \/>\nQS = RT<br \/>\nSo,<br \/>\n4x &#8211; 15 = 3x + 8<br \/>\n4x &#8211; 3x = 15 + 8<br \/>\nx = 23<br \/>\nNow,<br \/>\nQS = 4x &#8211; 15<br \/>\n= 4 (23) &#8211; 15<br \/>\n= 92 &#8211; 15<br \/>\n= 77<br \/>\nRT = 3x + 8<br \/>\n= 3 (23) + 8<br \/>\n= 69 + 8<br \/>\n= 77<br \/>\nHence, from the above,<br \/>\nWe can conclude that the lengths of the diagonals of the rectangle QRST are:<br \/>\nQS = RT = 77<\/p>\n<p>Question 8.<br \/>\nDecide whether <img loading=\"lazy\" class=\"alignnone size-full wp-image-44554\" style=\"font-weight: inherit;\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-51.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 51\" width=\"18\" height=\"18\" \/>PQRS with vertices P(- 5, 2), Q(0, 4), R(2, &#8211; 1), and S(- 3, &#8211; 3) is a rectangle, a rhombus, or a square. Give all names that apply.<br \/>\nAnswer:<br \/>\nThe given vertices of the parallelogram PQRS is:<br \/>\nP (-5, 2), Q (0, 4), R (2, -1), and S (-3, -3)<br \/>\nCompare the given points with (x1, y1), and (x2, y2)<br \/>\nHence,<br \/>\nThe representation of the given vertices of the parallelogram PQRS in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-98095\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-37.png\" alt=\"\" width=\"499\" height=\"348\" \/><br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe distance between the 2 points = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\nSo,<br \/>\nPR = \\(\\sqrt{(2 + 5)\u00b2 + (2 + 1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(7)\u00b2 + (3)\u00b2}\\)<br \/>\n= \\(\\sqrt{49 + 9}\\)<br \/>\n= 7.61<br \/>\nQS = \\(\\sqrt{(0 + 3)\u00b2 + (4 + 3)\u00b2}\\)<br \/>\n= \\(\\sqrt{(7)\u00b2 + (3)\u00b2}\\)<br \/>\n= \\(\\sqrt{49 + 9}\\)<br \/>\n= 7.61<br \/>\nSo,<br \/>\nThe diagonals of the parallelogram PQRS are congruent<br \/>\nSo,<br \/>\nThe parallelogram PQRS must be either a rectangle or a square<br \/>\nSo,<br \/>\nNow,<br \/>\nPQ = \\(\\sqrt{(0 + 5)\u00b2 + (4 &#8211; 2)\u00b2}\\)<br \/>\n= \\(\\sqrt{(5)\u00b2 + (2)\u00b2}\\)<br \/>\n= \\(\\sqrt{25 + 4}\\)<br \/>\n= 5.38<br \/>\nQR = \\(\\sqrt{(4 + 1)\u00b2 + (2 &#8211; 0)\u00b2}\\)<br \/>\n= \\(\\sqrt{(5)\u00b2 + (2)\u00b2}\\)<br \/>\n= \\(\\sqrt{25 + 4}\\)<br \/>\n= 5.38<br \/>\nRS = \\(\\sqrt{(2 + 3)\u00b2 + (3 &#8211; 1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(5)\u00b2 + (2)\u00b2}\\)<br \/>\n= \\(\\sqrt{25 + 4}\\)<br \/>\n= 5.38<br \/>\nSP = \\(\\sqrt{(3 + 2)\u00b2 + (5 &#8211; 3)\u00b2}\\)<br \/>\n= \\(\\sqrt{(5)\u00b2 + (2)\u00b2}\\)<br \/>\n= \\(\\sqrt{25 + 4}\\)<br \/>\n= 5.38<br \/>\nSo,<br \/>\nWe can observe that the lengths of all the sides are congruent<br \/>\nHence, from the above,<br \/>\nWe can conclude that the parallelogram ABCD is a square since the diagonals are congruent and all the sides are congruent<\/p>\n<h3><a id=\"Exercise_7.4_Properties_of_Special_Parallelograms\"><\/a>Exercise 7.4 Properties of Special Parallelograms<\/h3>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nWhat is another name for an equilateral rectangle?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49208\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 1\" width=\"499\" height=\"31\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-1.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-1-300x19.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nWhat should you look for in a parallelogram to know if the parallelogram is also a rhombus?<br \/>\nAnswer:<br \/>\nWhen you want to look at whether the given parallelogram is a rhombus or not, there are 2 conditions. They are:<br \/>\na. Check whether the diagonals are not congruent<br \/>\nb. Check whether the angle measures will not be equal to 90\u00b0<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3-8, for any rhombus JKLM, decide whether the statement is always or sometimes true. Draw a diagram and explain your reasoning.<\/p>\n<p>Question 3.<br \/>\n\u2220L \u2245\u2220M<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49209\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 3\" width=\"533\" height=\"212\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-3.png 533w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-3-300x119.png 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><\/p>\n<p>Question 4.<br \/>\n\u2220K \u2245\u2220M<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe opposite angles of a rhombus are always congruent<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-98884\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-38.png\" alt=\"\" width=\"380\" height=\"239\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that \u2220K is always congruent with \u2220M<\/p>\n<p>Question 5.<br \/>\n\\(\\overline{J M} \\cong \\overline{K L}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49210\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 5\" width=\"567\" height=\"203\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-5.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-5-300x107.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 6.<br \/>\n\\(\\overline{J K} \\cong \\overline{K L}\\)<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nIn a rhombus, the opposite sides are congruent<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-98886\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-40.png\" alt=\"\" width=\"199\" height=\"143\" \/><br \/>\nFrom the figure,<br \/>\nWe can say that JK and KL are the adjacent sides<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\overline{J K} \\cong \\overline{K L}\\) is sometimes true when the rhombus is a square<\/p>\n<p>Question 7.<br \/>\n\\(\\overline{J L} \\cong \\overline{K M}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49211\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-7.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 7\" width=\"513\" height=\"212\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-7.png 513w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-7-300x124.png 300w\" sizes=\"(max-width: 513px) 100vw, 513px\" \/><\/p>\n<p>Question 8.<br \/>\n\u2220JKM \u2245 \u2220LKM<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe diagonals of a rhombus bisect each other at the right angles i.e., 90\u00b0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-98910\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-41.png\" alt=\"\" width=\"271\" height=\"252\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220JKM \u2245 \u2220LKM is always true<\/p>\n<p>In Exercises 9-12. classify the quadrilateral. Explain your reasoning.<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45841\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-128.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 128\" width=\"169\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-128.png 169w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-128-150x150.png 150w\" sizes=\"(max-width: 169px) 100vw, 169px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49212\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-9.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 9\" width=\"576\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-9.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-9-300x29.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45840\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-129.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 129\" width=\"169\" height=\"168\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-129.png 169w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-129-150x150.png 150w\" sizes=\"(max-width: 169px) 100vw, 169px\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45840\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-129.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 129\" width=\"169\" height=\"168\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-129.png 169w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-129-150x150.png 150w\" sizes=\"(max-width: 169px) 100vw, 169px\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that the opposite sides are congruent and all the angles are the right angles<br \/>\nWe know that,<br \/>\nA rectangle has opposite sides that are congruent and all the angles are 90\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given figure is in the form of a rectangle<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45839\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-130.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 130\" width=\"169\" height=\"166\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49213\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-11.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 11\" width=\"563\" height=\"34\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-11.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-11-300x18.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45838\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-131.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 131\" width=\"168\" height=\"172\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45838\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-131.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 131\" width=\"168\" height=\"172\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nThe adjacent angle measures are equal to 180\u00b0<br \/>\nThe opposite sides are congruent<br \/>\nThe opposite angles are congruent<br \/>\nThe diagonals are not congruent<br \/>\nWe know that,<br \/>\nA rhombus has the above properties<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given figure is a rhombus<\/p>\n<p>In Exercises 13-16. find the measures of the numbered angles in rhombus DEFG.<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45837\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-132.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 132\" width=\"163\" height=\"112\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49214\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-13.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 13\" width=\"552\" height=\"332\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-13.png 552w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-13-300x180.png 300w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45836\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-133.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 133\" width=\"135\" height=\"135\" \/><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45835\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-134.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 134\" width=\"127\" height=\"135\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49215\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-15.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 15\" width=\"566\" height=\"237\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-15.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-15-300x126.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45834\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-135.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 135\" width=\"196\" height=\"155\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 17-22, for any rectangle WXYZ, decide whether the statement is always or sometimes true. Draw a diagram and explain your reasoning.<\/p>\n<p>Question 17.<br \/>\n\u2220W \u2245 \u2220X<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49216\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-17.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 17\" width=\"573\" height=\"184\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-17.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-17-300x96.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 18.<br \/>\n\\(\\overline{W X} \\cong \\overline{Y Z}\\)<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nA rectangle has the congruent opposite sides<br \/>\nSo,<br \/>\nFrom the rectangle WXYZ,<br \/>\nThe opposite sides are:<br \/>\nWX, YZ, WZ, and XY<br \/>\nThe representation of the rectangle WXYZ is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-99904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-42.png\" alt=\"\" width=\"281\" height=\"265\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\overline{W X} \\cong \\overline{Y Z}\\) is always true<\/p>\n<p>Question 19.<br \/>\n\\(\\overline{W X} \\cong \\overline{X Y}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49217\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-19.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 19\" width=\"507\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-19.png 507w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-19-300x131.png 300w\" sizes=\"(max-width: 507px) 100vw, 507px\" \/><\/p>\n<p>Question 20.<br \/>\n\\(\\overline{W Y} \\cong \\overline{X Z}\\)<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe length of the diagonals is the same in a rectangle<br \/>\nSo,<br \/>\nIn the rectangle WXYZ,<br \/>\nThe diagonals are:<br \/>\nWY and XZ<br \/>\nThe representation of the rectangle WXYZ is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-99907\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-43.png\" alt=\"\" width=\"272\" height=\"264\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\overline{W Y} \\cong \\overline{X Z}\\) is always true<\/p>\n<p>Question 21.<br \/>\n\\(\\overline{W Y}\\) \u22a5 \\(\\overline{X Z}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49218\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-21.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 21\" width=\"550\" height=\"219\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-21.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-21-300x119.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 22.<br \/>\n\u2220WXZ \u2245\u2220YXZ<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe diagonals of a rectangle bisect each other at the right angle i.e., 90\u00b0<br \/>\nThe representation of the rectangle WXYZ is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-99904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-42.png\" alt=\"\" width=\"281\" height=\"265\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220WXZ \u2245\u2220YXZ is always true<\/p>\n<p>In Exercises 23 and 24, determine whether the quadrilateral is a rectangle.<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45833\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-136.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 136\" width=\"124\" height=\"112\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49219\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-23.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 23\" width=\"541\" height=\"64\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-23.png 541w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-23-300x35.png 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45832\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-137.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 137\" width=\"190\" height=\"106\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45832\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-137.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 137\" width=\"190\" height=\"106\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that<br \/>\nThe length of the opposite sides are congruent<br \/>\nThe one angle is a right angle i.e., 90\u00b0<br \/>\nWe can also observe that<br \/>\nWe don&#8217;t know anything about the other three angles<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given quadrilateral is not a rectangle<\/p>\n<p>In Exercises 25-28, find the lengths of the diagonals of rectangle WXYZ.<\/p>\n<p>Question 25.<br \/>\nWY = 6x &#8211; 7<br \/>\nXZ = 3x + 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49220\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-25.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 25\" width=\"330\" height=\"219\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-25.png 330w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-25-300x199.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><\/p>\n<p>Question 26.<br \/>\nWY = 14x + 10<br \/>\nXZ = 11x + 22<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe length of the diagonals are congruent in a rectangle<br \/>\nSo,<br \/>\nWY = XZ<br \/>\nSo,<br \/>\n14x + 10 = 11x + 22<br \/>\n14x &#8211; 11x = 22 &#8211; 10<br \/>\n3x = 12<br \/>\nx = \\(\\frac{12}{3}\\)<br \/>\nx = 4<br \/>\nSo,<br \/>\nWY = 14 (4) + 10<br \/>\n= 56 + 10<br \/>\n= 66<br \/>\nXZ = 11 (4) + 22<br \/>\n= 44 + 22<br \/>\n= 66<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of the diagonals are:<br \/>\nWY = XZ = 66<\/p>\n<p>Question 27.<br \/>\nWY = 24x &#8211; 8<br \/>\nXZ = &#8211; 18x + 13<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49221\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-27.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 27\" width=\"378\" height=\"277\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-27.png 378w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-27-300x220.png 300w\" sizes=\"(max-width: 378px) 100vw, 378px\" \/><\/p>\n<p>Question 28.<br \/>\nWY = 16x &#8211; 2<br \/>\nXZ = 36x &#8211; 6<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe length of the diagonals are congruent in a rectangle<br \/>\nSo,<br \/>\nWY = XZ<br \/>\nSo,<br \/>\n16x &#8211; 2 = 36x &#8211; 6<br \/>\n16x &#8211; 36x = -6 + 2<br \/>\n-20x = -4<br \/>\n20x = 4<br \/>\nx = \\(\\frac{4}{20}\\)<br \/>\nx = \\(\\frac{1}{5}\\)<br \/>\nSo,<br \/>\nWY = 16 (\\(\\frac{1}{5}\\)) &#8211; 2<br \/>\n= 3.2 &#8211; 2<br \/>\n= 1<br \/>\nXZ = 36 (\\(\\frac{1}{5}\\)) &#8211; 6<br \/>\n= 7 &#8211; 6<br \/>\n= 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of the diagonals is:<br \/>\nWY = XZ = 1<\/p>\n<p>In Exercises 29-34, name each quadrilateral &#8211; parallelogram, rectangle, rhombus, or square &#8211; for which the statement is always true.<\/p>\n<p>Question 29.<br \/>\nIt is equiangular.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49222\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-29.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 29\" width=\"579\" height=\"34\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-29.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-29-300x18.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 30.<br \/>\nIt is equiangular and equilateral.<br \/>\nAnswer:<br \/>\nThe quadrilateral that is both equiangular and equilateral is a &#8220;Square&#8221;<\/p>\n<p>Question 31.<br \/>\nThe diagonals are perpendicular.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49223\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-31.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 31\" width=\"532\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-31.png 532w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-31-300x34.png 300w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><\/p>\n<p>Question 32.<br \/>\nThe opposite sides are congruent.<br \/>\nAnswer:<br \/>\nThe quadrilaterals where the opposite sides are congruent are:<br \/>\nParallelogram, Rectangle, Square, and Rhombus<\/p>\n<p>Question 33.<br \/>\nThe diagonals bisect each other.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49224\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-33.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 33\" width=\"551\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-33.png 551w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-33-300x31.png 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p>Question 34.<br \/>\nThe diagonals bisect opposite angles.<br \/>\nAnswer:<br \/>\nThe quadrilaterals that the diagonals bisect opposite angles are:<br \/>\nSquare, and Rhombus<\/p>\n<p>Question 35.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nQuadrilateral PQRS is a rectangle. Describe and correct the error in finding the value of x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45831\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-138.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 138\" width=\"285\" height=\"172\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49225\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-35.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 35\" width=\"560\" height=\"170\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-35.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-35-300x91.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nQuadrilateral PQRS is a rhombus. Describe and correct the error in finding the value of x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45830\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-139.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 139\" width=\"265\" height=\"181\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe sum of the adjacent angles of a rhombus is: 180\u00b0<br \/>\nSo,<br \/>\n\u2220Q + \u2220R = 180\u00b0<br \/>\n37\u00b0 + x\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 37\u00b0<br \/>\nx\u00b0 = 143\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x\u00b0 is: 143\u00b0<\/p>\n<p>In Exercises 37 &#8211; 42, the diagonals of rhombus ABCD intersect at E. Ghen that m\u2220BAC = 53\u00b0, DE = 8, and EC = 6, find the indicated measure.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-45829\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-140.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 140\" width=\"133\" height=\"112\" \/><\/p>\n<p>Question 37.<br \/>\nm\u2220DAC<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49226\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-37.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 37\" width=\"560\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-37.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-37-300x33.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 38.<br \/>\nm\u2220AED<br \/>\nAnswer:<br \/>\nBy using the Rhombus Opposite Angles Theorem,<br \/>\n\u2220A = \u2220E<br \/>\nSo,<br \/>\n\u2220E = 53\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of \u2220AED is: 53\u00b0<\/p>\n<p>Question 39.<br \/>\nm\u2220ADC<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49227\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-39.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 39\" width=\"322\" height=\"66\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-39.png 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-39-300x61.png 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><\/p>\n<p>Question 40.<br \/>\nDB<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe diagonals of a rhombus are equal<br \/>\nSo,<br \/>\nDB = 2 (DE)<br \/>\nIt is given that<br \/>\nDE = 8<br \/>\nSo,<br \/>\nDB = 2 (8)<br \/>\nDB = 16<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of DE is: 16<\/p>\n<p>Question 41.<br \/>\nAE<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49228\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-41.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 41\" width=\"581\" height=\"32\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-41.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-41-300x17.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 42.<br \/>\nAC<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe diagonals of a rhombus are equal<br \/>\nSo,<br \/>\nAC = 2 (AE)<br \/>\nIt is given that<br \/>\nAE = 6<br \/>\nSo,<br \/>\nAC = 2 (6)<br \/>\nAC = 12<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of AC is: 12<\/p>\n<p>In Exercises 43-48. the diagonals of rectangle QRST intersect at P. Given that n\u2220PTS = 34\u00b0 and QS = 10, find the indicated measure.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-101561\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-45.png\" alt=\"\" width=\"141\" height=\"96\" \/><\/p>\n<p>Question 43.<br \/>\nm\u2220QTR<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49229\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-43.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 43\" width=\"298\" height=\"34\" \/><\/p>\n<p>Question 44.<br \/>\nm\u2220QRT<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe opposite angles of a rectangle are equal<br \/>\nSo,<br \/>\nFrom Exercise 43,<br \/>\nWe can observe that,<br \/>\n\u2220QTR = 56\u00b0<br \/>\nSo,<br \/>\nBy using the Rectangle opposite angles Theorem,<br \/>\n\u2220QRT = 56\u00b0<br \/>\nHence, from te above,<br \/>\nWe can conclude that<br \/>\n\u2220QRT = 56\u00b0<\/p>\n<p>Question 45.<br \/>\nm\u2220SRT<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49230\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-45.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 45\" width=\"371\" height=\"30\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-45.png 371w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-45-300x24.png 300w\" sizes=\"(max-width: 371px) 100vw, 371px\" \/><\/p>\n<p>Question 46.<br \/>\nQP<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe diagonals of a rectangle are congruent and bisect each other<br \/>\nIt is given that<br \/>\nQS = 10<br \/>\nSo,<br \/>\nBy using the Diagonals Congruent Theorem,<br \/>\nQP = PS<br \/>\nSo,<br \/>\nQP = \\(\\frac{10}{2}\\)<br \/>\nQP = 5<br \/>\nHence, from the above,<br \/>\nWe can coclude that the length of QP is: 5<\/p>\n<p>Question 47.<br \/>\nRT<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49231\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-47.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 47\" width=\"485\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-47.png 485w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-47-300x35.png 300w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><\/p>\n<p>Question 48.<br \/>\nRP<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe diagonals of arectangle are congruent<br \/>\nSo,<br \/>\nQS = RT = 10<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe diagonals of a rectangle are congruent and bisect each other<br \/>\nSo,<br \/>\nBy using the rectangle diagonals Theorem,<br \/>\nRP = PT<br \/>\nSo,<br \/>\nRP = \\(\\frac{10}{2}\\)<br \/>\nRP = 5<br \/>\nHece, from the above,<br \/>\nWe can conclude that the length of RP is: 5<\/p>\n<p>In Exercises 49-54. the diagonals of square LMNP intersect at K. Given that LK = 1. find the indicated measure.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-45827\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-142.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 142\" width=\"110\" height=\"119\" \/><\/p>\n<p>Question 49.<br \/>\nm\u2220MKN<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49232\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-49.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 49\" width=\"504\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-49.png 504w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-49-300x35.png 300w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><\/p>\n<p>Question 50.<br \/>\nm\u2220LMK<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe diagonals of a square are congruent and they are perpendicular<br \/>\nSo,<br \/>\n\u2220LMK = 90\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of \u2220LMK is: 90\u00b0<\/p>\n<p>Question 51.<br \/>\nm\u2220LPK<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49233\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-51.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 51\" width=\"529\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-51.png 529w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-51-300x33.png 300w\" sizes=\"(max-width: 529px) 100vw, 529px\" \/><\/p>\n<p>Question 52.<br \/>\nKN<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe diagonals of a square are congruent and bisect each other<br \/>\nSo,<br \/>\nBy using the Square Dagonals Congruent Theorem,<br \/>\nLN = LK + KN<br \/>\nLK = KN<br \/>\nSo,<br \/>\nKN = 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of KN is: 1<\/p>\n<p>Question 53.<br \/>\nLN<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49234\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-53.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 53\" width=\"568\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-53.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-53-300x17.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 54.<br \/>\nMP<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe diagonals of a square are congruent and are perpendicular to each other<br \/>\nSo,<br \/>\nBy using the Square Diagonals Congruent Theorem,<br \/>\nLN = MP<br \/>\nSo,<br \/>\nMP = 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of MP is: 2<\/p>\n<p>In Exercises 55-69. decide whether<img loading=\"lazy\" class=\"alignnone size-full wp-image-44554\" style=\"font-weight: inherit;\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-51.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 51\" width=\"18\" height=\"18\" \/>JKLM is a rectangle, a rhombus. or a square. Give all names that apply. Explain your reasoning.<\/p>\n<p>Question 55.<br \/>\nJ(- 4, 2), K(0, 3), L(1, &#8211; 1), M(- 3, &#8211; 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49235\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-55.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 55\" width=\"594\" height=\"662\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-55.png 594w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-55-269x300.png 269w\" sizes=\"(max-width: 594px) 100vw, 594px\" \/><\/p>\n<p>Question 56.<br \/>\nJ(- 2, 7), K(7, 2), L(- 2, &#8211; 3), M(- 11, 2)<br \/>\nAnswer:<br \/>\nThe given vertices are :<br \/>\nJ (-2, 7), K (7, 2), L (-2, -3), M (-11, 2)<br \/>\nNow,<br \/>\nThe diagonals of the parallelogram JKLM are: JL and KM<br \/>\nNow,<br \/>\nJL = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(2 &#8211; 2)\u00b2 + (7 + 3)\u00b2}\\)<br \/>\n= \\(\\sqrt{(0)\u00b2 + (10)\u00b2}\\)<br \/>\n= 10<br \/>\nKM = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(2 &#8211; 2)\u00b2 + (7 + 11)\u00b2}\\)<br \/>\n= \\(\\sqrt{(0)\u00b2 + (18)\u00b2}\\)<br \/>\n= 18<br \/>\nJK = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(7 &#8211; 2)\u00b2 + (7 + 2)\u00b2}\\)<br \/>\n= \\(\\sqrt{(5)\u00b2 + (9)\u00b2}\\)<br \/>\n= 10.29<br \/>\nKL = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(2 + 3)\u00b2 + (7 + 2)\u00b2}\\)<br \/>\n= \\(\\sqrt{(5)\u00b2 + (9)\u00b2}\\)<br \/>\n= 10.29<br \/>\nLM = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(11 &#8211; 2)\u00b2 + (2 + 3)\u00b2}\\)<br \/>\n= \\(\\sqrt{(9)\u00b2 + (5)\u00b2}\\)<br \/>\n= 10.29<br \/>\nMJ = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(11 &#8211; 2)\u00b2 + (7 &#8211; 2)\u00b2}\\)<br \/>\n= \\(\\sqrt{(9)\u00b2 + (5)\u00b2}\\)<br \/>\n= 10.29<br \/>\nJL = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{-3 &#8211; 7}{2 &#8211; 2}\\)<br \/>\n= -10<br \/>\nKM = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{2 &#8211; 2}{-11 &#8211; 7}\\)<br \/>\n= -18<br \/>\nHence, from the above,<br \/>\nWe can conclude that the parallelogram JKLM is a rhombus<\/p>\n<p>Question 57.<br \/>\nJ(3, 1), K(3, &#8211; 3), L(- 2, &#8211; 3), M(- 2, 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49236\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-57.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 57\" width=\"584\" height=\"713\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-57.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-57-246x300.png 246w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 58.<br \/>\nJ(- 1, 4), K(- 3, 2), L(2, &#8211; 3), M(4, &#8211; 1)<br \/>\nAnswer:<br \/>\nThe given vertices are :<br \/>\nJ (-1, 4), K (-3, 2), L (2, -3), M (4, -1)<br \/>\nNow,<br \/>\nThe diagonals of the parallelogram JKLM are: JL and KM<br \/>\nNow,<br \/>\nJL = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(2 + 1)\u00b2 + (4 + 3)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3)\u00b2 + (7)\u00b2}\\)<br \/>\n= 7.61<br \/>\nKM = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4 + 3)\u00b2 + (2 + 1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(7)\u00b2 + (3)\u00b2}\\)<br \/>\n= 7.61<br \/>\nJK = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3 &#8211; 1)\u00b2 + (4 &#8211; 2)\u00b2}\\)<br \/>\n= \\(\\sqrt{(2)\u00b2 + (2)\u00b2}\\)<br \/>\n= 2.82<br \/>\nKL = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(2 + 3)\u00b2 + (2 + 3)\u00b2}\\)<br \/>\n= \\(\\sqrt{(5)\u00b2 + (5)\u00b2}\\)<br \/>\n= 7.07<br \/>\nLM = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4 &#8211; 2)\u00b2 + (1 &#8211; 3)\u00b2}\\)<br \/>\n= \\(\\sqrt{(2)\u00b2 + (2)\u00b2}\\)<br \/>\n= 2.82<br \/>\nMJ = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(4 + 1)\u00b2 + (4 + 1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(5)\u00b2 + (5)\u00b2}\\)<br \/>\n= 7.07<br \/>\nJL = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{-3 &#8211; 4}{2 + 1}\\)<br \/>\n= &#8211;\\(\\frac{7}{3}\\)<br \/>\nKM = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{-1 &#8211; 2}{4 + 3}\\)<br \/>\n= &#8211;\\(\\frac{3}{7}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the parallelogram JKLM is a rectangle<\/p>\n<p>Question 59.<br \/>\nJ(5, 2), K(1, 9), L(- 3, 2), M(1, &#8211; 5)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49237\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-59.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 59\" width=\"586\" height=\"623\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-59.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-59-282x300.png 282w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 60.<br \/>\nJ(5, 2), K(2, 5), L(- 1, 2), M(2, &#8211; 1)<br \/>\nAnswer:<br \/>\nThe given vertices are :<br \/>\nJ (5, 2), K (2, 5), L (-1, 2), M (2, -1)<br \/>\nNow,<br \/>\nThe diagonals of the parallelogram JKLM are: JL and KM<br \/>\nNow,<br \/>\nJL = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(2 &#8211; 2)\u00b2 + (5 + 1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(0)\u00b2 + (6)\u00b2}\\)<br \/>\n= 6<br \/>\nKM = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(2 &#8211; 2)\u00b2 + (5 + 1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(0)\u00b2 + (6)\u00b2}\\)<br \/>\n= 6<br \/>\nJK = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(5 &#8211; 2)\u00b2 + (5 &#8211; 2)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3)\u00b2 + (3)\u00b2}\\)<br \/>\n= 4.24<br \/>\nKL = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(2 + 1)\u00b2 + (5 &#8211; 2)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3)\u00b2 + (3)\u00b2}\\)<br \/>\n= 4.24<br \/>\nLM = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(-1 &#8211; 2)\u00b2 + (2 + 1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3)\u00b2 + (3)\u00b2}\\)<br \/>\n= 4.24<br \/>\nMJ = \\(\\sqrt{(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(5 &#8211; 2)\u00b2 + (2 + 1)\u00b2}\\)<br \/>\n= \\(\\sqrt{(3)\u00b2 + (3)\u00b2}\\)<br \/>\n= 4.24<br \/>\nKM = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{-1 &#8211; 5}{2 &#8211; 2}\\)<br \/>\n= Undefined<br \/>\nJL = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{2 &#8211; 2}{-1 &#8211; 5}\\)<br \/>\n= 0<br \/>\nSo,<br \/>\nJL \u22a5 KM<br \/>\nHence, from the above,<br \/>\nWe can conclude that the parallelogram JKLM is a square<\/p>\n<p><strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nIn Exercises 61 and 62, classify the quadrilateral. Explain your reasoning. Then find the values of x and y.<\/p>\n<p>Question 61.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45826\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-143.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 143\" width=\"147\" height=\"122\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49238\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-61.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 61\" width=\"519\" height=\"262\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-61.png 519w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-61-300x151.png 300w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><\/p>\n<p>Question 62.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45825\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-144.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 144\" width=\"180\" height=\"120\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45825\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-144.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 144\" width=\"180\" height=\"120\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that all the angles are 90\u00b0 and the diagonals are perpendicular<br \/>\nSo,<br \/>\nThe given figure is a Square<br \/>\nWe know that,<br \/>\nThe opposite angles are congruent in a square<br \/>\nSo,<br \/>\n5x\u00b0 = (3x + 18)\u00b0<br \/>\n5x\u00b0 &#8211; 3x\u00b0 = 18\u00b0<br \/>\n2x\u00b0 = 18\u00b0<br \/>\nx\u00b0 = \\(\\frac{18}{2}\\)<br \/>\nx\u00b0 = 9\u00b0<br \/>\n2y\u00b0 = 10<br \/>\ny\u00b0 = \\(\\frac{10}{2}\\)<br \/>\ny\u00b0 = 5\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe given figure is a Square<br \/>\nThe values of x and y are: 9 and 2 respectively<\/p>\n<p>Question 63.<br \/>\n<strong>DRAWING CONCLUSIONS<\/strong><br \/>\nIn the window, \\(\\overline{B D}\\) \u2245 \\(\\overline{D F}\\) \u2245 \\(\\overline{B H}\\) \u2245 \\(\\overline{H F}\\). Also, \u2220HAB, \u2220BCD, \u2220DEF, and \u2220FGH are right angles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45824\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-145.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 145\" width=\"245\" height=\"246\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-145.png 245w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-145-150x150.png 150w\" sizes=\"(max-width: 245px) 100vw, 245px\" \/><br \/>\na. Classify HBDF and ACEG. Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49239\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-63.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 63\" width=\"588\" height=\"187\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-63.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-63-300x95.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>b. What can you conclude about the lengths of the diagonals \\(\\overline{A E}\\) and \\(\\overline{G C}\\)? Given that these diagonals intersect at J, what can you conclude about the lengths of \\(\\overline{A J}\\), \\(\\overline{J E}\\), \\(\\overline{C J}\\) and \\(\\overline{J G}\\)? Explain.<br \/>\nAnswer:<br \/>\nFrom part (a),<br \/>\nWe can observe that ACEG is a rectangle<br \/>\nWe know that,<br \/>\nThe diagonals of a rectangle are congruent and bisect each other<br \/>\nSo,<br \/>\nAE and GC are the diagonals in the rectangle ACEG<br \/>\nSo,<br \/>\nAE = GC<br \/>\nSince we know that the diagonals of a rectangle bisect each other,<br \/>\nAJ = JE and CJ = JG<\/p>\n<p>Question 64.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nOrder the terms in a diagram so that each term builds off the previous term(s). Explain why each figure is in the location you chose.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-101761\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-46.png\" alt=\"\" width=\"290\" height=\"132\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe figure that has 4 sides is called a &#8220;Quadrilateral&#8221;<br \/>\nEx:<br \/>\nParallelogram, Square etc<br \/>\nHence,<br \/>\nThe order of the terms in a diagram so that each term builds off the previous term is:<br \/>\na. Quadrilateral &#8211; No equal sides<br \/>\nb. Parallelogram &#8211; The parallel sides are equal and the angles are not 90\u00b0<br \/>\nc. Rectangle &#8211; The parallel sides are equal and all the angles are 90\u00b0<br \/>\nd. Square &#8211; All the sides are equal and all the angles are 90\u00b0<br \/>\ne. Rhombus &#8211; All the sides are equal but only one angle is 90\u00b0<\/p>\n<p><strong>CRITICAL THINKING<\/strong><br \/>\nIn Exercises 65-70, complete each statement with always, sometimes, or never. Explain your reasoning.<br \/>\nQuestion 65.<br \/>\nA square is ____________ a rhombus.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49240\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-65.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 65\" width=\"514\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-65.png 514w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-65-300x34.png 300w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/><\/p>\n<p>Question 66.<br \/>\nA rectangle is __________ a square.<br \/>\nAnswer:<br \/>\nA rectangle is sometimes a square because a rectangle has the congruent opposite sides whereas a square has all the congruent sides<\/p>\n<p>Question 67.<br \/>\nA rectangle _____________ has congruent diagonals.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49241\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-67.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 67\" width=\"601\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-67.png 601w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-67-300x44.png 300w\" sizes=\"(max-width: 601px) 100vw, 601px\" \/><\/p>\n<p>Question 68.<br \/>\nThe diagonals of a square _____________ bisect its angles.<br \/>\nAnswer:<br \/>\nThe diagonals of a square always bisect its angles by using the Square Diagonals Congruent Theorem<\/p>\n<p>Question 69.<br \/>\nA rhombus __________ has four congruent angles.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49242\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-69.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 69\" width=\"532\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-69.png 532w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-69-300x33.png 300w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><\/p>\n<p>Question 70.<br \/>\nA rectangle ____________ has perpendicular diagonals.<br \/>\nAnswer:<br \/>\nA rectangle sometimes has perpendicular diagonals because the diagonals of a rectangle bisect each other ut not perpendicular to each other whereas a square has the perpendicular diagonals<\/p>\n<p>Question 71.<br \/>\n<strong>USING TOOLS<\/strong><br \/>\nYou want to mark off a square region for a garden at school. You use a tape measure to mark off a quadrilateral on the ground. Each side of the quadrilateral is 2.5 meters long. Explain how you can use the tape measure to make sure that the quadrilateral is a square.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49243\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-71.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 71\" width=\"532\" height=\"64\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-71.png 532w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-71-300x36.png 300w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><\/p>\n<p>Question 72.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nUse the plan for proof below to write a paragraph proof for one part of the Rhombus Diagonals Theorem (Theorem 7. 11).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45823\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-146.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 146\" width=\"221\" height=\"129\" \/><br \/>\nGiven ABCD is a parallelogram.<br \/>\n\\(\\overline{A C}\\) \u22a5 \\(\\overline{B D}\\)<br \/>\nProve: ABCD is a rhombus.<br \/>\nPlan for Proof: Because ABCD is a parallelogram. its diagonals bisect each other at X. Use \\(\\overline{A C}\\) \u22a5 \\(\\overline{B D}\\) to show that \u2206BXC \u2245 \u2206DXC. Then show that \\(\\overline{B C}\\) \u2245 \\(\\overline{D C}\\). Use the properties of a parallelogram to show that ABCD is a rhombus.<\/p>\n<p><strong>PROVING A THEOREM<\/strong><br \/>\nIn Exercises 73 and 74, write a proof for parts of the Rhombus Opposite Angles Theorem (Theorem 7.12).<\/p>\n<p>Question 73.<br \/>\nGiven: PQRS is a parallelogram.<br \/>\n\\(\\overline{P R}\\) bisects \u2220SPQ and \u2220QRS.<br \/>\n\\(\\overline{S Q}\\) bisects \u2220PSR and \u2220RQP.<br \/>\nProve: PQRS is a rhombus.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45822\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-147.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 147\" width=\"191\" height=\"118\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49244\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-73.1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 73.1\" width=\"559\" height=\"614\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-73.1.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-73.1-273x300.png 273w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49245\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-73.2.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 73.2\" width=\"561\" height=\"254\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-73.2.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-73.2-300x136.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 74.<br \/>\nGiven: WXYZ is a rhombus<br \/>\nProve: \\(\\overline{W Y}\\) bisects \u2220ZWX and \u2220XYZ.<br \/>\n\\(\\overline{Z X}\\) bisects \u2220WZY and \u2220YXW.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45821\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-148.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 148\" width=\"150\" height=\"117\" \/><br \/>\nAnswer:<\/p>\n<p>Question 75.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nWill a diagonal of a square ever divide the square into two equilateral triangles? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49246\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-75.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 75\" width=\"582\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-75.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-75-300x48.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 76.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nWill a diagonal of a rhombus ever divide the rhombus into two equilateral triangles? Explain your reasoning.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe diagonals of a rhombus are not congruent<br \/>\nWe know that,<br \/>\nSometimes, the interior angles of a rhombus are 120\u00b0, 120\u00b0, 60\u00b0, and 60\u00b0<br \/>\nWe know that,<br \/>\nThe interior angles of an equilateral triangle are: 60\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that it is possible that a diagonal of a rhombus divides the rhombus into two equilateral triangles<\/p>\n<p>Question 77.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nWhich quadrilateral could be called a regular quadrilateral? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49247\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-77.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 77\" width=\"578\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-77.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-77-300x31.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 78.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nWhat other information do you need to determine whether the figure is a rectangle?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45820\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-149.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 149\" width=\"161\" height=\"90\" \/><br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nWe can observe that the opposite sides are congruent and all the interior angles of the given figure are 90\u00b0<br \/>\nWe know that,<br \/>\nA quadrilateral that has the congruent opposite sides and all the interior angles are 90\u00b0 is called a &#8220;Rectangle&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given figure is a rectangle<\/p>\n<p>Question 79.<br \/>\n<strong>REASONING<\/strong><br \/>\nAre all rhombuses similar? Are all squares similar? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49248\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-79.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 79\" width=\"589\" height=\"124\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-79.png 589w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-79-300x63.png 300w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><\/p>\n<p>Question 80.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nUse the Rhombus Diagonals Theorem (Theorem 7. 1I) to explain why every rhombus has at least two lines of symmetry.<br \/>\nAnswer:<\/p>\n<p><strong>PROVING A COROLLARY<\/strong><br \/>\nIn Exercises 81-83, write the corollary as a conditional statement and its converse. Then explain why each statement is true.<\/p>\n<p>Question 81.<br \/>\nRhombus Corollary (Corollary 7.2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49249\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-81.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 81\" width=\"592\" height=\"348\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-81.png 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-81-300x176.png 300w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p>Question 82.<br \/>\nRectangle Corollary (Corollary 7.3)<br \/>\nAnswer:<br \/>\nConditional statement:<br \/>\nIf a quadrilateral is a rectangle, then it has four right angles<br \/>\nConverse:<br \/>\nIf a quadrilateral has four right angles, then it is a rectangle<br \/>\nThe conditional statement is true since a quadrilateral is a rectangle, it has 4 right angles<br \/>\nThe corollary is not right because by having 4 right angles, the quadrilateral should be either a rectangle or a square<\/p>\n<p>Question 83.<br \/>\nSquare Corollary (Corollary 7.4)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49250\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-83.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 83\" width=\"580\" height=\"420\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-83.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-83-300x217.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 84.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims a rhombus will never have congruent diagonals because it would have to be a rectangle. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nIf a rhombus has congruent diagonals, then it would have to be a square only when all the angles will be 90\u00b0<br \/>\nBut, it is not possible<br \/>\nA rhombus with non-congruent diagonals will never be a rectangle because a rhombus won&#8217;t have all the angles 90\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the claim of your friend is not correct<\/p>\n<p>Question 85.<br \/>\nPROOF<br \/>\nWrite a proof in the style of your choice.<br \/>\nGien \u2206XYZ \u2245 \u2206XWZ, \u2220XYW \u2245 \u2220ZWY<br \/>\nProve WVYZ is a rhombus.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45819\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-150.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 150\" width=\"160\" height=\"122\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49251\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-85.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 85\" width=\"550\" height=\"743\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-85.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-85-222x300.png 222w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 86.<br \/>\n<strong>PROOF<\/strong><br \/>\nWrite a proof in the style of your choice.<br \/>\nGiven <img loading=\"lazy\" class=\"alignnone size-full wp-image-45818\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-151.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 151\" width=\"216\" height=\"29\" \/><br \/>\nProve ABCD is a rectangle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45817\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-152.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 152\" width=\"176\" height=\"112\" \/><br \/>\nAnswer:<\/p>\n<p><strong>PROVING A THEOREM<\/strong><br \/>\nIn Exercises 87 and 88. write a proof for part of the Rectangle Diagonals Theorem (Theorem 7.13).<\/p>\n<p>Question 87.<br \/>\nGiven PQRS is a rectangle.<br \/>\nProve \\(\\overline{P R} \\cong \\overline{S Q}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49252\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-87.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 87\" width=\"579\" height=\"730\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-87.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-87-238x300.png 238w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 88.<br \/>\nGiven PQRS is a parallelogram.<br \/>\n\\(\\overline{P R} \\cong \\overline{S Q}\\)<br \/>\nProve PQRS is a rectangle.<br \/>\nAnswer:<\/p>\n<p>Maintaining Mathematical Proficiency<\/p>\n<p>\\(\\overline{D E}\\) is a midsegment of \u2206ABC. Find the values of x and y.<\/p>\n<p>Question 89.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45816\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-153.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 153\" width=\"247\" height=\"159\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49253\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-89.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 89\" width=\"176\" height=\"172\" \/><\/p>\n<p>Question 90.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45815\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-154.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 154\" width=\"162\" height=\"148\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45815\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-154.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 154\" width=\"162\" height=\"148\" \/><br \/>\nIt is given that \\(\\overline {D E}\\) is a midsegment of \u0394ABC<br \/>\nSo,<br \/>\nNow,<br \/>\nFrom the above figure,<br \/>\nWe can say that<br \/>\nAD = DB<br \/>\nSo,<br \/>\ny = 6<br \/>\nNow,<br \/>\nBC = 2 (DE)<br \/>\nBC = 2 (7)<br \/>\nBC = 14<br \/>\nx = 14<br \/>\nHence, from the above,<br \/>\nWe can conclude that the values of x and y are: 14 and 6 respectively<\/p>\n<p>Question 91.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45814\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-155.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 155\" width=\"164\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-155.png 164w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-155-150x150.png 150w\" sizes=\"(max-width: 164px) 100vw, 164px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49254\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-7.4-a-91.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 7.4 a 91\" width=\"147\" height=\"206\" \/><\/p>\n<h3><a id=\"7.5_Properties_of_Trapezoids_and_Kites\"><\/a>7.5 Properties of Trapezoids and Kites<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Making a conjecture about Trapezoids<\/p>\n<p>Sample<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46292\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-156.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 156\" width=\"305\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-156.png 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-156-300x235.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><\/p>\n<p>Work with a partner. Use dynamic geometry software.<\/p>\n<p>a. Construct a trapezoid whose base angles are congruent. Explain your process.<br \/>\nAnswer:<\/p>\n<p>b. Is the trapezoid isosceles? Justify your answer.<br \/>\nAnswer:<\/p>\n<p>c. Repeat parts (a) and (b) for several other trapezoids. Write a conjecture based on your results.<br \/>\n<strong>PERSEVERE IN SOLVING PROBLEMS<\/strong><br \/>\nTo be proficient in math, you need to draw diagrams of important features and relationships, and search for regularity or trends.<br \/>\nAnswer:<\/p>\n<p>Exploration 2<\/p>\n<p>Discovering a Property of Kites<\/p>\n<p>Work with a partner. Use dynamic geometry software.<\/p>\n<p>Sample<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46291\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-157.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 157\" width=\"305\" height=\"240\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-157.png 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-157-300x236.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><\/p>\n<p>a. Construct a kite. Explain your process.<br \/>\nAnswer:<\/p>\n<p>b. Measure the angles of the kite. What do you observe?<br \/>\nAnswer:<\/p>\n<p>c. Repeat parts (a) and (b) for several other kites. Write a conjecture based on your results.<br \/>\nAnswer:<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 3.<br \/>\nWhat are some properties of trapezoids and kites?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nIs the trapezoid at the left isosceles? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46290\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-158.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 158\" width=\"170\" height=\"102\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nA quadrilateral has angle measures of 7o, 70\u00b0, 1100, and 110\u00b0, Is the quadrilateral a kite? Explain.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_7.5_Properties_of_Trapezoids_and_Kites\"><\/a>Lesson 7.5 Properties of Trapezoids and Kites<\/h3>\n<p><strong>Monitoring progress<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-46289\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-159.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 159\" width=\"166\" height=\"109\" \/><\/p>\n<p>Question 1.<br \/>\nThe points A(- 5, 6), B(4, 9) C(4, 4), and D(- 2, 2) form the vertices of a quadrilateral. Show that ABCD is a trapezoid. Then decide whether it is isosceles.<br \/>\nAnswer:<\/p>\n<p>In Exercises 2 and 3, use trapezoid EFGH.<\/p>\n<p>Question 2.<br \/>\nIf EG = FH, is trapezoid EFGH isosceles? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nIf m\u2220HEF = 70\u00b0 and ,m\u2220FGH = 110\u00b0, is trapezoid EFGH isosceles? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nIn trapezoid JKLM, \u2220J and \u2220M are right angles, and JK = 9 centimeters. The length of midsegment \\(\\overline{N P}\\) of trapezoid JKLW is 12 centimeters. Sketch trapezoid JKLM and its midsegment. Find ML. Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nExplain another method you can use to find the length of \\(\\overline{Y Z}\\) in Example 4.<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nIn a kite. the measures of the angles are 3x\u00b0 75\u00b0, 90\u00b0, and 120\u00b0. Find the value of x. What are the measures of the angles that are congruent?<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nQuadrilateral DEFG has at least one pair of opposite sides congruent. What types of quadrilaterals meet this condition?<br \/>\nAnswer:<\/p>\n<p>Give the most specific name for the quadrilateral. Explain your reasoning.<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46288\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-160.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 160\" width=\"121\" height=\"104\" \/><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46287\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-161.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 161\" width=\"140\" height=\"109\" \/><br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46286\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-162.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 162\" width=\"114\" height=\"111\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Exercise_7.5_Properties_of_Trapezoids_and_Kites\"><\/a>Exercise 7.5 Properties of Trapezoids and Kites<\/h3>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nDescribe the differences between a trapezoid and a kite.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49255\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-1.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 1\" width=\"592\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-1.png 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-1-300x29.png 300w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find \u201cboth&#8221; answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46285\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-163.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 163\" width=\"182\" height=\"111\" \/><br \/>\nIs there enough information to prove that trapezoid ABCD is isosceles?<br \/>\nAnswer:<\/p>\n<p>Is there enough information to prove that \\(\\overline{A B}\\) \u2245 \\(\\overline{D C}\\)?<br \/>\nAnswer:<\/p>\n<p>Is there enough information to prove that the non-parallel sides of trapezoid ABCD are congruent?<br \/>\nAnswer:<\/p>\n<p>Is there enough information to prove that the legs of trapezoid ABCD are congruent?<br \/>\nAnswer:<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3-6, show that the quadrilateral with the given vertices is a trapezoid. Then decide whether it is isosceles.<\/p>\n<p>Question 3.<br \/>\nW(1, 4), X(1, 8), Y(- 3, 9), Z(- 3, 3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49256\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-3.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 3\" width=\"592\" height=\"530\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-3.png 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-3-300x269.png 300w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p>Question 4.<br \/>\nD(- 3, 3), E(- 1, 1), F(1, &#8211; 4), G(- 3, 0)<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nM(- 2, 0), N(0, 4), P(5, 4), Q(8, 0)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49257\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-5.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 5\" width=\"583\" height=\"520\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-5.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-5-300x268.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 6.<br \/>\nH(1, 9), J(4, 2), K(5, 2), L(8, 9)<br \/>\nAnswer:<\/p>\n<p>In Exercises 7 and 8, find the measure of each angle in the isosceles trapezoid.<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46284\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-164.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 164\" width=\"101\" height=\"110\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49258\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-7.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 7\" width=\"559\" height=\"176\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-7.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-7-300x94.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46283\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-165.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 165\" width=\"127\" height=\"101\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 9 and 10. find the length of the midsegment of the trapezoid.<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46282\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-166.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 166\" width=\"112\" height=\"106\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49259\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-9.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 9\" width=\"353\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-9.png 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-9-300x137.png 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46281\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-167.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 167\" width=\"166\" height=\"98\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 11 and 12, find AB.<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46280\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-168.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 168\" width=\"136\" height=\"92\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49260\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-11.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 11\" width=\"333\" height=\"205\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-11.png 333w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-11-300x185.png 300w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46279\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-169.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 169\" width=\"177\" height=\"99\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 13 and 14, find the length of the midsegment of the trapezoid with the given vertices.<\/p>\n<p>Question 13.<br \/>\nA(2, 0), B(8, &#8211; 4), C(12, 2), D(0, 10)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49261\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-13.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 13\" width=\"563\" height=\"458\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-13.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-13-300x244.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 14.<br \/>\nS(- 2, 4), T(- 2, &#8211; 4), U(3, &#8211; 2), V(13, 10)<br \/>\nAnswer:<\/p>\n<p>In Exercises 15 &#8211; 18, Find m \u2220 G.<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46278\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-170.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 170\" width=\"170\" height=\"117\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49262\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-15.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 15\" width=\"406\" height=\"224\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-15.png 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-15-300x166.png 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46277\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-171.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 171\" width=\"151\" height=\"117\" \/><br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46276\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-172.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 172\" width=\"154\" height=\"125\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49263\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-17.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 17\" width=\"400\" height=\"173\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-17.png 400w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-17-300x130.png 300w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46275\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-173.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 173\" width=\"108\" height=\"122\" \/><br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in finding DC.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46274\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-174.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 174\" width=\"264\" height=\"180\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49264\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-19.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 19\" width=\"570\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-19.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-19-300x111.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 20.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in finding m\u2220A.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46273\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-175.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 175\" width=\"300\" height=\"181\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 21 &#8211; 24. given the most specific name for the quadrilateral. Explain your reasoning.<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46272\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-176.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 176\" width=\"161\" height=\"102\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49265\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-21.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 21\" width=\"576\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-21.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-21-300x32.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46271\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-177.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 177\" width=\"118\" height=\"106\" \/><br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46270\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-178.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 178\" width=\"118\" height=\"117\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49266\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-23.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 23\" width=\"584\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-23.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-23-300x31.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46269\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-179.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 179\" width=\"146\" height=\"111\" \/><br \/>\nAnswer:<\/p>\n<p><strong>REASONING<\/strong><br \/>\nIn Exercises 25 and 26, tell whether enough information is given in the diagram to classify the quadrilateral by the indicated name. Explain.<\/p>\n<p>Question 25.<br \/>\nrhombus<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46268\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-180.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 180\" width=\"115\" height=\"97\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49267\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-25.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 25\" width=\"553\" height=\"64\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-25.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-25-300x35.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 26.<br \/>\nSquare<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46267\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-181.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 181\" width=\"89\" height=\"94\" \/><br \/>\nAnswer:<\/p>\n<p><strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nIn Exercises 27 and 28, find the value of x.<\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46266\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-182.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 182\" width=\"143\" height=\"97\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49268\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-27.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 27\" width=\"243\" height=\"139\" \/><\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46265\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-183.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 183\" width=\"126\" height=\"123\" \/><br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nIn the diagram, NP = 8 inches, and LR = 20 inches. What is the diameter of the bottom layer of the cake?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46264\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-184.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 184\" width=\"169\" height=\"174\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49269\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-29.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 29\" width=\"543\" height=\"352\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-29.png 543w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-29-300x194.png 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou and a friend arc building a kite. You need a stick to place from X to Wand a stick to place from W to Z to finish constructing the frame. You want the kite to have the geometric shape of a kite. How long does each stick need to be? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46263\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-185.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 185\" width=\"277\" height=\"154\" \/><br \/>\nAnswer:<\/p>\n<p><strong>REASONING<\/strong><br \/>\nIn Exercises 31 &#8211; 34, determine which pairs of segments or angles must be congruent so that you can prove that ABCD is the indicated quadrilateral. Explain our reasoning. (There may be more than one right answer.)<\/p>\n<p>Question 31.<br \/>\nisosceles trapezoid<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46262\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-186.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 186\" width=\"148\" height=\"100\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49270\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-31.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 31\" width=\"523\" height=\"95\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-31.png 523w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-31-300x54.png 300w\" sizes=\"(max-width: 523px) 100vw, 523px\" \/><\/p>\n<p>Question 32.<br \/>\nKite<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46261\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-187.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 187\" width=\"137\" height=\"111\" \/><br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\nParallelogram<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46260\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-188.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 188\" width=\"122\" height=\"99\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49271\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-33.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 33\" width=\"575\" height=\"64\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-33.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-33-300x33.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 34.<br \/>\nsquare<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46258\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-189.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 189\" width=\"104\" height=\"96\" \/><br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<strong>PROOF<\/strong><br \/>\nWrite a proof<br \/>\nGiven \\(\\overline{J L} \\cong \\overline{L N}\\), \\(\\overline{K M}\\) is a midsegment of \u2206JLN<br \/>\nProve Quadrilateral JKMN is an isosceles trapezoid.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46257\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-190.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 190\" width=\"147\" height=\"94\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49272\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-35.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 35\" width=\"584\" height=\"588\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-35.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-35-298x300.png 298w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-35-150x150.png 150w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>PROOF<\/strong><br \/>\nWrite a proof<br \/>\nGiven ABCD is a kite.<br \/>\n\\(\\overline{A B} \\cong \\overline{C B}\\), \\(\\overline{A D} \\cong \\overline{C D}\\)<br \/>\nProve \\(\\overline{C E} \\cong \\overline{A E}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46256\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-191.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 191\" width=\"169\" height=\"94\" \/><br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nPoint U lies on the perpendicular bisector of \\(\\overline{R T}\\). Describe the set of points S for which RSTU is a kite.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46255\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-192.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 192\" width=\"126\" height=\"81\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49273\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-37.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 37\" width=\"536\" height=\"75\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-37.png 536w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-37-300x42.png 300w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>REASONING<\/strong><br \/>\nDetermine whether the points A(4, 5), B(- 3, 3), C(- 6, &#8211; 13), and D(6, &#8211; 2) are the vertices of a kite. Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p><strong>PROVING A THEOREM<\/strong><br \/>\nIn Exercises 39 and 40, use the diagram to prove the given theorem. In the diagram, \\(\\overline{E C}\\)\u2019 is drawn parallel to \\(\\overline{A B}\\).<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-46254\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-193.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 193\" width=\"154\" height=\"96\" \/><\/p>\n<p>Question 39.<br \/>\nIsosceles Trapezoid Base Angles Theorem (Theorem 7.14)<br \/>\nGiven ABCD is an isosceles trapezoid.<br \/>\n\\(\\overline{B C}\\) || \\(\\overline{A D}\\)<br \/>\nProve \u2220A \u2245 \u2220D, \u2220B \u2245 \u2220BCD<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49274\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-39.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 39\" width=\"591\" height=\"470\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-39.png 591w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-39-300x239.png 300w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><\/p>\n<p>Question 40.<br \/>\nIsosceles Trapezoid Base Angles Theorem (Theorem 7.15)<br \/>\nGiven ABCD is a trapezoid<br \/>\n\u2220A \u2245 \u2220D, \\(\\overline{B C}\\) || \\(\\overline{A D}\\)<br \/>\nProve ABCD is an isosceles trapezoid.<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour cousin claims there is enough information to prove that JKLW is an isosceles trapezoid. Is your cousin correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46253\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-194.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 194\" width=\"113\" height=\"102\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49275\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-41.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 41\" width=\"380\" height=\"38\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-41.png 380w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-41-300x30.png 300w\" sizes=\"(max-width: 380px) 100vw, 380px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nThe bases of a trapezoid lie on the lines y = 2x + 7 and y = 2x &#8211; 5. Write the equation of the line that contains the midsegment of the trapezoid.<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<strong>CONSTRUCTION<\/strong><br \/>\n\\(\\overline{A C}\\) and \\(\\overline{B D}\\) bisect each other.<br \/>\na. Construct quadrilateral ABCD so that \\(\\overline{A C}\\) and \\(\\overline{B D}\\) are congruent. hut not perpendicular. Classify the quadrilateral. Justify your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49276\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-43.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 43\" width=\"542\" height=\"273\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-43.png 542w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-43-300x151.png 300w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><\/p>\n<p>b. Construct quadrilateral ABCD so that \\(\\overline{A C}\\) and \\(\\overline{B D}\\) are perpendicular. hut not congruent. Classify the quadrilateral. Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 44.<br \/>\nPROOF Write a proof.<br \/>\nGiven QRST is an isosceles trapezoid.<br \/>\nProve \u2220TQS \u2245 \u2220SRT<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46252\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-195.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 195\" width=\"184\" height=\"84\" \/><br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA plastic spiderweb is made in the shape of a regular dodecagon (12-sided polygon). \\(\\overline{A B}\\) || \\(\\overline{P Q}\\), and X is equidistant from the vertices of the dodecagon.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46251\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-196.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 196\" width=\"173\" height=\"179\" \/><br \/>\na. Are you given enough information to prove that ABPQ is an isosceles trapezoid?<br \/>\nb. What is the measure of each interior angle of ABPQ<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49277\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-45.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 45\" width=\"594\" height=\"171\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-45.png 594w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-45-300x86.png 300w\" sizes=\"(max-width: 594px) 100vw, 594px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>ATTENDING TO PRECISION<\/strong><br \/>\nIn trapezoid PQRS, \\(\\overline{P Q}\\) || \\(\\overline{R S}\\) and \\(\\overline{M N}\\) is the midsegment of PQRS. If RS = 5 . PQ. what is the ratio of MN to RS?<br \/>\n(A) 3 : 5<br \/>\n(B) 5 : 3<br \/>\n(C) 1 : 2<br \/>\n(D) 3 : 1<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nUse the plan for proof below to write a paragraph proof of the Kite Opposite Angles Theorem (Theorem 7.19).<br \/>\nGiven EFGH is a Kite.<br \/>\n\\(\\), \\(\\)<br \/>\nProve \u2220E \u2245 \u2220G, \u2220F <img loading=\"lazy\" class=\"alignnone size-full wp-image-46250\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-197.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 197\" width=\"17\" height=\"15\" \/> \u2220H<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46249\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-198.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 198\" width=\"171\" height=\"93\" \/><br \/>\nPlan for Proof: First show that \u2220E \u2245 \u2220G. Then use an indirect argument to show that \u2220F <img loading=\"lazy\" class=\"alignnone size-full wp-image-46250\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-197.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 197\" width=\"17\" height=\"15\" \/>\u2220H.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49278\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-47.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 47\" width=\"598\" height=\"451\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-47.png 598w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-47-300x226.png 300w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nOne of the earliest shapes used for cut diamonds is called the table cut, as shown in the figure. Each face of a cut gem is called a facet.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46248\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-199.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 199\" width=\"156\" height=\"112\" \/><br \/>\na. \\(\\overline{B C}\\) || \\(\\overline{A D}\\), and \\(\\overline{A B}\\) and \\(\\overline{D C}\\) are not parallel. What shape is the facet labeled ABCD?<br \/>\nb. \\(\\overline{D E}\\) || \\(\\overline{G F}\\), and \\(\\overline{D G}\\) and \\(\\overline{E F}\\) are congruent but not parallel. What shape is the facet labeled DEFG?<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nIn the diagram below, \\(\\overline{B G}\\) is the midsegment of \u2206ACD. and \\(\\overline{G E}\\) is the midsegment of \u2206ADF Use the diagram to prove the Trapezoid Midsegment Theorem (Theorem 7.17).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46247\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-200.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 200\" width=\"351\" height=\"91\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-200.png 351w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-200-300x78.png 300w\" sizes=\"(max-width: 351px) 100vw, 351px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49279\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-49.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 49\" width=\"584\" height=\"414\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-49.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-49-300x213.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 50.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nIs SSASS a valid congruence theorem be kites? Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nTo prove the biconditional statement in the Isosceles Trapezoid Diagonals Theorem (Theorem 7.16), you must prove both Parts separately.<br \/>\na. Prove part of the Isosceles Trapezoid Diagonals Theorem (Theorem 7. 16).<br \/>\nGiven JKLM is an isosecles trapezoid.<br \/>\n\\(\\overline{K L}\\) || \\(\\overline{J M}\\), \\(\\overline{J L} \\cong \\overline{K M}\\)<br \/>\nProve \\(\\overline{J L} \\cong \\overline{K M}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46246\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-201.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 201\" width=\"158\" height=\"90\" \/><br \/>\nb. Write the other parts of the Isosceles Trapezoid Diagonals Theorem (Theorem 7. 16) as a conditional. Then prove the statement is true.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49280\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-51.1.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 51.1\" width=\"597\" height=\"600\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-51.1.png 597w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-51.1-150x150.png 150w\" sizes=\"(max-width: 597px) 100vw, 597px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49281\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-51.2.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 51.2\" width=\"618\" height=\"493\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-51.2.png 618w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-51.2-300x239.png 300w\" sizes=\"(max-width: 618px) 100vw, 618px\" \/><\/p>\n<p>Question 52.<br \/>\n<strong>PROOF<\/strong><br \/>\nWhat special type of quadrilateral is EFGH? Write a proof to show that your answer is Correct.<br \/>\nGiven In the three-dimensional figure, \\(\\overline{J L} \\cong \\overline{K M}\\). E, F, G, and H arc the midpoints of \\(\\overline{J L}\\). \\(\\overline{K l}\\), \\(\\overline{K M}\\), and \\(\\overline{J M}\\). respectively.<br \/>\nProve EFGH is a ____________ .<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46245\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-202.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 202\" width=\"142\" height=\"148\" \/><br \/>\nAnswer:<\/p>\n<p>Maintaining Mathematical Proficiency<\/p>\n<p>Describe a similarity transformation that maps the blue preimage to the green image.<\/p>\n<p>Question 53.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46244\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-203.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 203\" width=\"205\" height=\"169\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49282\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-53.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 7 Quadrilaterals and Other Polygons 7.5 a 53\" width=\"560\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-53.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-7-Quadrilaterals-and-Other-Polygons-7.5-a-53-300x47.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 54.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46243\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-204.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 7 Quadrilaterals and Other Polygons 204\" width=\"306\" height=\"166\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-204.png 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-204-300x163.png 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Quadrilaterals_and_Other_Polygons_Review\"><\/a>Quadrilaterals and Other Polygons Review<\/h3>\n<h3>7.1 Angles of Polygons<\/h3>\n<p>Question 1.<br \/>\nFind the sum of the measures of the interior angles of a regular 30-gon. Then find the measure of each interior angle and each exterior angle.<br \/>\nAnswer:<\/p>\n<p>Find the va1ue of x.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46556\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-205.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 205\" width=\"132\" height=\"110\" \/><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46555\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-206.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 206\" width=\"163\" height=\"109\" \/><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46554\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-207.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 207\" width=\"133\" height=\"120\" \/><br \/>\nAnswer:<\/p>\n<h3>7.2 Properties of Parallelograms<\/h3>\n<p>Find the value of each variable in the parallelogram.<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46553\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-208.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 208\" width=\"150\" height=\"90\" \/><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46552\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-209.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 209\" width=\"143\" height=\"98\" \/><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46551\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-210.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 210\" width=\"159\" height=\"82\" \/><br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nFind the coordinates of the intersection of the diagonals of <img loading=\"lazy\" class=\"alignnone size-full wp-image-44554\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-51.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 51\" width=\"18\" height=\"18\" \/>QRST with vertices Q(- 8, 1), R(2, 1). S(4, &#8211; 3), and T(- 6, &#8211; 3).<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nThree vertices of <img loading=\"lazy\" class=\"alignnone size-full wp-image-44554\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-51.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 51\" width=\"18\" height=\"18\" \/>JKLM are J(1, 4), K(5, 3), and L(6, &#8211; 3). Find the coordinates of vertex M.<br \/>\nAnswer:<\/p>\n<h3>7.3 Proving that a Quadrilateral is a Parallelogram<\/h3>\n<p>State which theorem you can use to show that the quadrilateral is a parallelogram.<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46550\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-211.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 211\" width=\"107\" height=\"98\" \/><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46549\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-212.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 212\" width=\"130\" height=\"90\" \/><br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46548\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-213.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 213\" width=\"156\" height=\"86\" \/><br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nFind the values of x and y that make the quadrilateral a parallelogram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46547\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-214.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 214\" width=\"214\" height=\"113\" \/><br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nFind the value of x that makes the quadrilateral a parallelogram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46546\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-215.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 215\" width=\"171\" height=\"106\" \/><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nShow that quadrilateral WXYZ with vertices W(- 1, 6), X(2, 8), Y(1, 0), and Z(- 2, &#8211; 2) is a parallelogram.<br \/>\nAnswer:<\/p>\n<h3>7.4 Properties of Special Parallelograms<\/h3>\n<p>Classify the special quadrilateral. Explain your reasoning.<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46545\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-216.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 216\" width=\"117\" height=\"78\" \/><br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46544\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-217.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 217\" width=\"156\" height=\"72\" \/><br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46543\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-218.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 218\" width=\"113\" height=\"118\" \/><br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\nFind the lengths of the diagonals of rectangle WXYZ where WY = &#8211; 2y + 34 and XZ = 3x &#8211; 26.<br \/>\nAnswer:<\/p>\n<p>Question 20.<br \/>\nDecide whether\u00a0<img loading=\"lazy\" class=\"alignnone size-full wp-image-44554\" style=\"font-weight: inherit;\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-51.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 51\" width=\"18\" height=\"18\" \/><span style=\"font-size: 16px;\">JKLM with vertices J(5, 8), K(9, 6), L(7, 2), and M(3, 4) is a rectangle. a rhombus, or a square. Give all names that apply. Explain.<\/span><\/p>\n<p>Answer:<\/p>\n<h3>7.5 Properties of Trapezoids and Kites<\/h3>\n<p>Question 21.<br \/>\nFind the measure of each angle in the isosceles trapezoid WXYZ.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46542\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-219.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 219\" width=\"175\" height=\"93\" \/><br \/>\nAnswer:<\/p>\n<p>Question 22.<br \/>\nFind the length of the midsegment of trapezoid ABCD.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46541\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-220.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 220\" width=\"184\" height=\"116\" \/><br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\nFind the length of the midsegment of trapezoid JKLM with vertices J(6, 10), K(10, 6), L(8, 2), and M(2, 2).<br \/>\nAnswer:<\/p>\n<p>Question 24.<br \/>\nA kite has angle measures of 7x\u00b0, 65\u00b0, 85\u00b0, and 105\u00b0. Find the value of x. What are the measures of the angles that are congruent?<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\nQuadrilateral WXYZ is a trapezoid with one pair of congruent base angles. Is WXYZ all isosceles trapezoid? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Give the most specific name for the quadrilateral. Explain your reasoning.<\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46540\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-221.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 221\" width=\"113\" height=\"90\" \/><br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46539\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-222.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 222\" width=\"99\" height=\"99\" \/><br \/>\nAnswer:<\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46538\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-223.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 223\" width=\"135\" height=\"87\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Quadrilaterals_and_Other_Polygons_Test\"><\/a>Quadrilaterals and Other Polygons Test<\/h3>\n<p>Find the value of each variable in the parallelogram.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46793\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-224.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 224\" width=\"200\" height=\"89\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46792\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-225.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 225\" width=\"166\" height=\"95\" \/><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46791\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-226.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 226\" width=\"146\" height=\"94\" \/><br \/>\nAnswer:<\/p>\n<p>Give the most specific name for the quadrilateral. Explain your reasoning.<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46790\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-227.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 227\" width=\"99\" height=\"80\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46789\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-228.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 228\" width=\"83\" height=\"83\" \/><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46788\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-229.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 229\" width=\"120\" height=\"64\" \/><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nIn a convex octagon. three of the exterior angles each have a measure of x\u00b0. The other five exterior angles each have a measure of (2x + 7)\u00b0. Find the measure of each exterior angle.<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nQuadrilateral PQRS has vertices P(5, 1), Q(9, 6), R(5, 11), and 5(1, 6), Classify quadrilateral PQRS using the most specific name.<br \/>\nAnswer:<\/p>\n<p>Determine whether enough information is given to show that the quadrilateral is a parallelogram. Explain your reasoning.<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46787\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-230.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 230\" width=\"180\" height=\"101\" \/><br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46786\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-231.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 231\" width=\"152\" height=\"114\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-231.png 152w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-231-150x114.png 150w\" sizes=\"(max-width: 152px) 100vw, 152px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46785\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-232.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 232\" width=\"158\" height=\"105\" \/><br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nExplain why a parallelogram with one right angle must be a rectangle.<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nSummarize the ways you can prove that a quadrilateral is a square.<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nThree vertices of <img loading=\"lazy\" class=\"alignnone size-full wp-image-44554\" style=\"font-weight: inherit;\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-51.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 51\" width=\"18\" height=\"18\" \/>JKLM are J(- 2, &#8211; 1), K(0, 2), and L(4, 3),<br \/>\na. Find the coordinates of vertex M.<br \/>\nAnswer:<\/p>\n<p>b. Find the coordinates of the intersection of the diagonals of <img loading=\"lazy\" class=\"alignnone size-full wp-image-44554\" style=\"font-weight: inherit;\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-51.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 51\" width=\"18\" height=\"18\" \/>JKLM.<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nYou are building a plant stand with three equally-spaced circular shelves. The diagram shows a vertical cross section of the plant stand. What is the diameter of the middle shell?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46784\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-233.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 233\" width=\"232\" height=\"127\" \/><br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\nThe Pentagon in Washington. D.C., is shaped like a regular pentagon. Find the measure of each interior angle.<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\nYou are designing a binocular mount. If \\(\\overline{B C}\\) is always vertical, the binoculars will point in the same direction while they are raised and lowered for different viewers. How can you design the mount so \\(\\overline{B C}\\) is always vertical? Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\nThe measure of one angle of a kite is 90\u00b0. The measure of another angle in the kite is 30\u00b0. Sketch a kite that matches this description.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46783\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7-Quadrilaterals-and-Other-Polygons-234.png\" alt=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons 234\" width=\"185\" height=\"182\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Quadrilaterals_and_Other_Polygons_Cummulative_Assessment\"><\/a>Quadrilaterals and Other Polygons Cummulative Assessment<\/h3>\n<p>Question 1.<br \/>\nCopy and complete the flowchart proof of the Parallelogram Opposite Angles Theorem (Thm. 7.4).<br \/>\nGiven ABCD is a parallelogram.<br \/>\nProve \u2220A \u2245 \u2220C, \u2220B \u2245 \u2220D<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46831\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-235.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 235\" width=\"176\" height=\"98\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46830\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-236.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 236\" width=\"657\" height=\"343\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-236.png 657w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-236-300x157.png 300w\" sizes=\"(max-width: 657px) 100vw, 657px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nUse the steps in the construction to explain how you know that the circle is inscribed within \u2206ABC.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46829\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-237.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 237\" width=\"516\" height=\"355\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-237.png 516w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-237-300x206.png 300w\" sizes=\"(max-width: 516px) 100vw, 516px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nYour friend claims that he can prove the Parallelogram Opposite Sides Theorem (Thm. 7.3) using the SSS Congruence Theorem (Thm. 5.8) and the Parallelogram Opposite Sides Theorem (Thin. 7.3). Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nFind the perimeter of polygon QRSTUV Is the polygon equilateral? equiangular? regular? Explain your reasoni ng.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46828\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-238.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 238\" width=\"175\" height=\"176\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-238.png 175w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-238-150x150.png 150w\" sizes=\"(max-width: 175px) 100vw, 175px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nChoose the correct symbols to complete the proof of the Converse of the Hinge Theorem (Theorem 6. 13).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46827\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-239.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 239\" width=\"286\" height=\"93\" \/><br \/>\nGiven <img loading=\"lazy\" class=\"alignnone size-full wp-image-46826\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-240.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 240\" width=\"209\" height=\"26\" \/><br \/>\nProve m \u2220 B &gt; m \u2220 E<br \/>\nStep 1 Assume temporarily that m \u2220 B <img loading=\"lazy\" class=\"alignnone size-full wp-image-46825\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-241.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 241\" width=\"18\" height=\"19\" \/> m \u2220 E. Then it follows that either m\u2220B____ m\u2220E or m\u2220B ______ m \u2220 E.<\/p>\n<p>Step 2 If m \u2220 B ______ m\u2220E. then AC _____ DF by the Hinge Theorem (Theorem 6. 12). If, m\u2220B _______ m \u2220 E. then \u2220B _____ \u2220E. So. \u2206ABC ______ \u2206DEF by the SAS Congruence Theorem (Theorem 5.5) and AC _______ DF.<\/p>\n<p>Step 3 Both conclusions contradict the given statement that AC _______ DF. So, the temporary assumption that m \u2220 B &gt; <img loading=\"lazy\" class=\"alignnone size-full wp-image-46825\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-241.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 241\" width=\"18\" height=\"19\" \/> m \u2220 E Cannot be true. This proves that m \u2220 B ______ m \u2220 E.<br \/>\n&gt;\u00a0 \u00a0 \u00a0&lt;\u00a0 \u00a0 =\u00a0 \u00a0 \u2260\u00a0 \u00a0 \u2245<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nUse the Isosceles Trapctoid Base Angles Conersc (Thm. 7.15) to prove that ABCD is an isosceles trapezoid.<br \/>\nGiven \\(\\overline{B C}\\) || \\(\\overline{A D}\\). \u2220EBC \u2245 \u2220\u00bfECB, \u2220ABE \u2245 \u2220DCE<br \/>\nProve ABCD is an isoscelcs trapezoid.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46824\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-242.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 242\" width=\"186\" height=\"102\" \/><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nOne part of the Rectangle Diagonals Theorem (Thm. 7.13) says. \u201cIf the diagonals of a parallelogram are congruent, then it is a rectangle.\u201d Using the reasons given. there are multiple ways to prove this part of the theorem. Provide a statement for each reason to form one possible proof of this part of the theorem.<br \/>\nGiven QRST is a parallelogram<br \/>\n\\(\\overline{Q S} \\cong \\overline{R T}\\)<br \/>\nProve QRST is a rectangle<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46823\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-7-Quadrilaterals-and-Other-Polygons-243.png\" alt=\"Big Ideas Math Answers Geometry Chapter 7 Quadrilaterals and Other Polygons 243\" width=\"227\" height=\"109\" \/><\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"246\">Statements<\/td>\n<td style=\"text-align: center;\" width=\"228\">Reasons<\/td>\n<\/tr>\n<tr>\n<td width=\"246\">1. \\(\\overline{Q S} \\cong \\overline{R T}\\)<\/td>\n<td width=\"228\">1. Given<\/td>\n<\/tr>\n<tr>\n<td width=\"246\">2. __________________________<\/td>\n<td width=\"228\">2. Parallelogram Opposite Sides Theorem (Thm. 7.3)<\/td>\n<\/tr>\n<tr>\n<td width=\"246\">3. __________________________<\/td>\n<td width=\"228\">3. SSS Congruence Theorem (Thm. 5.8)<\/td>\n<\/tr>\n<tr>\n<td width=\"246\">4. __________________________<\/td>\n<td width=\"228\">4. Corresponding parts of congruent triangles are congruent.<\/td>\n<\/tr>\n<tr>\n<td width=\"246\">5. __________________________<\/td>\n<td width=\"228\">5. Parallelogram Consecutive Angles Theorem (Thm. 7.5<\/td>\n<\/tr>\n<tr>\n<td width=\"246\">6. __________________________<\/td>\n<td width=\"228\">6. Congruent supplementary angles have the same measure.<\/td>\n<\/tr>\n<tr>\n<td width=\"246\">7. __________________________<\/td>\n<td width=\"228\">7. Parallelogram Consecutive Angles Theorem (Thm. 7.5)<\/td>\n<\/tr>\n<tr>\n<td width=\"246\">8. __________________________<\/td>\n<td width=\"228\">8. Subtraction Property of Equality<\/td>\n<\/tr>\n<tr>\n<td width=\"246\">9. __________________________<\/td>\n<td width=\"228\">9. Definition of a right angle<\/td>\n<\/tr>\n<tr>\n<td width=\"246\">10. __________________________<\/td>\n<td width=\"228\">10. Definition of a rectangle<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Answer:<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Polygons present here will help you get good ideas on the associated lessons in it easily. Utilize the quick resources available here for Big Ideas Math Geometry Ch 7 Solutions and attempt the final exam with confidence. Solving the BIM Book Geometry Ch 7 Quadrilaterals and &#8230; <a title=\"Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-geometry-answers-chapter-7\/\" aria-label=\"More on Big Ideas Math Geometry Answers Chapter 7 Quadrilaterals and Other Polygons\">Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":89493,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[4],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-7.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/44024"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=44024"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/44024\/revisions"}],"predecessor-version":[{"id":90286,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/44024\/revisions\/90286"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89493"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=44024"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=44024"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=44024"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}