{"id":39742,"date":"2022-04-07T10:02:27","date_gmt":"2022-04-07T04:32:27","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=39742"},"modified":"2022-04-07T11:11:26","modified_gmt":"2022-04-07T05:41:26","slug":"big-ideas-math-geometry-answers-chapter-5","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-geometry-answers-chapter-5\/","title":{"rendered":"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles"},"content":{"rendered":"<p>If you are looking across the web for better preparation resources regarding the Big Ideas Math Geometry Ch 5 Congruent Triangles then this is the one stop destination for all your needs. For better understanding of the concepts we have compiled all the <a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-geometry-answers\/\">Big Ideas Math Geometry Answers<\/a> Ch 5 Congruent Triangles in a simple and easy to understand language. Boost your math skills and have a deeper understanding of concepts taking help from the Congruent Triangles BIM Book Geometry Solution Key.<\/p>\n<h2>Big Ideas Math Book Geometry Answer Key Chapter 5 Congruent Triangles<\/h2>\n<p>Prepare using the Big Ideas Math Book Geometry chapter 5 Congruent Triangles Answer Key and get a good hold of the entire concepts. Clarify all your doubts taking help of the BIM Book Geometry Ch 5 Congruent Triangles Solutions provided. Simply tap on the BIM Geometry Chapter 5 Congruent Triangles Answers and prepare the corresponding topic in no time. Big Ideas Math Geometry Congruent Triangles Solution Key covers questions from Lessons 5.1 to 5.8, Practice Tests, Assessment Tests, Chapter Tests, etc. Attempt the exam with confidence and score better grades in exams.<\/p>\n<ul>\n<li><a href=\"#Congruent_Triangles_Maintaining_Mathematical_Proficiency\">Congruent Triangles Maintaining Mathematical Proficiency -Page 229<\/a><\/li>\n<li><a href=\"#Congruent_Triangles_Mathematical_Practices\">Congruent Triangles Mathematical Practices &#8211; Page 230<\/a><\/li>\n<li><a href=\"#5.1_Angles_of_Triangles\">5.1 Angles of Triangles &#8211; Page 231<\/a><\/li>\n<li><a href=\"#Lesson_5.1_Angles_of_Triangles\">Lesson 5.1 Angles of Triangles &#8211; Page(232-238)<\/a><\/li>\n<li><a href=\"#Exercise_5.1_Angles_of_Triangles\">Exercise 5.1 Angles of Triangles &#8211; Page(236-238)<\/a><\/li>\n<li><a href=\"#5.2_Congruent_Polygons\">5.2 Congruent Polygons &#8211; Page 239<\/a><\/li>\n<li><a href=\"#Lesson_5.2_Congruent_Polygons\">Lesson 5.2 Congruent Polygons &#8211; Page(240-244)<\/a><\/li>\n<li><a href=\"#Exercise_5.2_Congruent_Polygons\">Exercise 5.2 Congruent Polygons &#8211; Page(243-244)<\/a><\/li>\n<li><a href=\"#5.3_Proving_Triangle_Congruence_by_SAS\">5.3 Proving Triangle Congruence by SAS &#8211; Page 245<\/a><\/li>\n<li><a href=\"#Lesson_5.3_Proving_Triangle_Congruence_by_SAS\">Lesson 5.3 Proving Triangle Congruence by SAS &#8211; Page(246-250)<\/a><\/li>\n<li><a href=\"#Exercise_5.3_Proving_Triangle_Congruence_by_SAS\">Exercise 5.3 Proving Triangle Congruence by SAS &#8211; Page(249-250)<\/a><\/li>\n<li><a href=\"#5.4_Equilateral_and_Isosceles_Triangles\">5.4 Equilateral and Isosceles Triangles &#8211; Page 251<\/a><\/li>\n<li><a href=\"#Lesson_5.4_Equilateral_and_Isosceles_Triangles\">Lesson 5.4 Equilateral and Isosceles Triangles &#8211; Page(252-258)<\/a><\/li>\n<li><a href=\"#Exercise_5.4_Equilateral_and_Isosceles_Triangles\">Exercise 5.4 Equilateral and Isosceles Triangles &#8211; Page(256-258)<\/a><\/li>\n<li><a href=\"#5.1_to_5.4_Quiz\">5.1 to 5.4 Quiz &#8211; Page 260<\/a><\/li>\n<li><a href=\"#5.5_Proving_Triangle_Congruence_by_SSS\">5.5 Proving Triangle Congruence by SSS &#8211; Page 261<\/a><\/li>\n<li><a href=\"#Lesson_5.5_Proving_Triangle_Congruence_by_SSS\">Lesson 5.5 Proving Triangle Congruence by SSS &#8211; Page(262-268)<\/a><\/li>\n<li><a href=\"#Exercise_5.5_Proving_Triangle_Congruence_by_SSS\">Exercise 5.5 Proving Triangle Congruence by SSS &#8211; Page(266-268)<\/a><\/li>\n<li><a href=\"#5.6_Proving_Triangle_Congruence_by_ASA_and_AAS\">5.6 Proving Triangle Congruence by ASA and AAS &#8211; Page 269<\/a><\/li>\n<li><a href=\"#Lesson_5.6_Proving_Triangle_Congruence_by_ASA_and_AAS\">Lesson 5.6 Proving Triangle Congruence by ASA and AAS &#8211; Page(270-276)<\/a><\/li>\n<li><a href=\"#Lesson_5.6_Proving_Triangle_Congruence_by_ASA_and_AAS\">Lesson 5.6 Proving Triangle Congruence by ASA and AAS &#8211; Page(274-276)<\/a><\/li>\n<li><a href=\"#5.7_Using_Congruent_Triangles\">5.7 Using Congruent Triangles &#8211; Page 277<\/a><\/li>\n<li><a href=\"#Lesson_5.7_Using_Congruent_Triangles\">Lesson 5.7 Using Congruent Triangles &#8211; Page(278-282)<\/a><\/li>\n<li><a href=\"#Exercise_5.7_Using_Congruent_Triangles\">Exercise 5.7 Using Congruent Triangles &#8211; Page(281-282)<\/a><\/li>\n<li><a href=\"#5.8_Coordinate_Proofs\">5.8 Coordinate Proofs &#8211; Page 283<\/a><\/li>\n<li><a href=\"#Lesson_5.8_Coordinate_Proofs\">Lesson 5.8 Coordinate Proofs &#8211; Page(284-288)<\/a><\/li>\n<li><a href=\"#Exercise_5.8_Coordinate_Proofs\">Exercise 5.8 Coordinate Proofs &#8211; Page(287-288)<\/a><\/li>\n<li><a href=\"#Congruent_Triangles_Chapter_Review\">Congruent Triangles Chapter Review &#8211; Page(290-294)<\/a><\/li>\n<li><a href=\"#Congruent_Triangles_Test\">Congruent Triangles Test &#8211; Page 295<\/a><\/li>\n<li><a href=\"#Congruent_Triangles_Cumulative_Assessment\">Congruent Triangles Cumulative Assessment &#8211; Page(296-297)<\/a><\/li>\n<\/ul>\n<h3><a id=\"Congruent_Triangles_Maintaining_Mathematical_Proficiency\"><\/a>Congruent Triangles Maintaining Mathematical Proficiency<\/h3>\n<p>Find the coordinates of the midpoint M of the segment with the given endpoints. Then find the distance between the two points.<\/p>\n<p>Question 1.<br \/>\nP(- 4, 1) and Q(0, 7)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nP (-4, 1), Q (0, 7)<br \/>\nWe know that,<br \/>\nThe midpoint M of the segment with the 2 endpoints is:<br \/>\n( \\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\) )<br \/>\nLet the give points are:<br \/>\n(x1, y1) and (x2, y2)<br \/>\nSo,<br \/>\nBy comparing the given poits,<br \/>\nWe will get<br \/>\nx1 = -4, x2 = 0, y1 = 1, y2 = 7<br \/>\nHence,<br \/>\nThe midpoint M = ( \\(\\frac{-4 + 0}{2}\\), \\(\\frac{1 + 7}{2}\\) )<br \/>\n= ( \\(\\frac{-4}{2}\\), \\(\\frac{8}{2}\\) )<br \/>\n= (-2, 4)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the midpoint M of the segment with the given endpoints is: (-2, 4)<\/p>\n<p>Question 2.<br \/>\nG(3, 6) and H(9, &#8211; 2)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nG (3, 6), H (9, -2)<br \/>\nWe know that,<br \/>\nThe midpoint M of the segment with the 2 endpoints is:<br \/>\n( \\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\) )<br \/>\nLet the give points are:<br \/>\n(x1, y1) and (x2, y2)<br \/>\nSo,<br \/>\nBy comparing the given poits,<br \/>\nWe will get<br \/>\nx1 = 3, x2 = 9, y1 = 6, y2 = -2<br \/>\nHence,<br \/>\nThe midpoint M = ( \\(\\frac{3 + 9}{2}\\), \\(\\frac{6 &#8211; 2}{2}\\) )<br \/>\n= ( \\(\\frac{12}{2}\\), \\(\\frac{4}{2}\\) )<br \/>\n= (6, 2)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the midpoint M of the segment with the given endpoints is: (6, 2)<\/p>\n<p>Question 3.<br \/>\nU(- 1, &#8211; 2) and V(8, 0)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nU (-1, -2), V (8, 0)<br \/>\nWe know that,<br \/>\nThe midpoint M of the segment with the 2 endpoints is:<br \/>\n( \\(\\frac{x1 + x2}{2}\\), \\(\\frac{y1 + y2}{2}\\) )<br \/>\nLet the give points are:<br \/>\n(x1, y1) and (x2, y2)<br \/>\nSo,<br \/>\nBy comparing the given poits,<br \/>\nWe will get<br \/>\nx1 = -1, x2 = 8, y1 = -2, y2 = 0<br \/>\nHence,<br \/>\nThe midpoint M = ( \\(\\frac{-1 + 8}{2}\\), \\(\\frac{-2 + 0}{2}\\) )<br \/>\n= ( \\(\\frac{7}{2}\\), \\(\\frac{-2}{2}\\) )<br \/>\n= ( \\(\\frac{7}{2}\\), -1 )<br \/>\nHence, from the above,<br \/>\nWe can conclude that the midpoint M of the segment with the given endpoints is: ( \\(\\frac{7}{2}\\), -1 )<\/p>\n<p>Solve the equation.<\/p>\n<p>Question 4.<br \/>\n7x + 12 = 3x<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n7x + 12 = 3x<br \/>\nSo,<br \/>\n7x &#8211; 3x = 12<br \/>\n4x = 12<br \/>\nx = \\(\\frac{12}{4}\\)<br \/>\nx = 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 3<\/p>\n<p>Question 5.<br \/>\n14 &#8211; 6t = t<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n14 &#8211; 6t = t<br \/>\nSo,<br \/>\n14 = 6t + t<br \/>\n7t = 14<br \/>\nt = \\(\\frac{14}{7}\\)<br \/>\nt = 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of t is: 2<\/p>\n<p>Question 6.<br \/>\n5p + 10 = 8p + 1<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n5p + 10 = 8p + 1<br \/>\nSo,<br \/>\n5p &#8211; 8p = 1 &#8211; 10<br \/>\n-3p = -9<br \/>\n3p = 9<br \/>\np = \\(\\frac{9}{3}\\)<br \/>\np = 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of p is: 3<\/p>\n<p>Question 7.<br \/>\nw + 13 = 11w &#8211; 7<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\nw + 13 = 11w &#8211; 7<br \/>\nSo,<br \/>\nw &#8211; 11w = -7 &#8211; 13<br \/>\n-10w = -20<br \/>\n10w = 20<br \/>\nw = \\(\\frac{20}{10}\\)<br \/>\nw = 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of w is: 2<\/p>\n<p>Question 8.<br \/>\n4x + 1 = 3 &#8211; 2x<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n4x + 1 = 3 &#8211; 2x<br \/>\nSo,<br \/>\n4x + 2x = 3 &#8211; 1<br \/>\n6x = 2<br \/>\nx = \\(\\frac{2}{6}\\)<br \/>\nx = \\(\\frac{1}{3}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: \\(\\frac{1}{3}\\)<\/p>\n<p>Question 9.<br \/>\nz &#8211; 2 = 4 + 9z<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\nz &#8211; 2 = 4 + 9z<br \/>\nSo,<br \/>\nz &#8211; 9z = 4 + 2<br \/>\n-8z = 6<br \/>\nz = &#8211;\\(\\frac{6}{8}\\)<br \/>\nz = &#8211;\\(\\frac{3}{4}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of z is: &#8211;\\(\\frac{3}{4}\\)<\/p>\n<p>Question 10.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nIs it possible to find the length of a segment in a coordinate plane without using the Distance Formula? Explain your reasoning.<br \/>\nAnswer:<br \/>\nYes, it is possible to find the length of a segment in a coordinate plane without using the distance formula<br \/>\nSince the segment is a portion of a line, we can use the graph to calculate the distance of a segment even though it would not provide accurate results.<br \/>\nHence,<br \/>\nWe use the distance formula to find the length of a segment in a coordinate plane<\/p>\n<h3><a id=\"Congruent_Triangles_Mathematical_Practices\"><\/a>Congruent Triangles Mathematical Practices<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Classify each statement as a definition, a postulate, or a theorem. Explain your reasoning.<\/p>\n<p>Question 1.<br \/>\nIn a coordinate plane, two non-vertical lines are perpendicular if and only if the product of their slopes is &#8211; 1.<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nIn a coordinate plane, two non-vertical lines are perpendicular if and only if the product of their slopes is &#8211; 1.<br \/>\nWe know that,<br \/>\nAccording to the &#8220;parallel and perpendicular lines theorem&#8221;, two non-vertical lines are perpendicular if and only if the product of their slopes is -1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given statement is a Theorem<\/p>\n<p>Question 2.<br \/>\nIf two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nIf two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.<br \/>\nWe know that,<br \/>\nAccording to the &#8220;Linear pair perpendicular theorem&#8221;,<br \/>\nWhen two straight lines intersect at a point and form a linear pair of congruent angles, then the lines are perpendicular<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given statement is a Theorem<\/p>\n<p>Question 3.<br \/>\nIf two lines intersect to form a right angle. then the lines are perpendicular.<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nIf two lines intersect to form a right angle. then the lines are perpendicular.<br \/>\nWe know that,<br \/>\nAccording to the &#8220;Perpendicular lines theorem&#8221;,<br \/>\nWhen two lines intersect to form a right angle, the lines are perpendicular<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given statement is a Theorem<\/p>\n<p>Question 4.<br \/>\nThrough any two points, there exists exactly one line.<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nThrough any two points, there exists exactly one line<br \/>\nWe know that,<br \/>\nBetween two points, only one line can be drawn and we don&#8217;t need any proof to prove the above statement<br \/>\nWe know that,<br \/>\nThe statement that is true without proof to prove is called &#8220;Postulate&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given statement is a Postulate<\/p>\n<h3><a id=\"5.1_Angles_of_Triangles\"><\/a>5.1 Angles of Triangles<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Writing a Conjecture<\/p>\n<p>Work with a partner.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-39788\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 1\" width=\"424\" height=\"244\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-1.png 424w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-1-300x173.png 300w\" sizes=\"(max-width: 424px) 100vw, 424px\" \/><\/p>\n<p>a. Use dynamic geometry software to draw any triangle and label it \u2206ABC.<br \/>\nAnswer:<br \/>\nBy using the dynamic geometry software, the triangle drawn is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-66050\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5.png\" alt=\"\" width=\"398\" height=\"242\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5.png 398w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-300x182.png 300w\" sizes=\"(max-width: 398px) 100vw, 398px\" \/><\/p>\n<p>b. Find the measures of the interior angles of the triangle.<br \/>\nAnswer:<br \/>\nFrom part (a),<br \/>\nWe can observe that the vertices of the triangle are: A, B, and C<br \/>\nLet the interior angles of the vertices A, B, and C be \u03b1, \u03b2, and \u03b3 respectively<br \/>\nHence,<br \/>\nThe measures of the given triangle are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-66057\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-1.png\" alt=\"\" width=\"392\" height=\"304\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-1.png 392w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-1-300x233.png 300w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><br \/>\nHence, from the above,<br \/>\nThe measures of the interior angles are:<br \/>\n\u03b1 = 62.1\u00b0, \u03b2 = 64.1\u00b0, and \u03b3 = 53.8\u00b0<\/p>\n<p>c. Find the sum of the interior angle measures.<br \/>\nAnswer:<br \/>\nFrom part (b),<br \/>\nThe measures of the interior angles are:<br \/>\n\u03b1 = 62.1\u00b0, \u03b2 = 64.1\u00b0, and \u03b3 = 53.8\u00b0<br \/>\nHence,<br \/>\nThe sum of the interior angles = 62.1\u00b0 + 64.1\u00b0 + 53.1\u00b0 = 180\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the sum of the interior angle measures is: 180\u00b0<\/p>\n<p>d. Repeat parts (a)-(c) with several other triangles. Then write a conjecture about the sum of the measures of the interior angles of a triangle.<br \/>\nAnswer:<br \/>\nThe representation of the 3 different triangles and their internal angle measures is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-66059\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-2.png\" alt=\"\" width=\"904\" height=\"261\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-2.png 904w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-2-300x87.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-2-768x222.png 768w\" sizes=\"(max-width: 904px) 100vw, 904px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that the conjecture about the sum of the measures of the interior angles of a triangle is:<br \/>\nThe sum of the internal angle measures of a triangle is always: 180\u00b0<\/p>\n<p><strong>CONSTRUCTING VIABLE ARGUMENTS<\/strong><br \/>\nTo be proficient in math, you need to reason inductively about data and write conjectures.<br \/>\nAnswer:<br \/>\nInductive reasoning:<br \/>\nInductive reasoning is the process of arriving at a conclusion based on a set of observations.<br \/>\nInductive reasoning is used in geometry in a similar way.<br \/>\nConjecture:<br \/>\nA statement you believe to be true based on\u00a0inductive reasoning.<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Writing a Conjecture<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-39787\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-2.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 2\" width=\"315\" height=\"351\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-2.png 315w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-2-269x300.png 269w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><\/p>\n<p>Work With a partner.<\/p>\n<p>a. Use dynamic geometry software to draw any triangle and label it \u2206ABC.<br \/>\nAnswer:<br \/>\nThe triangle drawn by using the dynamic geometry software is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-66190\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-4.png\" alt=\"\" width=\"342\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-4.png 342w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-4-300x144.png 300w\" sizes=\"(max-width: 342px) 100vw, 342px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that the vertices of the triangle are: A, B, and C<\/p>\n<p>b. Draw an exterior angle at any vertex and find its measure.<br \/>\nAnswer:<br \/>\nFrom part (a),<br \/>\nThe vertices of the triangle are: A, B, and C<br \/>\nLet the external angle measures of the triangle are: \u03b1, \u03b2, and \u03b3<br \/>\nHence,<br \/>\nThe representation of the external angle measures of the triangle are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-66282\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-5.png\" alt=\"\" width=\"423\" height=\"230\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-5.png 423w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-5-300x163.png 300w\" sizes=\"(max-width: 423px) 100vw, 423px\" \/><br \/>\nHence,<br \/>\nFrom the above,<br \/>\nWe can conclude that<br \/>\nThe external angle measures of the triangle are:<br \/>\n\u03b1 = 310.7\u00b0, \u03b2 = 299.3\u00b0, and \u03b3 = 290\u00b0<\/p>\n<p>c. Find the measures of the two nonadjacent interior angles of the triangle.<br \/>\nAnswer:<br \/>\nFrom part (b),<br \/>\nThe external angle measures of the triangle are:<br \/>\n\u03b1 = 310.7\u00b0, \u03b2 = 299.3\u00b0, and \u03b3 = 290\u00b0<br \/>\nHence,<br \/>\nThe representation of the non-adjacent interior angles and the external angle measures of the triangle are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-66292\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-6.png\" alt=\"\" width=\"741\" height=\"258\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-6.png 741w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-6-300x104.png 300w\" sizes=\"(max-width: 741px) 100vw, 741px\" \/><br \/>\nHence, from the above,<br \/>\nThe angle measures of two non-adjacent sides are:<br \/>\n\u03b1 = 70\u00b0, \u03b2 = 60.7\u00b0, and \u03b3 = 49.3\u00b0<\/p>\n<p>d. Find the sum of the measures of the two nonadjacent interior angles. Compare this sum to the measure of the exterior angle.<br \/>\nAnswer:<br \/>\nFrom part (b),<br \/>\nThe external angle measures of the triangle are:<br \/>\n\u03b1 = 310.7\u00b0, \u03b2 = 299.3\u00b0, and \u03b3 = 290\u00b0<br \/>\nFrom part (c),<br \/>\nThe measures of the two non-adjacent interior angles are:<br \/>\n\u03b1 = 70\u00b0, \u03b2 = 60.7\u00b0, and \u03b3 = 49.3\u00b0<br \/>\nNow,<br \/>\nThe sum of the measures of the external angles of the triangle are:<br \/>\n\u03b1 + \u03b2 + \u03b3 = 310.7\u00b0 + 299.3\u00b0+ 290\u00b0<br \/>\n= 900.0\u00b0<br \/>\nThe sum of the measures of the two non-adjacent interior angles is:<br \/>\n\u03b1 + \u03b2 + \u03b3 = 70\u00b0 + 60.7\u00b0 + 49.3\u00b0<br \/>\n= 180.0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the sum of the measures of the external angles is 5 times the sum of the measures of the two non-adjacent interior angles<\/p>\n<p>e. Repeat parts (a)-(d) with several other triangles. Then write a conjecture that compares the measure of an exterior angle with the sum of the measures of the two nonadjacent interior angles.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-66347\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-7.png\" alt=\"\" width=\"743\" height=\"404\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-7.png 743w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-7-300x163.png 300w\" sizes=\"(max-width: 743px) 100vw, 743px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe external angle measure of a vertex for a given triangle = 360\u00b0 &#8211; (Internal angle measure of a vertex that we are finding the external angle measure)<br \/>\nThe sum of the internal angle measures of the triangle is: 180\u00b0<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 3.<br \/>\nHow are the angle measures of a triangle related?<br \/>\nAnswer:<br \/>\nThe angle measures of a triangle are related as shown below:<br \/>\nThe external angle measure of a vertex for a given triangle = 360\u00b0 &#8211; (Internal angle measure of a vertex that we are finding the external angle measure)<br \/>\nThe sum of the internal angle measures of the triangle is: 180\u00b0<\/p>\n<p>Question 4.<br \/>\nAn exterior angle of a triangle measures 32\u00b0 What do you know about the measures of the interior angles? Explain your reasoning.<br \/>\nAnswer:<br \/>\nIt is given that an exterior angle of a triangle measures 32\u00b0<br \/>\nWe know that,<br \/>\nThe external angle measure of a vertex for a given triangle = 360\u00b0 &#8211; (Internal angle measure of a vertex that we are finding the external angle measure)<br \/>\nSo,<br \/>\n32\u00b0 = 360\u00b0 &#8211; (The internal angle measure of 32\u00b0)<br \/>\nThe internal angle measure of 32\u00b0 = 360\u00b0 &#8211; 32\u00b0<br \/>\nThe interior angle measure of 32\u00b0 = 328\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the interior angle measure of a triangle for an external angle measure of 32\u00b0 is: 328\u00b0<\/p>\n<h3><a id=\"Lesson_5.1_Angles_of_Triangles\"><\/a>Lesson 5.1 Angles of Triangles<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nDraw an obtuse isosceles triangle and an acute scalene triangle.<br \/>\nAnswer:<br \/>\nThe figures of an obtuse isosceles triangle and an acute triangle are as follows:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-66472\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-8.png\" alt=\"\" width=\"723\" height=\"244\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-8.png 723w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-8-300x101.png 300w\" sizes=\"(max-width: 723px) 100vw, 723px\" \/><\/p>\n<p>Question 2.<br \/>\n\u2206ABC has vertices A(0, 0), B(3, 3), and C(- 3, 3), Classify the triangle by its sides. Then determine whether it is a right triangle.<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nA (0, 0), B (3, 3), and C (-3, 3)<br \/>\nand the triangle is \u0394ABC<br \/>\nWe know that,<br \/>\nTo find whether the given triangle is a right-angled triangle or not,<br \/>\nWe have to prove,<br \/>\nAC\u00b2 = AB\u00b2 + BC\u00b2<br \/>\nWhere,<br \/>\nAC is the distance between A and C points<br \/>\nAB is the distance between A and B points<br \/>\nBC is the distance between B and C points<br \/>\nWe know that,<br \/>\nThe distance between 2 points = \u221a(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2<br \/>\nNow,<br \/>\nLet the given points be considered as A(x1, y1), B(x2, y2), and C( x3, y3)<br \/>\nSo,<br \/>\nAB = \u221a(3 &#8211; 0)\u00b2 + (3 &#8211; 0)\u00b2 = \u221a3\u00b2 + 3\u00b2<br \/>\n= \u221a9 + 9 = \u221a18<br \/>\nBC = \u221a(-3 &#8211; 3)\u00b2 + (3 &#8211; 3)\u00b2<br \/>\n= \u221a(-6)\u00b2 + 0\u00b2<br \/>\n= \u221a6\u00b2 = 6<br \/>\nAC = \u221a(-3 &#8211; 0)\u00b2 + (3 &#8211; 0)\u00b2<br \/>\n= \u221a(-3)\u00b2 + 3\u00b2<br \/>\n= \u221a9 + 9 = \u221a18<br \/>\nNow,<br \/>\nAC\u00b2 = AB\u00b2<strong> + <\/strong>BC\u00b2<br \/>\n(\u221a18)\u00b2 = (\u221a18)\u00b2 + 6\u00b2<br \/>\n18 = 18 + 36<br \/>\n18 \u226054<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given triangle is not a right-angled triangle<\/p>\n<p>Question 3.<br \/>\nFind the measure of \u22201<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39786\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 3\" width=\"216\" height=\"83\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39786\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 3\" width=\"216\" height=\"83\" \/><br \/>\nWe know that,<br \/>\nThe measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles<br \/>\nFrom the given triangle,<br \/>\nThe exterior angle is: (5x &#8211; 10)\u00b0<br \/>\nThe interior angles are: 40\u00b0, 3x\u00b0, \u22201<br \/>\nSo,<br \/>\n(5x &#8211; 10)\u00b0 = 40\u00b0 + 3x\u00b0<br \/>\n5x\u00b0 &#8211; 3x\u00b0 = 40\u00b0 + 10\u00b0<br \/>\n2x\u00b0 = 50\u00b0<br \/>\nx = 50\u00b0 \u00f7 2<br \/>\nx = 25\u00b0<br \/>\nSo,<br \/>\nThe interior angles are 40\u00b0, 3 (25)\u00b0, \u22201<br \/>\n= 40\u00b0, 75\u00b0, \u22201<br \/>\nWe know that,<br \/>\nThe sum of the interior angles of a triangle is: 180\u00b0<br \/>\nSo,<br \/>\n40\u00b0 + 75\u00b0 + \u22201 = 180\u00b0<br \/>\n115\u00b0 + \u22201 = 180\u00b0<br \/>\n\u22201 = 180\u00b0 &#8211; 115\u00b0<br \/>\n\u22201 = 65\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of \u22201 is: 65\u00b0<\/p>\n<p>Question 4.<br \/>\nFind the measure of each acute angle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39789\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-36.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 36\" width=\"118\" height=\"89\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39789\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-36.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 36\" width=\"118\" height=\"89\" \/><br \/>\nWe know that,<br \/>\nThe sum of the interior angles in a triangle is: 180\u00b0<br \/>\nFrom the given figure,<br \/>\nThe interior angles of the right-angled triangle are: 90\u00b0, 2x\u00b0, and (x &#8211; 6)\u00b0<br \/>\nSo,<br \/>\n90\u00b0 + 2x\u00b0 + (x &#8211; 6)\u00b0 = 180\u00b0<br \/>\n84\u00b0+ 3x\u00b0 = 180\u00b0<br \/>\n3x\u00b0 = 180\u00b0 &#8211; 84\u00b0<br \/>\n3x\u00b0 = 96\u00b0<br \/>\nx = 96\u00b0 \u00f7 3\u00b0<br \/>\nx = 32\u00b0<br \/>\nSo,<br \/>\nThe measure of each acute angle is 90\u00b0, 2x\u00b0, (x &#8211; 6)\u00b0<br \/>\n= 90\u00b0, 2(32)\u00b0, (32 &#8211; 6)\u00b0<br \/>\n= 90\u00b0, 64\u00b0, 26\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that,<br \/>\nThe measure of each acute angle is 90\u00b0, 64\u00b0, and 26\u00b0<\/p>\n<h3><a id=\"Exercise_5.1_Angles_of_Triangles\"><\/a>Exercise 5.1 Angles of Triangles<\/h3>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nCan a right triangle also be obtuse? Explain our reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48711\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-1.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 1\" width=\"560\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-1.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-1-300x59.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nThe measure of an exterior angle of a triangle is equal to the sum of the measures of the two ____________ interior angles.<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nThe measure of an exterior angle of a triangle is equal to the sum of the measures of the two ____________ interior angles.<br \/>\nHence,<br \/>\nThe completed form of the given statement is:<br \/>\nThe measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p>In Exercises 3-6, classify the triangle by its sides and by measuring its angles.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39785\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-4.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 4\" width=\"121\" height=\"121\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48712\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-3.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 3\" width=\"522\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-3.png 522w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-3-300x34.png 300w\" sizes=\"(max-width: 522px) 100vw, 522px\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39784\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5\" width=\"127\" height=\"110\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39784\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5\" width=\"127\" height=\"110\" \/><br \/>\nWe know that,<br \/>\n&#8220;|&#8221; represents the &#8220;Congruent&#8221; or &#8220;Equal&#8221; in geometry<br \/>\nSo,<br \/>\nFrom the given figure,<br \/>\nWe can observe that all three sides of the given triangle are equal<br \/>\nWe know that,<br \/>\nIf a triangle has all the sides equal, then the triangle is called an &#8220;Equilateral triangle&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that the \u0394LMN is an &#8220;Equilateral triangle&#8221;<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39783\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-6.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 6\" width=\"147\" height=\"118\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48713\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-5.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 5\" width=\"533\" height=\"54\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-5.png 533w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-5-300x30.png 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39782\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-7.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 7\" width=\"137\" height=\"115\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39782\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-7.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 7\" width=\"137\" height=\"115\" \/><br \/>\nWe know that,<br \/>\nIf any side is not equal to each other in the triangle, then the triangle is called a &#8220;Scalene triangle&#8221;<br \/>\nThe angle greater than 90\u00b0 is called as &#8220;Obtuse angle&#8221;<br \/>\nAn angle less than 90\u00b0 is called an &#8220;Acute angle&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that \u0394ABC is an &#8220;Acute scalene triangle&#8221;<\/p>\n<p><strong>In Exercises 7-10, classify \u2206ABC by its sides. Then determine whether it is a right triangle.<\/strong><\/p>\n<p>Question 7.<br \/>\nA(2, 3), B(6, 3), (2, 7)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48714\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-7.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 7\" width=\"587\" height=\"491\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-7.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-7-300x251.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 8.<br \/>\nA(3, 3), B(6, 9), (6, &#8211; 3)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nA (3, 3), B(6, 9), and C (6, -3)<br \/>\nWe know that,<br \/>\nTo find whether the given triangle is a right angle or not,<br \/>\nWe have to prove,<br \/>\nAC\u00b2 = AB\u00b2 + BC\u00b2<br \/>\nWhere,<br \/>\nAC is the distance between points A and C<br \/>\nAB is the distance between points A and B<br \/>\nBC is the distance between points B and C<br \/>\nThe slope of any one side must be equal to -1<br \/>\nNow,<br \/>\nLet the given points be<br \/>\nA (x1, y1), B(x2, y2), and C (x3, y3)<br \/>\nSo,<br \/>\nA (x1, y1)= (3, 3), B (x2, y2) = (6, 9), and C (x3, y3) = (6, -3)<br \/>\nWe know that,<br \/>\nThe distance between 2 points = \u221a(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2<br \/>\nSo,<br \/>\nAB = \u221a(6 &#8211; 3)\u00b2 + (9 &#8211; 3)\u00b2<br \/>\n= \u221a3\u00b2 + 6\u00b2<br \/>\n= \u221a9 + 36 = \u221a45<br \/>\nBC = \u221a6 &#8211; 6)\u00b2 + (-3 &#8211; 9)\u00b2<br \/>\n= \u221a0 + 12\u00b2<br \/>\n= \u221a12\u00b2 = 12<br \/>\nAC = \u221a(6 &#8211; 3)\u00b2 + (-3 &#8211; 3)\u00b2<br \/>\n= \u221a(3)\u00b2 + (-6)\u00b2<br \/>\n= \u221a9 + 36 = \u221a45<br \/>\nSo,<br \/>\nFrom the length of the sides,<br \/>\nWe can say that the given triangle is an Isosceles triangle,<br \/>\nWe know that,<br \/>\nSlope (m) = \\(\\frac{y2 &#8211; y1} {x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\nSlope of AB = \\(\\frac{9 &#8211; 3} {6 &#8211; 3}\\)<br \/>\n= \\(\\frac{6} {3}\\)<br \/>\n= 2<br \/>\nSlope of BC = \\(\\frac{-9 &#8211; 3} {6 &#8211; 6}\\)<br \/>\n= \\(\\frac{-12} {0}\\)<br \/>\n= Undefined<br \/>\nSlope of AC = \\(\\frac{-3 &#8211; 3} {6 &#8211; 3}\\)<br \/>\n= \\(\\frac{-6} {3}\\)<br \/>\n= -2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given triangle is not a right triangle<\/p>\n<p>Question 9.<br \/>\nA(1, 9), B(4, 8), C(2, 5)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48715\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-9.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 9\" width=\"592\" height=\"539\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-9.png 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-9-300x273.png 300w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p>Question 10.<br \/>\nA(- 2, 3), B(0, &#8211; 3), C(3, &#8211; 2)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\nA (-2, 3), B(0, -3), and C (3, -2)<br \/>\nWe know that,<br \/>\nTo find whether the given triangle is a right angle or not,<br \/>\nWe have to prove,<br \/>\nAC\u00b2 = AB\u00b2 + BC\u00b2<br \/>\nWhere,<br \/>\nAC is the distance between points A and C<br \/>\nAB is the distance between points A and B<br \/>\nBC is the distance between points B and C<br \/>\nThe slope of any one side must be equal to -1<br \/>\nNow,<br \/>\nLet the given points be<br \/>\nA (x1, y1), B(x2, y2), and C (x3, y3)<br \/>\nSo,<br \/>\nA (x1, y1)= (-2, 3), B (x2, y2) = (0, -3), and C (x3, y3) = (3, -2)<br \/>\nWe know that,<br \/>\nThe distance between 2 points = \u221a(x2 &#8211; x1)\u00b2 + (y2 &#8211; y1)\u00b2<br \/>\nSo,<br \/>\nAB = \u221a(0 &#8211; [-2])\u00b2 + (3 &#8211; 3)\u00b2<br \/>\n= \u221a2\u00b2 + 0\u00b2<br \/>\n= \u221a4 + 0 = 2<br \/>\nBC = \u221a3 &#8211; 0)\u00b2 + (-2 -[-3] )\u00b2<br \/>\n= \u221a9 + 1\u00b2<br \/>\n= \u221a10<br \/>\nAC = \u221a(3 &#8211; [-2])\u00b2 + (-2 &#8211; 3)\u00b2<br \/>\n= \u221a(5)\u00b2 + (-5)\u00b2<br \/>\n= \u221a25 + 25 = \u221a50<br \/>\nNow,<br \/>\nAC\u00b2 = AB\u00b2 + BC\u00b2<br \/>\n50 = 10 + 4<br \/>\n50 \u2260 14<br \/>\nSo,<br \/>\nFrom the length of the sides,<br \/>\nWe can say that the given triangle is a scalene triangle since all the lengths of the sides are different<br \/>\nWe know that,<br \/>\nSlope (m) = \\(\\frac{y2 &#8211; y1} {x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\nSlope of AB = \\(\\frac{9 &#8211; 3} {6 &#8211; 3}\\)<br \/>\n= \\(\\frac{6} {3}\\)<br \/>\n= 2<br \/>\nSlope of BC = \\(\\frac{-9 &#8211; 3} {6 &#8211; 6}\\)<br \/>\n= \\(\\frac{-12} {0}\\)<br \/>\n= Undefined<br \/>\nSlope of AC = \\(\\frac{-3 &#8211; 3} {6 &#8211; 3}\\)<br \/>\n= \\(\\frac{-6} {3}\\)<br \/>\n= -2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given triangle is not a right triangle<\/p>\n<p><strong>In Exercises 11 &#8211; 14. find m\u22201. Then classify the triangle by its angles<\/strong><\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39781\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-8.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 8\" width=\"152\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-8.png 152w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-8-150x90.png 150w\" sizes=\"(max-width: 152px) 100vw, 152px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48716\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-11.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 11\" width=\"321\" height=\"140\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-11.png 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-11-300x131.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39780\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-9.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 9\" width=\"156\" height=\"96\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39780\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-9.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 9\" width=\"156\" height=\"96\" \/><br \/>\nWe know that,<br \/>\nThe sum of interior angles in a triangle is: 180\u00b0<br \/>\nSo,<br \/>\nFrom the above,<br \/>\nThe interior angles of the given triangle are: 40\u00b0,\u00a0 30\u00b0,\u00a0 \u22201<br \/>\nNow,<br \/>\n40\u00b0 + 30\u00b0 + \u22201 = 180\u00b0<br \/>\n70 + \u22201 = 180\u00b0<br \/>\n\u22201 = 180\u00b0 &#8211; 70\u00b0<br \/>\n\u22201 = 110\u00b0<br \/>\nWe know that,<br \/>\nThe angle greater than 90\u00b0 is called an &#8220;Obtuse angle&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given triangle is an &#8220;Obtuse angled triangle&#8221;<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39779\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-10.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 10\" width=\"72\" height=\"88\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48717\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-13.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 13\" width=\"310\" height=\"140\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-13.png 310w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-13-300x135.png 300w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39778\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-11.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 11\" width=\"78\" height=\"88\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39778\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-11.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 11\" width=\"78\" height=\"88\" \/><br \/>\nWe know that,<br \/>\nThe sum of interior angles in a triangle is: 180\u00b0<br \/>\nSo,<br \/>\nFrom the above,<br \/>\nThe interior angles of the given triangle are: 60\u00b0,\u00a0 60\u00b0,\u00a0 \u22201<br \/>\nNow,<br \/>\n60\u00b0 + 60\u00b0 + \u22201 = 180\u00b0<br \/>\n120 + \u22201 = 180\u00b0<br \/>\n\u22201 = 180\u00b0 &#8211; 120\u00b0<br \/>\n\u22201 = 60\u00b0<br \/>\nWe know that,<br \/>\nAn angle less than 90\u00b0 is called an &#8220;Acute angle&#8221;<br \/>\nThe triangle that all the angles 60\u00b0 is called an &#8220;Equilateral triangle&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given triangle is an &#8220;Equilateral triangle&#8221;<\/p>\n<p>In Exercises 15-18, find the measure of the exterior angle.<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39777\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-12.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 12\" width=\"156\" height=\"83\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48718\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-15.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 15\" width=\"287\" height=\"30\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39776\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-13.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 13\" width=\"152\" height=\"121\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39776\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-13.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 13\" width=\"152\" height=\"121\" \/><br \/>\nWe know that,<br \/>\nAn exterior angle is equal to the sum of the two non-adjacent interior angles in a triangle<br \/>\nSo,<br \/>\n(2x &#8211; 2)\u00b0 = x\u00b0 + 45\u00b0<br \/>\n2x\u00b0 &#8211; x\u00b0 = 45\u00b0 + 2\u00b0<br \/>\nx = 47\u00b0<br \/>\nHence,<br \/>\nThe measure of the exterior angle is: (2x &#8211; 2)\u00b0<br \/>\n= (2 (47) &#8211; 2)\u00b0<br \/>\n= (94 &#8211; 2)\u00b0<br \/>\n= 92\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the measure of the exterior angle is: 92\u00b0<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39775\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-14.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 14\" width=\"196\" height=\"109\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48719\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-17.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 17\" width=\"403\" height=\"263\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-17.png 403w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-17-300x196.png 300w\" sizes=\"(max-width: 403px) 100vw, 403px\" \/><\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39774\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-15.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 15\" width=\"229\" height=\"139\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39774\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-15.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 15\" width=\"229\" height=\"139\" \/><br \/>\nWe know that,<br \/>\nAn exterior angle is equal to the sum of the two non-adjacent interior angles in a triangle<br \/>\nSo,<br \/>\n(7x &#8211; 16)\u00b0 = (x + 8)\u00b0 + 4x\u00b0<br \/>\n7x\u00b0 &#8211; 5x\u00b0 = 16\u00b0 + 8\u00b0<br \/>\n2x = 24\u00b0<br \/>\nx = 24\u00b0 \u00f7 2<br \/>\nx = 12\u00b0<br \/>\nHence,<br \/>\nThe measure of the exterior angle is: (7x &#8211; 16)\u00b0<br \/>\n= (7 (12) &#8211; 16)\u00b0<br \/>\n= (84 &#8211; 16)\u00b0<br \/>\n= 68\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the measure of the exterior angle is: 68\u00b0<\/p>\n<p>In Exercises 19-22, find the measure of each acute angle.<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39773\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-16.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 16\" width=\"136\" height=\"101\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48720\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-19.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 19\" width=\"419\" height=\"225\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-19.png 419w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-19-300x161.png 300w\" sizes=\"(max-width: 419px) 100vw, 419px\" \/><\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39772\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-17.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 17\" width=\"168\" height=\"78\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39772\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-17.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 17\" width=\"168\" height=\"78\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that one angle is 90\u00b0 and the 2 sides are perpendicular<br \/>\nSo,<br \/>\nWe can say that the given triangle is a right-angled triangle<br \/>\nWe know that,<br \/>\nThe sum of interior angles of a triangle is: 180\u00b0<br \/>\nSo,<br \/>\nx\u00b0 + (3x + 2)\u00b0 + 90\u00b0 = 180\u00b0<br \/>\n4x\u00b0 + 2\u00b0 + 90\u00b0 = 180\u00b0<br \/>\n4x\u00b0 = 180\u00b0 &#8211; 90\u00b0 &#8211; 2\u00b0<br \/>\n4x\u00b0 = 88\u00b0<br \/>\nx = 88\u00b0 \u00f7 4\u00b0<br \/>\nx = 22\u00b0<br \/>\nSo,<br \/>\nThe 2 acute angle measures are: x\u00b0 and (3x + 2)\u00b0<br \/>\n= 22\u00b0 and (3(22) + 2)\u00b0<br \/>\n= 22\u00b0 and (66 + 2)\u00b0<br \/>\n= 22\u00b0 and 68\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the 2 acute angle measures are: 22\u00b0 and 68\u00b0<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39771\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-18.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 18\" width=\"127\" height=\"131\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48721\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-21.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 21\" width=\"419\" height=\"252\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-21.png 419w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-21-300x180.png 300w\" sizes=\"(max-width: 419px) 100vw, 419px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39770\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-19.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 19\" width=\"136\" height=\"134\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39770\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-19.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 19\" width=\"136\" height=\"134\" \/><br \/>\nFrom the given figure,<br \/>\nWe can observe that one angle is 90\u00b0 and the 2 sides are perpendicular<br \/>\nSo,<br \/>\nWe can say that the given triangle is a right-angled triangle<br \/>\nWe know that,<br \/>\nThe sum of interior angles of a triangle is: 180\u00b0<br \/>\nSo,<br \/>\n(19x &#8211; 1)\u00b0 + (13x &#8211; 5)\u00b0 + 90\u00b0 = 180\u00b0<br \/>\n32x\u00b0 &#8211; 6\u00b0 + 90\u00b0 = 180\u00b0<br \/>\n32x\u00b0 = 180\u00b0 &#8211; 90\u00b0 &#8211; 6\u00b0<br \/>\n4x\u00b0 = 84\u00b0<br \/>\nx = 84\u00b0 \u00f7 4\u00b0<br \/>\nx = 21\u00b0<br \/>\nSo,<br \/>\nThe 2 acute angle measures are: (19x &#8211; 1)\u00b0 and (13x &#8211; 5)\u00b0<br \/>\n= (19 (21) &#8211; 1)\u00b0 and (13(21) &#8211; 5)\u00b0<br \/>\n= 398\u00b0 and (273 &#8211; 5)\u00b0<br \/>\n= 398\u00b0 and 268\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the 2 acute angle measures are: 398\u00b0 and 268\u00b0<\/p>\n<p>In Exercises 23-26. find the measure of each acute angle in the right triangle.<\/p>\n<p>Question 23.<br \/>\nThe measure of one acute angle is 5 times the measure of the other acute angle.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48722\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-23.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 23\" width=\"428\" height=\"187\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-23.png 428w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-23-300x131.png 300w\" sizes=\"(max-width: 428px) 100vw, 428px\" \/><\/p>\n<p>Question 24.<br \/>\nThe measure of one acute angle is times the measure of the other acute angle.<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\nThe measure of one acute angle is 3 times the sum of the measure of the other acute angle and 8.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48723\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-25.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 25\" width=\"465\" height=\"223\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-25.png 465w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-25-300x144.png 300w\" sizes=\"(max-width: 465px) 100vw, 465px\" \/><\/p>\n<p>Question 26.<br \/>\nThe measure of one acute angle is twice the difference of the measure of the other acute angle and 12.<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nThe measure of one acute angle is twice the difference of the measure of the other acute angle and 12.<br \/>\nSo,<br \/>\nx\u00b0 + [2 (x &#8211; 12)]\u00b0 = 90\u00b0<br \/>\nx\u00b0 + 2x\u00b0 &#8211; 2(12)\u00b0 = 90\u00b0<br \/>\n3x\u00b0 &#8211; 24\u00b0 = 90\u00b0<br \/>\n3x\u00b0 = 90\u00b0 + 24\u00b0<br \/>\n3x\u00b0 = 114\u00b0<br \/>\nx = 114\u00b0 \u00f7 3<br \/>\nx = 38\u00b0<br \/>\nSo,<br \/>\nThe 2 acute angle measures are: x\u00b0, 2 (x &#8211; 12)\u00b0<br \/>\n= 38\u00b0, 2 (38 &#8211; 12)\u00b0<br \/>\n= 38\u00b0, 2(26)\u00b0<br \/>\n= 38\u00b0 , 52\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the acute angle measures are: 38\u00b0, 52\u00b0<\/p>\n<p><strong>ERROR ANALYSIS<\/strong><br \/>\nIn Exercises 27 and 28, describe and correct the error in finding m\u22201.<\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39769\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-20.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 20\" width=\"332\" height=\"129\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-20.png 332w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-20-300x117.png 300w\" sizes=\"(max-width: 332px) 100vw, 332px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48724\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-27.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 27\" width=\"590\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-27.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-27-300x90.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39768\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-21.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 21\" width=\"299\" height=\"168\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe exterior angle of a triangle is equal to the sum of the non-adjacent interior angles of a triangle<br \/>\nSo,<br \/>\nFrom the figure,<br \/>\nThe external angle is: \u22201<br \/>\nThe interior angles are 80\u00b0, 50\u00b0<br \/>\nSo,<br \/>\n\u22201 = 80\u00b0 + 50\u00b0<br \/>\n\u22201 = 130\u00b0<br \/>\nNow,<br \/>\nThe interior angle measure of \u22201= 180\u00b0 &#8211; (External angle measure of 130\u00b0)<br \/>\n= 180\u00b0 &#8211; 130\u00b0<br \/>\n= 50\u00b0<br \/>\nHence, from the above,<br \/>\nThe internal angle measure of \u22201 is: 50\u00b0<\/p>\n<p>In Exercises 29-36, find the measure of the numbered angle.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-39767\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-22.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 22\" width=\"268\" height=\"155\" \/><\/p>\n<p>Question 29.<br \/>\n\u22201<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48725\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-29.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 29\" width=\"265\" height=\"31\" \/><\/p>\n<p>Question 30.<br \/>\n\u22202<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe external angle measure is equal to the sum of the non-adjacent interior angles<br \/>\nSo,<br \/>\n\u22202 = 90\u00b0 + 40\u00b0<br \/>\n\u22202 = 130\u00b0<\/p>\n<p>Question 31.<br \/>\n\u22203<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48726\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-31.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 31\" width=\"244\" height=\"24\" \/><\/p>\n<p>Question 32.<br \/>\n\u22203<br \/>\nAnswer:<br \/>\nFrom the above figure,<br \/>\n\u22202 = \u22204<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u22202 = \u22204 = 130\u00b0<\/p>\n<p>Question 33.<br \/>\n\u22205<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48727\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-33.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 33\" width=\"274\" height=\"31\" \/><\/p>\n<p>Question 34.<br \/>\n\u22206<br \/>\nAnswer:<br \/>\nThe external angle measure is equal to the sum of the non-adjacent interior angles<br \/>\nSo,<br \/>\n\u22206 = 90\u00b0 + \u22203<br \/>\n\u22206 = 90\u00b0 + 50\u00b0<br \/>\n\u22206 = 140\u00b0<\/p>\n<p>Question 35.<br \/>\n\u22207<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48728\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-35.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 35\" width=\"152\" height=\"31\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-35.png 152w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-35-150x31.png 150w\" sizes=\"(max-width: 152px) 100vw, 152px\" \/><\/p>\n<p>Question 36.<br \/>\n\u22208<br \/>\nAnswer:<br \/>\nThe external angle measure is equal to the sum of the non-adjacent interior angles<br \/>\nSo,<br \/>\n\u22208 = 90\u00b0 + \u22201<br \/>\n\u22206 = 90\u00b0 + 50\u00b0<br \/>\n\u22206 = 140\u00b0<\/p>\n<p>Question 37.<br \/>\n<strong>USING TOOLS<\/strong><br \/>\nThree people are standing on a stage. The distances between the three people are shown in the diagram. Classify the triangle by its sides and by measuring its angles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39766\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-23.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 23\" width=\"208\" height=\"121\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48729\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-37.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 37\" width=\"574\" height=\"142\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-37.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-37-300x74.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>USING STRUCTURE<\/strong><br \/>\nWhich of the following sets of angle measures could form a triangle? Select all that apply.<br \/>\n(A) 100\u00b0, 50\u00b0, 40\u00b0<br \/>\nAnswer:<br \/>\nThe given angles are: 100\u00b0, 50\u00b0, 40\u00b0<br \/>\nWe know that,<br \/>\nThe sum of the angles of a triangle should be equal to 180\u00b0<br \/>\nSo,<br \/>\nThe sum of the given angles = 100\u00b0 + 50\u00b0 + 40\u00b0<br \/>\n= 100\u00b0 + 90\u00b0<br \/>\n= 190\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given angles do not form a triangle<\/p>\n<p>(B) 96\u00b0, 74\u00b0, 10\u00b0<br \/>\nAnswer:<br \/>\nThe given angles are: 96\u00b0, 74\u00b0, 10\u00b0<br \/>\nWe know that,<br \/>\nThe sum of the angles of a triangle should be equal to 180\u00b0<br \/>\nSo,<br \/>\nThe sum of the given angles = 96\u00b0 + 74\u00b0 + 10\u00b0<br \/>\n= 96\u00b0 + 84\u00b0<br \/>\n= 180\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given angles forms a triangle<\/p>\n<p>(C) 165\u00b0, 113\u00b0, 82\u00b0<br \/>\nAnswer:<br \/>\nThe given angles are: 165\u00b0, 113\u00b0, 82\u00b0<br \/>\nWe know that,<br \/>\nThe sum of the angles of a triangle should be equal to 180\u00b0<br \/>\nSo,<br \/>\nThe sum of the given angles = 165\u00b0 + 113\u00b0 + 82\u00b0<br \/>\n= 165\u00b0 + 195\u00b0<br \/>\n= 360\u00b0<br \/>\nBut,<br \/>\nWe know that,<br \/>\nThe sum of exterior angles of a triangle is: 360\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given angles forms a triangle<\/p>\n<p>(D) 101\u00b0, 41\u00b0, 38\u00b0<br \/>\nAnswer:<br \/>\nThe given angles are: 101\u00b0, 41\u00b0, 38\u00b0<br \/>\nWe know that,<br \/>\nThe sum of the angles of a triangle should be equal to 180\u00b0<br \/>\nSo,<br \/>\nThe sum of the given angles = 101\u00b0 + 38\u00b0 + 41\u00b0<br \/>\n= 101\u00b0 + 79\u00b0<br \/>\n= 180\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given angles forms a triangle<\/p>\n<p>(E) 90\u00b0, 45\u00b0, 45\u00b0<br \/>\nAnswer:<br \/>\nThe given angles are: 90\u00b0, 45\u00b0, 45\u00b0<br \/>\nWe know that,<br \/>\nThe sum of the angles of a triangle should be equal to 180\u00b0<br \/>\nSo,<br \/>\nThe sum of the given angles = 90\u00b0 + 45\u00b0 + 45\u00b0<br \/>\n= 90\u00b0 + 90\u00b0<br \/>\n= 180\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given angles forms a triangle<\/p>\n<p>(F) 84\u00b0, 62\u00b0, 34\u00b0<br \/>\nAnswer:<br \/>\nThe given angles are: 84\u00b0, 62\u00b0, 34\u00b0<br \/>\nWe know that,<br \/>\nThe sum of the angles of a triangle should be equal to 180\u00b0<br \/>\nSo,<br \/>\nThe sum of the given angles = 84\u00b0 + 62\u00b0 + 34\u00b0<br \/>\n= 84\u00b0 + 96\u00b0<br \/>\n= 180\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given angles forms a triangle<\/p>\n<p>Question 39.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou are bending a strip of metal into an isosceles triangle for a sculpture. The strip of metal is 20 inches long. The first bend is made 6 inches from one end. Describe two ways you could complete the triangle.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48730\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-39.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 39\" width=\"588\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-39.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-39-300x113.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nFind and draw an object (or part of an object) that can be modeled by a triangle and an exterior angle. Describe the relationship between the interior angles of the triangle and the exterior angle in terms of the object.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-67115\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-9.png\" alt=\"\" width=\"417\" height=\"185\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-9.png 417w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-9-300x133.png 300w\" sizes=\"(max-width: 417px) 100vw, 417px\" \/><br \/>\nFrom the above figure,<br \/>\nWe can say that<br \/>\nThe sum of the interior angles of a given triangle is: 180\u00b0<br \/>\nThe sum of the exterior angles of a given triangle is: 360\u00b0<br \/>\nThe relation between the interior angles and the exterior angles is:<br \/>\nThe exterior angle measure = Sum of the two non-adjacent interior angles<\/p>\n<p>Question 41.<br \/>\n<strong>PROVING A COROLLARY<\/strong><br \/>\nProve the Corollary to the Triangle Sum Theorem (Corollary 5. 1).<br \/>\nGiven \u2206ABC is a right triangle<br \/>\nProve \u2220A and \u2220B are complementary<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39765\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-24.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 24\" width=\"162\" height=\"123\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48731\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-41.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 41\" width=\"557\" height=\"710\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-41.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-41-235x300.png 235w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nProve the Exterior Angle Theorem (Theorem 5.2).<br \/>\nGiven \u2206ABC, exterior \u2220ACD<br \/>\nProve m\u2220A + m\u2220B = m\u2220ACD<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-67122\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5.jpg\" alt=\"\" width=\"222\" height=\"90\" \/><br \/>\nAnswer:<br \/>\nIt is given that<br \/>\nIn \u0394ABC, the exterior angle is \u2220ACD<br \/>\nWe have to prove that<br \/>\nm\u2220A + m\u2220B = m\u2220ACD<br \/>\nProof:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-67117\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-10.png\" alt=\"\" width=\"645\" height=\"306\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-10.png 645w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-10-300x142.png 300w\" sizes=\"(max-width: 645px) 100vw, 645px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nm\u2220A + m\u2220B = m\u2220ACD is proven<\/p>\n<p>Question 43.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nIs it possible to draw an obtuse isosceles triangle? obtuse equilateral triangle? If so, provide examples. If not, explain why it is not possible.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48732\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-43.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 43\" width=\"546\" height=\"212\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-43.png 546w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-43-300x116.png 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nIs it possible to draw a right isosceles triangle? right equilateral triangle? If so, provide an example. If not, explain why it is not possible.<br \/>\nAnswer:<br \/>\nIt is possible to draw a right isosceles triangle but it is not possible to draw a right equilateral triangle<br \/>\nWe know that,<br \/>\nIn a triangle, if the length of the 2 sides are equal and one angle is a right-angle, then, it is called an &#8220;Right Isosceles triangle&#8221;<br \/>\nIn a triangle, if the length of all the sides are equal and each angle is 60\u00b0, then it is an &#8220;Equilateral triangle&#8221;<br \/>\nHence,<br \/>\nFrom the above definitions,<br \/>\nWe can observe that it is possible to draw right isosceles triangle but it is not possible to dran a right equilateral triangle<\/p>\n<p>Question 45.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\n\u2206ABC is isosceles.<br \/>\nAB = x, and BC = 2x &#8211; 4.<br \/>\na. Find two possible values for x when the perimeter of \u2206ABC is 32.<br \/>\nb. How many possible values are there for x when the perimeter of \u2206ABC is 12?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48733\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-45.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 45\" width=\"378\" height=\"752\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-45.png 378w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-45-151x300.png 151w\" sizes=\"(max-width: 378px) 100vw, 378px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nClassify the triangles, in as many ways as possible. without finding any measurements.<br \/>\na. <img loading=\"lazy\" class=\"alignnone size-full wp-image-39763\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-26.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 26\" width=\"103\" height=\"93\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39763\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-26.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 26\" width=\"103\" height=\"93\" \/><br \/>\nFrom the figure,<br \/>\nWe can observe that all the length of the sides of the triangle are equal<br \/>\nWe know that,<br \/>\nThe triangle that has the length of all the sides equal is called an &#8220;Equilateral triangle&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given triangle is an &#8220;Equilateral triangle&#8221;<\/p>\n<p>b. <img loading=\"lazy\" class=\"alignnone size-full wp-image-39762\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-27.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 27\" width=\"67\" height=\"114\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39762\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-27.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 27\" width=\"67\" height=\"114\" \/><br \/>\nFrom the figure,<br \/>\nWe can observe that the lengths of all the 3 sides are different<br \/>\nWe know that,<br \/>\nThe triangle that has all the different side lengths is called a &#8220;Scalene triangle&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given triangle is called a &#8220;Scalene triangle&#8221;<\/p>\n<p>c. <img loading=\"lazy\" class=\"alignnone size-full wp-image-39761\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-28.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 28\" width=\"145\" height=\"84\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39761\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-28.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 28\" width=\"145\" height=\"84\" \/><br \/>\nFrom the figure,<br \/>\nWe can observe that the length of all the 3 sides are different and 1 angle is obtuse i.e., greater than 90\u00b0<br \/>\nWe know that,<br \/>\nThe triangle that has any angle obtuse is called an &#8220;Obtuse angled triangle&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given triangle is an &#8220;Obtuse angled scalene triangle&#8221;<\/p>\n<p>d. <img loading=\"lazy\" class=\"alignnone size-full wp-image-39760\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-29.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 29\" width=\"53\" height=\"78\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39760\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-29.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 29\" width=\"53\" height=\"78\" \/><br \/>\nFrom the figure,<br \/>\nWe can observe that 1 angle is 90\u00b0 and the 2 sides are perpendicular to each other<br \/>\nWe know that,<br \/>\nThe triangle that has an angle of 90\u00b0 and the slope -1 is called a &#8220;Right-angled triangle&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given triangle is called a &#8220;Right-angled triangle&#8221;<\/p>\n<p>Question 47.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nWhich of the following could represent the measures of an exterior angle and two interior angles of a triangle? Select all that apply.<br \/>\nA) 100\u00b0, 62\u00b0, 38\u00b0<br \/>\n(B) 81\u00b0, 57\u00b0, 24\u00b0<br \/>\n(C) 119\u00b0, 68\u00b0, 49\u00b0<br \/>\n(D) 95\u00b0, 85\u00b0, 28\u00b0<br \/>\n(E) 92\u00b0, 78\u00b0, 68\u00b0<br \/>\n(F) 149\u00b0, 101\u00b0, 48\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48734\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-47.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 47\" width=\"565\" height=\"196\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-47.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-47-300x104.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims the measure of an exterior angle will always be greater than the sum of the nonadjacent interior angle measures. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\nNo, your friend is not correct<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nAccording to the exterior angle theorem,<br \/>\nThe external angle measure is always equal to the sum of the non-adjacent internal angle measures<br \/>\nBut,<br \/>\nAccording to your friend,<br \/>\nThe external angle measure will always be greater than the sum of the non-adjacent interior angle measures<br \/>\nHence, from the above,<br \/>\nWe can conclude that your friend is not correct<\/p>\n<p><strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nIn Exercises 49-52, find the values of x and y.<\/p>\n<p>Question 49.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39759\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-30.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 30\" width=\"158\" height=\"100\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48735\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-49.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 49\" width=\"537\" height=\"200\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-49.png 537w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-49-300x112.png 300w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><\/p>\n<p>Question 50.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39758\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-31.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 31\" width=\"153\" height=\"109\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39758\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-31.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 31\" width=\"153\" height=\"109\" \/><br \/>\nFrom the figure,<br \/>\nWe have to obtain the values of x and y<br \/>\nNow,<br \/>\nBy using the alternate angles theorem,<br \/>\nx = 118\u00b0<br \/>\nNow,<br \/>\nBy using the exterior angle theorem,<br \/>\nx = y + 22\u00b0<br \/>\ny = x &#8211; 22\u00b0<br \/>\ny = 118\u00b0 &#8211; 22\u00b0<br \/>\ny = 96\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the values of x and y are: 118\u00b0 and 96\u00b0 respectively<\/p>\n<p>Question 51.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39757\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-32.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 32\" width=\"135\" height=\"138\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48736\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-51.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 51\" width=\"570\" height=\"261\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-51.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-51-300x137.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 52.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39756\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-33.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 33\" width=\"166\" height=\"76\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39756\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-33.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 33\" width=\"166\" height=\"76\" \/><br \/>\nFrom the above figure,<br \/>\nWe have to find the values of x and y<br \/>\nNow,<br \/>\nBy using the sum of interior angle measures,<br \/>\nx\u00b0 + 64\u00b0 + 90\u00b0 = 180\u00b0<br \/>\nx\u00b0 + 154\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 154\u00b0<br \/>\nx\u00b0 = 26\u00b0<br \/>\nNow,<br \/>\nBy using the exterior angle theorem,<br \/>\ny\u00b0 = x\u00b0 + 64\u00b0<br \/>\ny\u00b0 = 26\u00b0 + 64\u00b0<br \/>\ny\u00b0 = 90\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the values of x and y are: 26\u00b0 and 90\u00b0 respectively<\/p>\n<p>Question 53.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nUse the diagram to write a proof of the Triangle Sum Theorem (Theorem 5. 1). Your proof should be different from the proof of the Triangle Sum Theorem shown in this lesson.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39755\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-34.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 34\" width=\"337\" height=\"130\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-34.png 337w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-34-300x116.png 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48737\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-53.1.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 53.1\" width=\"587\" height=\"638\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-53.1.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-53.1-276x300.png 276w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48738\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-53.2.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 53.2\" width=\"605\" height=\"294\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-53.2.png 605w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-53.2-300x146.png 300w\" sizes=\"(max-width: 605px) 100vw, 605px\" \/><\/p>\n<p>Maintaining Mathematical Proficiency<\/p>\n<p>Use the diagram to find the measure of the segment or angle.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-39754\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-35.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 35\" width=\"338\" height=\"139\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-35.png 338w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-35-300x123.png 300w\" sizes=\"(max-width: 338px) 100vw, 338px\" \/><\/p>\n<p>Question 54.<br \/>\nm\u2220KHL<br \/>\nAnswer:<br \/>\nFrom the given figures,<br \/>\nWe can observe that<br \/>\n\u2220ABC = \u2220GHK<br \/>\n\u2220KHL = \u2220GHK \/ 2<br \/>\nSo,<br \/>\n(6x + 2)\u00b0 = (3x + 1)\u00b0 + (5x &#8211; 27)\u00b0<br \/>\n6x &#8211; 3x &#8211; 5x = 1 &#8211; 27 &#8211; 2<br \/>\n6x &#8211; 8x = -27 &#8211; 1<br \/>\n-2x = -28<br \/>\n2x = 28<br \/>\nx = 28 \u00f7 2<br \/>\nx = 14<br \/>\nSo,<br \/>\n\u2220KHL = \u2220GHK \/ 2<br \/>\n= [(3 (14) + 1)\u00b0 + (5 (14) &#8211; 27)\u00b0] \/ 2<br \/>\n= [43\u00b0 + 43\u00b0] \/ 2<br \/>\n= 86\u00b0 \/ 2<br \/>\n= 43\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\u2220KHL = 43\u00b0<\/p>\n<p>Question 55.<br \/>\nm\u2220ABC<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48739\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-55.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 55\" width=\"384\" height=\"257\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-55.png 384w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-55-300x201.png 300w\" sizes=\"(max-width: 384px) 100vw, 384px\" \/><\/p>\n<p>Question 56.<br \/>\nGH<br \/>\nAnswer:<br \/>\nFrom the given figures,<br \/>\nWe can observe that<br \/>\nAB = GH<br \/>\nSo,<br \/>\n3y = 5y &#8211; 8<br \/>\n3y &#8211; 5y = -8<br \/>\n-2y = -8<br \/>\n2y = 8<br \/>\ny = 8 \u00f7 2<br \/>\ny = 4<br \/>\nSo,<br \/>\nThe value of GH = 3y = 3 (4) = 12<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of GH is: 12<\/p>\n<p>Question 57.<br \/>\nBC<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48740\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-57.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.1 a 57\" width=\"345\" height=\"200\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-57.png 345w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.1-a-57-300x174.png 300w\" sizes=\"(max-width: 345px) 100vw, 345px\" \/><\/p>\n<h3><a id=\"5.2_Congruent_Polygons\"><\/a>5.2 Congruent Polygons<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Describing Rigid Motions<\/p>\n<p>Work with a partner: of the four transformations you studied in Chapter 4, which are rigid motions? Under a rigid motion. why is the image of a triangle always congruent to the original triangle? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39829\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-37.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 37\" width=\"419\" height=\"71\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-37.png 419w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-37-300x51.png 300w\" sizes=\"(max-width: 419px) 100vw, 419px\" \/><br \/>\nAnswer:<br \/>\nRigid motion occurs in geometry when an object moves but maintains its shape and size, which is unlike non-rigid motions, such as dilations, in which the object&#8217;s size changes. All rigid motion starts with the original object, called the\u00a0pre-image, and results in the transformed object, called the image.<br \/>\nThere are 4 types of rigid motion. They are:<br \/>\na. Translation<br \/>\nb. Rotation<br \/>\nc. Reflection<br \/>\nd. Glide reflection<br \/>\nWe know that,<br \/>\nRotation only occurs in terms of 90\u00b0 or 180\u00b0<br \/>\nNow,<br \/>\nThe given transformations are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39829\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-37.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 37\" width=\"419\" height=\"71\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-37.png 419w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-37-300x51.png 300w\" sizes=\"(max-width: 419px) 100vw, 419px\" \/><br \/>\nSo,<br \/>\nFrom the above figure,<br \/>\nThe first figure and the second figure are different<br \/>\nThe second figure and the third figure are the same in shape<br \/>\nThe first figure and the fourth figure are the same in shape<br \/>\nSo,<br \/>\nWe can say that the first and the fourth figures are rigid motions<br \/>\nW can say that the second and the third figures are rigid motions<br \/>\nIn the second and the third figures,<br \/>\nThe &#8220;Rotation&#8221; takes place i.e., the second figure is rotated 180\u00b0 keeping the original shape<br \/>\nIn the first and the fourth figures,<br \/>\nThe &#8220;Reflection&#8221; takes place i.e., the first figure is reflected keeping the original shape<br \/>\nNow,<br \/>\nThe image of the triangle is always congruent to the original triangle because of the &#8220;Translation&#8221; i.e., the original triangle and the image of the triangle have the same sides and the same angles but not in the same position.<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Finding a Composition of Rigid Motions<\/p>\n<p>Work with a partner. Describe a composition of rigid motions that maps \u2206ABC to \u2206DEF. Use dynamic geometry software to verify your answer.<br \/>\n<strong>LOOKING FOR STRUCTURE<\/strong><br \/>\nTo be proficient in math, you need to look closely to discern a pattern or structure.<\/p>\n<p>a. \u2206ABC \u2245 \u2206DEF<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39828\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-38.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 38\" width=\"302\" height=\"241\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-38.png 302w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-38-300x239.png 300w\" sizes=\"(max-width: 302px) 100vw, 302px\" \/><br \/>\nAnswer:<\/p>\n<p>b. \u2206ABC \u2245 \u2206DEF<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39827\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-39.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 39\" width=\"305\" height=\"240\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-39.png 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-39-300x236.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><br \/>\nAnswer:<\/p>\n<p>c. \u2206ABC \u2245 \u2206DEF<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39826\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-40.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 40\" width=\"309\" height=\"241\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-40.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-40-300x234.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><br \/>\nAnswer:<\/p>\n<p>d. \u2206ABC \u2245 \u2206DEF<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39825\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-41.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 41\" width=\"307\" height=\"241\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-41.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-41-300x236.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><br \/>\nAnswer:<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 3.<br \/>\nGiven two congruent triangles. how can you use rigid motions to map one triangle to the other triangle?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nThe vertices of \u2206ABC are A(1, 1), B(3, 2), and C(4, 4). The vertices of \u2206DEF are D(2, &#8211; 1), E(0, 0), and F(- 1, 2). Describe a composition of rigid motions that maps \u2206ABC to \u2206DEF.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_5.2_Congruent_Polygons\"><\/a>Lesson 5.2 Congruent Polygons<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>In the diagram, ABGH \u2245 CDEF.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-39824\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-42.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 42\" width=\"232\" height=\"113\" \/><\/p>\n<p>Question 1.<br \/>\nIdentify all pairs of congruent corresponding parts.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nFind the value of x.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nIn the diagram at the left. show that \u2206PTS \u2245 \u2206RTQ.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39823\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-43.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 43\" width=\"193\" height=\"91\" \/><br \/>\nAnswer:<\/p>\n<p>Use the diagram.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-39822\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-44.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 44\" width=\"157\" height=\"119\" \/><\/p>\n<p>Question 4.<br \/>\nFind m\u2220DCN.<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nWhat additional information is needed to conclude that \u2206NDC \u2245 \u2206NSR?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Exercise_5.2_Congruent_Polygons\"><\/a>Exercise 5.2 Congruent Polygons<\/h3>\n<p>Question 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nBased on this lesson. what information do you need to prove that two triangles are congruent? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48741\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-1.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.2 a 1\" width=\"577\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-1.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-1-300x58.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find &#8220;both&#8221; answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39821\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-45.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 45\" width=\"342\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-45.png 342w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-45-300x79.png 300w\" sizes=\"(max-width: 342px) 100vw, 342px\" \/><\/p>\n<p>Is \u2206ABC \u2245 \u2206RST?<br \/>\nAnswer:<\/p>\n<p>Is \u2206KJL \u2245 \u2206SRT?<br \/>\nAnswer:<\/p>\n<p>Is \u2206JLK \u2245 \u2206STR?<br \/>\nAnswer:<\/p>\n<p>Is \u2206LKJ \u2245 \u2206TSR?<br \/>\nAnswer:<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3 and 4. identify all pairs of congruent corresponding parts. Then write another congruence statement for the polygons.<\/p>\n<p>Question 3.<br \/>\n\u2206ABC \u2245 \u2206DEF<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39820\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-46.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 46\" width=\"211\" height=\"126\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48742\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-3.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.2 a 3\" width=\"567\" height=\"98\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-3.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-3-300x52.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 4.<br \/>\nGHJK \u2245 \u2206QRST<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39819\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-47.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 47\" width=\"224\" height=\"120\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 5-8, \u2206XYZ \u2245 \u2206MNL. Copy and complete the statement.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-39818\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-48.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 48\" width=\"238\" height=\"97\" \/><\/p>\n<p>Question 5.<br \/>\nm\u2220Y = ______<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48743\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-5.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.2 a 5\" width=\"296\" height=\"31\" \/><\/p>\n<p>Question 6.<br \/>\nm\u2220M = ______<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nm\u2220Z = _______<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48744\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-7.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.2 a 7\" width=\"514\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-7.png 514w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-7-300x34.png 300w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/><\/p>\n<p>Question 8.<br \/>\nXY= _______<br \/>\nAnswer:<\/p>\n<p>In Exercises 9 and 10. find the values of x and y.<\/p>\n<p>Question 9.<br \/>\nABCD \u2245 EFGH<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39817\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-49.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 49\" width=\"281\" height=\"148\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48745\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-9.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.2 a 9\" width=\"227\" height=\"238\" \/><\/p>\n<p>Question 10.<br \/>\n\u2206MNP \u2245 \u2206TUS<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39816\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-50.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 50\" width=\"326\" height=\"104\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-50.png 326w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-50-300x96.png 300w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 11 and 12. show that the polygons are congruent. Explain your reasoning.<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39815\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-51.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 51\" width=\"222\" height=\"114\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48746\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-11.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.2 a 11\" width=\"589\" height=\"133\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-11.png 589w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-11-300x68.png 300w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39814\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-52.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 52\" width=\"230\" height=\"106\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 13 and 14, find m\u22201.<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39813\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-53.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 53\" width=\"240\" height=\"80\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48747\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-13.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.2 a 13\" width=\"591\" height=\"82\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-13.png 591w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-13-300x42.png 300w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39812\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-54.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 54\" width=\"217\" height=\"103\" \/><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n<strong>PROOF<\/strong><br \/>\nTriangular postage stamps, like the ones shown, are highly valued by stamp collectors. Prove that \u2206AEB \u2245 \u2206CED.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39811\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-55.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 55\" width=\"141\" height=\"142\" \/><br \/>\nGiven \\(\\overline{A B}\\) || \\(\\overline{D C}\\), \\(\\overline{A B}\\) \u2245 \\(\\overline{D C}\\) is the midpoint of \\(\\overline{A C}\\) and \\(\\overline{B D}\\)<br \/>\nProve \u2206AEB \u2245 \u2206CED<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48748\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-15.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.2 a 15\" width=\"581\" height=\"627\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-15.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-15-278x300.png 278w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 16.<br \/>\n<strong>PROOF<\/strong><br \/>\nUse the information in the figure to prove that \u2206ABG \u2245 \u2206DCF<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39810\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-56.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 56\" width=\"212\" height=\"108\" \/><br \/>\nAnswer:<\/p>\n<p><strong>ERROR ANALYSIS<\/strong><br \/>\nIn Exercises 17 and 18, describe and correct the error.<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39809\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-57.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 57\" width=\"351\" height=\"120\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-57.png 351w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-57-300x103.png 300w\" sizes=\"(max-width: 351px) 100vw, 351px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48749\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-17.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.2 a 17\" width=\"512\" height=\"158\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-17.png 512w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-17-300x93.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39808\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-58.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 58\" width=\"352\" height=\"117\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-58.png 352w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-58-300x100.png 300w\" sizes=\"(max-width: 352px) 100vw, 352px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nProve the Third Angles Theorem (Theorem 5.4) by using the Triangle Sum Theorem (Theorem 5. 1).<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48750\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-19.1.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.2 a 19.1\" width=\"588\" height=\"615\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-19.1.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-19.1-287x300.png 287w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48751\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-19.2.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.2 a 19.2\" width=\"602\" height=\"234\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-19.2.png 602w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-19.2-300x117.png 300w\" sizes=\"(max-width: 602px) 100vw, 602px\" \/><\/p>\n<p>Question 20.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nDraw a triangle. Copy the triangle multiple times to create a rug design made of congruent triangles. Which property guarantees that all the triangles are congruent?<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<strong>REASONING<\/strong><br \/>\n\u2206JKL is congruent to \u2206XYZ Identify all pairs of congruent corresponding parts.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48752\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-21.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.2 a 21\" width=\"549\" height=\"70\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-21.png 549w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-21-300x38.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p>Question 22.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nIn the diagram, ABEF \u2245 CDEF<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39807\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-59.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 59\" width=\"176\" height=\"128\" \/><br \/>\na. Explain how you know that \\(\\overline{B E}\\) \u2245 \\(\\overline{D E}\\) and \u2220ABE \u2245\u2220CDE.<br \/>\nAnswer:<\/p>\n<p>b. Explain how you know that \u2220GBE \u2245 \u2220GDE.<br \/>\nAnswer:<\/p>\n<p>c. Explain how you know that \u2220GEB \u2245 \u2220GED.<br \/>\nAnswer:<\/p>\n<p>d. Do you have enough information to prove that \u2220BEG \u2245 \u2220DEG? Explain.<br \/>\nAnswer:<\/p>\n<p><strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nIn Exercises 23 and 24, use the given information to write and solve a system of linear equations to find the values of x and y.<\/p>\n<p>Question 23.<br \/>\n\u2206LMN \u2245 \u2206PQR. m\u2220L = 40\u00b0, m\u2220M = 90\u00b0 m\u2220P = (17x &#8211; y)\u00b0. m\u2220R (2x + 4y)\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48753\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-23.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.2 a 23\" width=\"526\" height=\"658\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-23.png 526w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-23-240x300.png 240w\" sizes=\"(max-width: 526px) 100vw, 526px\" \/><\/p>\n<p>Question 24.<br \/>\n\u2206STL \u2245 \u2206XYZ, m\u2220T = 28\u00b0, m\u2220U = (4x + y)\u00b0, m\u2220X = 130\u00b0, m\u2220Y = (8x &#8211; 6y)\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n<strong>PROOF<\/strong><br \/>\nProve that the criteria for congruent triangles in this lesson is equivalent to the definition of congruence in terms of rigid motions.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48754\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-25.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.2 a 25\" width=\"571\" height=\"139\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-25.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-25-300x73.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Maintaining Mathematical Proficiency<\/p>\n<p>What can you conclude from the diagram?<\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39806\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-60.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 60\" width=\"175\" height=\"93\" \/><br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39805\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-61.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 61\" width=\"127\" height=\"78\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48755\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-27.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.2 a 27\" width=\"222\" height=\"36\" \/><\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39804\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-62.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 62\" width=\"146\" height=\"95\" \/><br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39803\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-63.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 63\" width=\"156\" height=\"115\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48756\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-29.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.2 a 29\" width=\"472\" height=\"39\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-29.png 472w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.2-a-29-300x25.png 300w\" sizes=\"(max-width: 472px) 100vw, 472px\" \/><\/p>\n<h3><a id=\"5.3_Proving_Triangle_Congruence_by_SAS\"><\/a>5.3 Proving Triangle Congruence by SAS<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Drawing Triangles<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40192\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-64.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 64\" width=\"302\" height=\"240\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-64.png 302w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-64-300x238.png 300w\" sizes=\"(max-width: 302px) 100vw, 302px\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40191\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-65.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 65\" width=\"308\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-65.png 308w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-65-300x233.png 300w\" sizes=\"(max-width: 308px) 100vw, 308px\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40190\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-66.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 66\" width=\"577\" height=\"205\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-66.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-66-300x107.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Work with a partner.<\/p>\n<p>Use dynamic geometry software.<br \/>\na. Construct circles with radii of 2 units and 3 units centered at the origin. Construct a 40\u00b0 angle with its vertex at the origin. Label the vertex A.<br \/>\nAnswer:<\/p>\n<p>b. Locate the point where one ray of the angle intersects the smaller circle and label this point B. Locate the point where the other ray of the angle intersects the larger circle and label this point C. Then draw \u2206ABC.<br \/>\nAnswer:<\/p>\n<p>c. Find BC, m\u2220B, and m\u2220C.<br \/>\nAnswer:<\/p>\n<p>d. Repeat parts (a)-(c) several times. redrawing the angle indifferent positions. Keep track of your results by copying and completing the table below. What can you conclude?<br \/>\n<strong>USING TOOLS STRATEGICALLY<\/strong><br \/>\nTo be proficient in math, you need to use technology to help visualize the results of varying assumptions, explore consequences, and compare predictions with data.<br \/>\nAnswer:<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 2.<br \/>\nWhat can you conclude about two triangles when you know that two pairs of corresponding sides and the corresponding included angles are congruent?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nHow would you prove your conclusion in Exploration 1(d)?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_5.3_Proving_Triangle_Congruence_by_SAS\"><\/a>Lesson 5.3 Proving Triangle Congruence by SAS<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>In the diagram, ABCD is a square with four congruent sides and four right<br \/>\nangles. R, S, T, and U are the midpoints of the sides of ABCD. Also, \\(\\overline{R T}\\) \u22a5 \\(\\overline{S U}\\) and \\(\\overline{S V}\\) \u2245 \\(\\overline{V U}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40189\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-67.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 67\" width=\"148\" height=\"150\" \/><br \/>\nQuestion 1.<br \/>\nProve that \u2206SVR \u2245 \u2206UVR.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nProve that \u2206BSR \u2245 \u2206DUT.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nYou are designing the window shown in the photo. You want to make \u2206DRA congruent to \u2206DRG. You design the window so that \\(\\overline{D A}\\) \u2245 \\(\\overline{D G}\\) and \u2220ADR \u2245 \u2220GDR. Use the SAS Congruence Theorem to prove \u2206DRA \u2245 \u2206DRG.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40188\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-68.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 68\" width=\"266\" height=\"142\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Exercise_5.3_Proving_Triangle_Congruence_by_SAS\"><\/a>Exercise 5.3 Proving Triangle Congruence by SAS<\/h3>\n<p>vocabulary and core concept check<\/p>\n<p>Question 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nWhat is an included angle?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48757\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-1.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.3 a 1\" width=\"513\" height=\"55\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-1.png 513w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-1-300x32.png 300w\" sizes=\"(max-width: 513px) 100vw, 513px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nIf two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then __________ .<br \/>\nAnswer:<\/p>\n<p>Monitoring progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3-8, name the included an1e between the pair of sides given.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40187\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-69.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 69\" width=\"178\" height=\"98\" \/><\/p>\n<p>Question 3.<br \/>\n\\(\\overline{J K}\\) and \\(\\overline{K L}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48758\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-3.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.3 a 3\" width=\"462\" height=\"38\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-3.png 462w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-3-300x25.png 300w\" sizes=\"(max-width: 462px) 100vw, 462px\" \/><\/p>\n<p>Question 4.<br \/>\n\\(\\overline{P K}\\) and \\(\\overline{L K}\\)<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n\\(\\overline{L P}\\) and \\(\\overline{L K}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48759\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-5.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.3 a 5\" width=\"472\" height=\"37\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-5.png 472w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-5-300x24.png 300w\" sizes=\"(max-width: 472px) 100vw, 472px\" \/><\/p>\n<p>Question 6.<br \/>\n\\(\\overline{J L}\\) and \\(\\overline{J K}\\)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n\\(\\overline{K L}\\) and \\(\\overline{J L}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48760\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-7.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.3 a 7\" width=\"469\" height=\"38\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-7.png 469w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-7-300x24.png 300w\" sizes=\"(max-width: 469px) 100vw, 469px\" \/><\/p>\n<p>Question 8.<br \/>\n\\(\\overline{K P}\\) and \\(\\overline{P L}\\)<br \/>\nAnswer:<\/p>\n<p>In Exercises 9-14, decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Theorem (Theorem 5.5). Explain.<\/p>\n<p>Question 9.<br \/>\n\u2206ABD, \u2206CDB<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40186\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-70.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 70\" width=\"170\" height=\"97\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48761\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-9.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.3 a 9\" width=\"524\" height=\"42\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-9.png 524w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-9-300x24.png 300w\" sizes=\"(max-width: 524px) 100vw, 524px\" \/><\/p>\n<p>Question 10.<br \/>\n\u2206LMN, \u2206NQP<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40185\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-71.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 71\" width=\"166\" height=\"99\" \/><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n\u2206YXZ, \u2206WXZ<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40184\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-72.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 72\" width=\"165\" height=\"82\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48762\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-11.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.3 a 11\" width=\"546\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-11.png 546w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-11-300x18.png 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p>Question 12.<br \/>\n\u2206QRV, \u2206TSU<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40183\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-73.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 73\" width=\"193\" height=\"102\" \/><br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n\u2206EFH, \u2206GHF<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40182\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-74.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 74\" width=\"171\" height=\"100\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48763\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-13.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.3 a 13\" width=\"577\" height=\"34\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-13.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-13-300x18.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 14.<br \/>\n\u2206KLM, \u2206MNK<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40181\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-75.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 75\" width=\"185\" height=\"108\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 15 &#8211; 18, write a proof.<\/p>\n<p>Question 15.<br \/>\nGiven \\(\\overline{P Q}\\) bisects \u2220SPT, \\(\\overline{S P}\\) \u2245 \\(\\overline{T P}\\)<br \/>\nProve \u2206SPQ \u2245 \u2206TPQ<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40180\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-76.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 76\" width=\"153\" height=\"123\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48764\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-15.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.3 a 15\" width=\"562\" height=\"460\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-15.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-15-300x246.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 16.<br \/>\nGiven \\(\\overline{A B}\\) \u2245 \\(\\overline{C D}\\), \\(\\overline{A B}\\) || \\(\\overline{C D}\\)<br \/>\nProve \u2206ABC \u2245 \u2206CDA<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40179\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-77.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 77\" width=\"104\" height=\"141\" \/><br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\nGiven C is the midpoint of \\(\\overline{A E}\\) and \\(\\overline{B D}\\)<br \/>\nProve \u2206ABC \u2245 \u2206EDC<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40178\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-78.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 78\" width=\"205\" height=\"131\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48765\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-17.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.3 a 17\" width=\"583\" height=\"495\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-17.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-17-300x255.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 18.<br \/>\nGiven \\(\\overline{P T}\\) \u2245 \\(\\overline{R T}\\), \\(\\overline{Q T}\\) \u2245 \\(\\overline{S T}\\)<br \/>\nProve \u2206PQT \u2245 \u2206RST<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40177\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-79.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 79\" width=\"198\" height=\"111\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 19-22, use the given information to name two triangles that are congruent. Explain your reasoning.<\/p>\n<p>Question 19.<br \/>\n\u2220SRT \u2245 \u2220URT, and R is the center of the circle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40176\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-80.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 80\" width=\"97\" height=\"101\" \/><br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-48766\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-19.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.3 a 19\" width=\"588\" height=\"151\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-19.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-19-300x77.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 20.<br \/>\nABCD is a square with four congruent sides and four congruent angles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40175\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-81.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 81\" width=\"114\" height=\"109\" \/><br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\nRSTUV is a regular pentagon.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40174\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-82.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 82\" width=\"115\" height=\"118\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48767\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-21.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.3 a 21\" width=\"588\" height=\"152\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-21.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-21-300x78.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 22.<br \/>\n\\(\\overline{M K}\\) \u22a5 \\(\\overline{M N}\\), \\(\\overline{K L}\\) \u22a5 \\(\\overline{N L}\\), and M and L are centers of circles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40173\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-83.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 83\" width=\"173\" height=\"120\" \/><br \/>\nAnswer:<\/p>\n<p><strong>CONSTRUCTION<\/strong><br \/>\nIn Exercises 23 and 24, construct a triangle that is congruent to \u2206ABC using the SAS Congruence Theorem (Theorem 5.5).<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40172\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-84.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 84\" width=\"165\" height=\"100\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48768\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-23.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.3 a 23\" width=\"575\" height=\"287\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-23.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-23-300x150.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40171\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-85.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 85\" width=\"166\" height=\"101\" \/><br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in finding the value of x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40170\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-86.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 86\" width=\"353\" height=\"121\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-86.png 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-86-300x103.png 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48769\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-25.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.3 a 25\" width=\"597\" height=\"222\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-25.png 597w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-25-300x112.png 300w\" sizes=\"(max-width: 597px) 100vw, 597px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nWhat additional information do you need to prove that \u2206ABC \u2245 \u2206DBC?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40169\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-87.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 87\" width=\"151\" height=\"127\" \/><br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<strong>PROOF<\/strong><br \/>\nThe Navajo rug is made of isosceles triangles. You know \u2220B \u2245\u2220D. Use the SAS Congruence Theorem (Theorem 5.5 to show that \u2206ABC \u2245 \u2206CDE. (See Example 3.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40168\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-88.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 88\" width=\"370\" height=\"137\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-88.png 370w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-88-300x111.png 300w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48770\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-27.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.3 a 27\" width=\"586\" height=\"343\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-27.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-27-300x176.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nThere are six possible subsets of three sides or angles of a triangle: SSS, SAS, SSA, AAA, ASA, and AAS. Which of these correspond to congruence theorems? For those that do not, give a counterexample.<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nProve that<br \/>\n\u2206ABC \u2245 \u2206DEC<br \/>\nThen find the values of x and y.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40167\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-89.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 89\" width=\"174\" height=\"128\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48771\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-29.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.3 a 29\" width=\"584\" height=\"752\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-29.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-29-233x300.png 233w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims it is possible to Construct a triangle congruent to \u2206ABC by first constructing \\(\\overline{A B}\\) and \\(\\overline{A C}\\), and then copying \u2220C. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40166\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-90.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 90\" width=\"106\" height=\"91\" \/><br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nProve the Reflections in Intersecting Lines Theorem (Theorem 4.3).<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48772\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-31.1.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.3 a 31.1\" width=\"624\" height=\"548\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-31.1.png 624w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-31.1-300x263.png 300w\" sizes=\"(max-width: 624px) 100vw, 624px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48773\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-31.2.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.3 a 31.2\" width=\"603\" height=\"641\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-31.2.png 603w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-31.2-282x300.png 282w\" sizes=\"(max-width: 603px) 100vw, 603px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48774\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-31.3.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.3 a 31.3\" width=\"602\" height=\"619\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-31.3.png 602w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-31.3-292x300.png 292w\" sizes=\"(max-width: 602px) 100vw, 602px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48775\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-31.4.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.3 a 31.4\" width=\"575\" height=\"202\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-31.4.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-31.4-300x105.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Maintaining Mathematical Proficiency<\/p>\n<p>Classify the triangle by its sides and by measuring its angles.<\/p>\n<p>Question 32.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40165\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-91.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 91\" width=\"89\" height=\"88\" \/><br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40164\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-92.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 92\" width=\"117\" height=\"70\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48776\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-33.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.3 a 33\" width=\"537\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-33.png 537w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-33-300x35.png 300w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><\/p>\n<p>Question 34.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40163\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-93.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 93\" width=\"91\" height=\"83\" \/><br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40162\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-94.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 94\" width=\"161\" height=\"80\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48777\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-35.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.3 a 35\" width=\"528\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-35.png 528w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.3-a-35-300x32.png 300w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><\/p>\n<h3><a id=\"5.4_Equilateral_and_Isosceles_Triangles\"><\/a>5.4 Equilateral and Isosceles Triangles<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Writing a Conjecture about Isosceles Triangles<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40369\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-95.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 95\" width=\"446\" height=\"261\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-95.png 446w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-95-300x176.png 300w\" sizes=\"(max-width: 446px) 100vw, 446px\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40368\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-96.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 96\" width=\"622\" height=\"203\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-96.png 622w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-96-300x98.png 300w\" sizes=\"(max-width: 622px) 100vw, 622px\" \/><\/p>\n<p>Work with a partner: Use dynamic geometry software.<\/p>\n<p>a. Construct a circle with a radius of 3 units centered at the origin.<br \/>\nAnswer:<\/p>\n<p>b. Construct \u2206ABC so that B and C are on the circle and A is at the origin.<br \/>\nAnswer:<\/p>\n<p>c. Recall that a triangle is isosceles if it has at least two congruent sides. Explain why \u2206ABC is an isosceles triangle.<br \/>\nAnswer:<\/p>\n<p>d. What do you observe about the angles of \u2206ABC?<br \/>\nAnswer:<\/p>\n<p>e. Repeat parts (a)-(d) with several other isosceles triangles using circles of different radii. Keep track of your observations by copying and completing the table below. Then write a conjecture about the angle measures of an isosceles triangle.<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:<\/p>\n<p>f. Write the converse of the conjecture you wrote in part (e). Is the converse true?<br \/>\nAnswer:<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 2.<br \/>\nWhat conjectures can you make about the side lengths and angle measures of an<br \/>\nisosceles triangle?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nHow would you prove your conclusion in Exploration 1 (e)? in Exploration 1(f)?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_5.4_Equilateral_and_Isosceles_Triangles\"><\/a>Lesson 5.4 Equilateral and Isosceles Triangles<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Copy and complete the statement.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40215\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-97.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 97\" width=\"146\" height=\"90\" \/><\/p>\n<p>Question 1.<br \/>\nIf \\(\\overline{H G}\\) \u2245 \\(\\overline{H K}\\), then \u2220 _______ \u2245 \u2220 _______ .<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nIf \u2220KHJ \u2245\u2220KJH, then ______ \u2245 ______ .<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nFind the length of \\(\\overline{S T}\\) of the triangle at the left.<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nFind the value of x and y in the diagram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40214\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-98.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 98\" width=\"88\" height=\"80\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nIn Example 4, show that \u2206PTS \u2245 \u2206QTR<br \/>\nAnswer:<\/p>\n<h3><a id=\"Exercise_5.4_Equilateral_and_Isosceles_Triangles\"><\/a>Exercise 5.4 Equilateral and Isosceles Triangles<\/h3>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nDescribe how to identify the vertex angle of an isosceles triangle.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48778\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5.4 a 1\" width=\"586\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-1.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-1-300x32.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nWhat is the relationship between the base angles of an isosceles triangle? Explain.<br \/>\nAnswer:<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3-6. copy and complete the statement. State which theorem you used.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40213\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-99.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 99\" width=\"187\" height=\"83\" \/><\/p>\n<p>Question 3.<br \/>\nIf \\(\\overline{A E}\\) \u2245 \\(\\overline{D E}\\) then \u2220_____ \u2245 \u2220_____ .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48779\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5.4 a 3\" width=\"555\" height=\"65\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-3.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-3-300x35.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p>Question 4.<br \/>\nIf \\(\\overline{A B}\\) \u2245 \\(\\overline{E B}\\) then \u2220_____ \u2245 \u2220_____ .<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nIf \u2220D \u2245 \u2220CED, then _______ \u2245 _______ .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48780\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5.4 a 5\" width=\"546\" height=\"69\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-5.png 546w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-5-300x38.png 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p>Question 6.<br \/>\nIf \u2220EBC \u2245 \u2220ECB, then _______ \u2245 _______ .<br \/>\nAnswer:<\/p>\n<p>In Exercises 7-10. find the value of x.<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40212\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-100.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 100\" width=\"114\" height=\"102\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48781\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-7.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5.4 a 7\" width=\"495\" height=\"69\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-7.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-7-300x42.png 300w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40211\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-101.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 101\" width=\"113\" height=\"112\" \/><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40210\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-102.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 102\" width=\"116\" height=\"102\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48783\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-9.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5.4 a 9\" width=\"493\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-9.png 493w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-9-300x38.png 300w\" sizes=\"(max-width: 493px) 100vw, 493px\" \/><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40209\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-103.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 103\" width=\"101\" height=\"117\" \/><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe dimensions of a sports pennant are given in the diagram. Find the values of x and y.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40208\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-104.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 104\" width=\"270\" height=\"110\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48784\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-11.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5.4 a 11\" width=\"488\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-11.png 488w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-11-300x36.png 300w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><\/p>\n<p>Question 12.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA logo in an advertisement is an equilateral triangle with a side length of 7 centimeters. Sketch the logo and give the measure of each side.<br \/>\nAnswer:<\/p>\n<p>In Exercises 13-16, find the values of x and y.<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40207\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-105.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 105\" width=\"139\" height=\"74\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48785\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-13.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5.4 a 13\" width=\"588\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-13.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-13-300x57.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40206\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-106.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 106\" width=\"149\" height=\"79\" \/><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40205\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-107.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 107\" width=\"164\" height=\"96\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48786\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-15.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5.4 a 15\" width=\"587\" height=\"259\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-15.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-15-300x132.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40204\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-108.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 108\" width=\"197\" height=\"104\" \/><br \/>\nAnswer:<\/p>\n<p><strong>CONSTRUCTION<\/strong><br \/>\nIn Exercises 17 and 18, construct an equilateral triangle whose sides are the given length.<\/p>\n<p>Question 17.<br \/>\n3 inches<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48787\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-17.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5.4 a 17\" width=\"580\" height=\"358\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-17.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-17-300x185.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 18.<br \/>\n1.25 inches<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in finding the length of \\(\\overline{B C}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40203\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-109.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 109\" width=\"313\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-109.png 313w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-109-300x106.png 300w\" sizes=\"(max-width: 313px) 100vw, 313px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48788\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-19.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5.4 a 19\" width=\"532\" height=\"95\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-19.png 532w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-19-300x54.png 300w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><\/p>\n<p>Question 20.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe diagram represents part of the exterior of the Bow Tower in Calgary. Alberta, Canada, In the diagram. \u2206ABD and \u2206CBD arc congruent equilateral triangles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40202\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-110.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 110\" width=\"170\" height=\"294\" \/><\/p>\n<p>a. Explain why \u2206ABC is isosceles.<br \/>\nAnswer:<\/p>\n<p>b. Explain \u2220BAE \u2245 \u2220BCE.<br \/>\nAnswer:<\/p>\n<p>c. Show that \u2206ABE and \u2206CBE arc congruent.<br \/>\nAnswer:<\/p>\n<p>d. Find the measure of \u2220BAE.<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<strong>FINDING A PATTERN<\/strong><br \/>\nIn the pattern shown. each small triangle is an equilateral triangle with an area of 1 square unit.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40201\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-111.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 111\" width=\"207\" height=\"304\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-111.png 207w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-111-204x300.png 204w\" sizes=\"(max-width: 207px) 100vw, 207px\" \/><br \/>\na. Explain how you know that an triangle made out of equilateral triangles is equilateral.<br \/>\nb. Find the areas of the first four triangles in the pattern.<br \/>\nc. Describe any patterns in the areas. Predict the area of the seventh triangle in the pattern. Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48789\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-21.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5.4 a 21\" width=\"602\" height=\"319\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-21.png 602w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-21-300x159.png 300w\" sizes=\"(max-width: 602px) 100vw, 602px\" \/><\/p>\n<p>Question 22.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe base of isosceles \u2206XYZ is \\(\\overline{Y Z}\\). What<br \/>\ncan you prove? Select all that apply.<br \/>\n(A) \\(\\overline{X Y}\\) \u2245 \\(\\overline{X Z}\\)<br \/>\n(B) \u2220X \u2245 \u2220Y<br \/>\n(C) \u2220Y \u2245 \u2220Z<br \/>\n(D) \\(\\overline{Y Z}\\) \u2245 \\(\\overline{Z X}\\)<br \/>\nAnswer:<\/p>\n<p>In Exercises 23 and 24, find the perimeter of the triangle.<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40200\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-112.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 112\" width=\"179\" height=\"124\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48790\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-23.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5.4 a 23\" width=\"427\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-23.png 427w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-23-300x119.png 300w\" sizes=\"(max-width: 427px) 100vw, 427px\" \/><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40199\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-113.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 113\" width=\"174\" height=\"126\" \/><br \/>\nAnswer:<\/p>\n<p><strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nIn Exercises 25 &#8211; 28. use the diagram based on the color wheel. The 12 triangles in the diagram are isosceles triangles with congruent vertex angles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40198\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-114.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 114\" width=\"278\" height=\"224\" \/><\/p>\n<p>Question 25.<br \/>\nComplementary colors lie directly opposite each other on the color wheel. Explain how you know that the yellow triangle is congruent to the purple triangle.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48791\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-25.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5.4 a 25\" width=\"573\" height=\"332\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-25.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-25-300x174.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 26.<br \/>\nThe measure of the vertex angle of the yellow triangle is 30\u00b0. Find the measures of the base angles.<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\nTrace the color wheel. Then form a triangle whose vertices are the midpoints of the bases of the red. yellow. and blue triangles. (These colors are the primary colors.) What type of triangle is this?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48792\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-27.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5.4 a 27\" width=\"582\" height=\"376\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-27.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-27-300x194.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 28.<br \/>\nOther triangles can be brined on the color wheel that are congruent to the triangle in Exercise 27. The colors on the vertices of these triangles are called triads. What are the possible triads?<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nAre isosceles triangles always acute triangles? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48793\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-29.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5.4 a 29\" width=\"572\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-29.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-29-300x33.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nIs it possible for an equilateral triangle to have an angle measure other than 60\u00b0? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nThe lengths of the sides of a triangle are 3t, 5t &#8211; 12, and t + 20. Find the values of t that make the triangle isosceles. Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48794\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-31.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5.4 a 31\" width=\"507\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-31.png 507w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-31-300x80.png 300w\" sizes=\"(max-width: 507px) 100vw, 507px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nThe measure of an exterior angle of an isosceles triangle is x\u00b0. Write expressions representing the possible angle measures of the triangle in terms of x.<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain why the measure of the vertex angle of an isosceles triangle must be an even number of degrees when the measures of all the angles of the triangle are whole numbers.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48795\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-33.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5.4 a 33\" width=\"589\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-33.png 589w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-33-300x44.png 300w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe triangular faces of the peaks on a roof arc congruent isosceles triangles with vertex angles U and V.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40197\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-115.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 115\" width=\"357\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-115.png 357w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-115-300x149.png 300w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/><br \/>\na. Name two angles congruent to \u2220WUX. Explain your reasoning.<br \/>\nb. Find the distance between points U and V.<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA boat is traveling parallel to the shore along \\(\\vec{R}\\)T. When the boat is at point R, the captain measures the angle to the lighthouse as 35\u00b0. After the boat has traveled 2.1 miles, the captain measures the angle to the lighthouse to be 70\u00b0.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40196\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-116.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 116\" width=\"312\" height=\"176\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-116.png 312w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-116-300x169.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><br \/>\na. Find SL. Explain your reasoning.<br \/>\nb. Explain how to find the distance between the boat and the shoreline.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48796\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-35.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5.4 a 35\" width=\"573\" height=\"288\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-35.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-35-300x151.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nThe postulates and theorems in this book represent Euclidean geometry. In spherical geometry, all points are points on the surface of a sphere. A line is a circle on the sphere whose diameter is equal to the diameter of the sphere. In spherical geometry, do all equiangular triangles have the same angle measures? Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<strong>PROVING A COROLLARY<\/strong><br \/>\nProve that the Corollary to the Base Angles Theorem (Corollary 5.2) follows from the Base Angles Theorem (Theorem 5.6).<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48797\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-37.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5.4 a 37\" width=\"558\" height=\"523\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-37.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-37-300x281.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nYou are designing fabric purses to sell at the school fair.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40195\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-117.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 117\" width=\"155\" height=\"131\" \/><br \/>\na. Explain why \u2206ABE \u2245 \u2206DCE.<br \/>\nb. Name the isosceles triangles in the purse.<br \/>\nc. Name three angles that are congruent to \u2220EAD.<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<strong>PROVING A COROLLARY<\/strong><br \/>\nProve that the Corollary to the Converse of the Base Angles Theorem (Corollary 5.3) follows from the Converse of the Base Angles Theorem (Theorem 5.7)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48798\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-39.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5.4 a 39\" width=\"561\" height=\"523\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-39.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-39-300x280.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nThe coordinates of two points are T(0, 6) and U(6, 0) Your friend claims that points T, U, and V will always be the vertices of an isosceles triangle when V is any point on the line y = x. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<strong>PROOF<\/strong><br \/>\nUse the diagram to prove that \u2206DEF is equilateral.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40194\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-118.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 118\" width=\"133\" height=\"117\" \/><br \/>\nGiven \u2206ABC is equilateral<br \/>\n\u2220CAD \u2245 \u2220ABE \u2245 \u2220BCF<br \/>\nProve \u2206DEF is equilateral<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48799\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-41.1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5.4 a 41.1\" width=\"700\" height=\"510\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-41.1.png 700w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-41.1-300x219.png 300w\" sizes=\"(max-width: 700px) 100vw, 700px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48800\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-41.2.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5.4 a 41.2\" width=\"690\" height=\"598\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-41.2.png 690w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-41.2-300x260.png 300w\" sizes=\"(max-width: 690px) 100vw, 690px\" \/><\/p>\n<p>Maintaining Mathematical Proficiency<\/p>\n<p>Use the given property to complete the statement.<\/p>\n<p>Question 42.<br \/>\nReflexive Property of Congruence (Theorem 2. 1): ________ \u2245 \\(\\overline{S E}\\)<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\nSymmetric Property of Congruence (Theorem 2.1): If ________ \u2245 ________, then \\(\\overline{R S}\\) \u2245 \\(\\overline{J K}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48801\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-43.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 5.4 a 43\" width=\"502\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-43.png 502w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-5.4-a-43-300x34.png 300w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/><\/p>\n<p>Question 44.<br \/>\nTransitive Property of Congruence (Theorem 2.1): If \\(\\overline{E F}\\) \u2245 \\(\\overline{P Q}\\), and \\(\\overline{P Q}\\) \u2245 \\(\\overline{U V}\\) ________ \u2245 ________.<br \/>\nAnswer:<\/p>\n<h3><a id=\"5.1_to_5.4_Quiz\"><\/a>5.1 to 5.4 Quiz<\/h3>\n<p>Find the measure of the exterior angle.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40339\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-119.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 119\" width=\"202\" height=\"79\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40338\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-120.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 120\" width=\"158\" height=\"89\" \/><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40337\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-121.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 121\" width=\"258\" height=\"89\" \/><br \/>\nAnswer:<\/p>\n<p>Identify all pairs of congruent corresponding parts. Then write another congruence statement for the polygons.<\/p>\n<p>Question 4.<br \/>\n\u2206ABC \u2245 \u2206DEF<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40336\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-122.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 122\" width=\"264\" height=\"110\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nQRST \u2245 WXYZ<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40335\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-123.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 123\" width=\"225\" height=\"97\" \/><br \/>\nAnswer:<\/p>\n<p>Decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Theorem (Thm 5.5). If so, write a proof. If not, explain why.<\/p>\n<p>Question 6.<br \/>\n\u2206CAD, \u2206CBD<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40333\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-124.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 124\" width=\"143\" height=\"115\" \/><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n\u2206GHF, \u2206KHJ<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40331\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-125.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 125\" width=\"161\" height=\"126\" \/><br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n\u2206LWP, \u2206NMP<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40330\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-126.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 126\" width=\"134\" height=\"129\" \/><br \/>\nAnswer:<\/p>\n<p>Copy and complete the statement. State which theorem you used.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40329\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-127.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 127\" width=\"193\" height=\"112\" \/><\/p>\n<p>Question 9.<br \/>\nIf VW \u2245 WX, then \u2220______ \u2245 \u2220 ________.<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nIf XZ \u2245 XY. then\u2220______ \u2245 \u2220 ________.<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nIf \u2220ZVX \u2245\u2220ZXV, then \u2220______ \u2245 \u2220 ________.<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nIf \u2220XYZ \u2245\u2220ZXY, then \u2220______ \u2245 \u2220 ________.<br \/>\nAnswer:<\/p>\n<p>Find the values of x and y.<\/p>\n<p>Question 13.<br \/>\n\u2206DEF \u2245 \u2206QRS<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40327\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-128.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 128\" width=\"320\" height=\"116\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-128.png 320w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-128-300x109.png 300w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40325\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-129.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 129\" width=\"187\" height=\"106\" \/><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nIn a right triangle, the measure of one acute angle is 4 times the difference of the measure of the other acute angle and 5. Find the measure ol each acute angle in the triangle. (Section 5.1)<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\nThe figure shows a stained glass window. (Section 5.1 and Section 5.3)<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40324\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-130.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 130\" width=\"197\" height=\"211\" \/><\/p>\n<p>a. Classify triangles 1 &#8211; 4 by their angles.<br \/>\nAnswer:<\/p>\n<p>b. Classify triangles 4 &#8211; 6 by their sides.<br \/>\nAnswer:<\/p>\n<p>c. Is there enough information given to prove that \u22067 \u2245 \u22068? If so, label the vertices<br \/>\nand write a proof. If not, determine what additional information is needed.<br \/>\nAnswer:<\/p>\n<h3><a id=\"5.5_Proving_Triangle_Congruence_by_SSS\"><\/a>5.5 Proving Triangle Congruence by SSS<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Drawing Triangles<\/p>\n<p>Work with a partner.<br \/>\nUse dynamic geometry software.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40449\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-131.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 131\" width=\"309\" height=\"244\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-131.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-131-300x237.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40448\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-132.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 132\" width=\"307\" height=\"236\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-132.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-132-300x231.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40447\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-133.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 133\" width=\"556\" height=\"204\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-133.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-133-300x110.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>a. Construct circles with radii of 2 units and 3 units centered at the origin. Label the origin A. Then draw \\(\\overline{B C}\\) of length 4 units.<br \/>\nAnswer:<\/p>\n<p>b. Move \\(\\overline{B C}\\) so that B is on the smaller circle and C is on the larger circle. Then draw \u2206ABC.<br \/>\nAnswer:<\/p>\n<p>c. Explain why the side lengths of \u2206ABC are 2, 3, and 4 units.<br \/>\nAnswer:<\/p>\n<p>d. Find m\u2220A, m\u2220B, and m\u2220C.<br \/>\nAnswer:<\/p>\n<p>e. Repeat parts (b)and (d) several times, moving \\(\\overline{B C}\\) to different locations. Keep track of \u2018our results by copying and completing the table below. What can you conclude?<br \/>\n<strong>USING TOOLS STRATEGICALLY<\/strong><br \/>\nTo be proficient in math, you need to use technology to help visualize the results of varying assumptions, explore consequences, and compare predictions with data.<br \/>\nAnswer:<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 2.<br \/>\nWhat can you conclude about two triangles when you know the corresponding sides are congruent?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nHow would you prove your conclusion in Exploration 1(e)?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_5.5_Proving_Triangle_Congruence_by_SSS\"><\/a>Lesson 5.5 Proving Triangle Congruence by SSS<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Decide whether the congruence statement is true. Explain your reasoning.<\/p>\n<p>Question 1.<br \/>\n\u2206DFG \u2245 \u2206HJK<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40446\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-134.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 134\" width=\"162\" height=\"93\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n\u2206ACB \u2245 \u2206CAD<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40445\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-135.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 135\" width=\"141\" height=\"96\" \/><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n\u2206QPT \u2245 \u2206RST<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40444\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-136.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 136\" width=\"146\" height=\"85\" \/><br \/>\nAnswer:<\/p>\n<p>Determine whether the figure is stable. Explain your reasoning.<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40443\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-137.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 137\" width=\"116\" height=\"108\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40442\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-138.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 138\" width=\"130\" height=\"113\" \/><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40441\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-139.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 139\" width=\"133\" height=\"100\" \/><br \/>\nAnswer:<\/p>\n<p>Use the diagram.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40440\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-140.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 140\" width=\"163\" height=\"129\" \/><\/p>\n<p>Question 7.<br \/>\nRedraw \u2206ABC and \u2206DCB side by side with corresponding parts in the same position.<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nUse the information in the diagram to prove that \u2206ABC \u2245 \u2206DCB.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Exercise_5.5_Proving_Triangle_Congruence_by_SSS\"><\/a>Exercise 5.5 Proving Triangle Congruence by SSS<\/h3>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nThe side opposite the right angle is called the __________of the right triangle.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48802\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-1.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 5.5 a 1\" width=\"574\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-1.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-1-300x31.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WHICH ONE DOESNT BELONG?<\/strong><br \/>\nWhich triangles legs do not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40438\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-142.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 142\" width=\"708\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-142.png 708w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-142-300x45.png 300w\" sizes=\"(max-width: 708px) 100vw, 708px\" \/><br \/>\nAnswer:<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3 and 4, decide whether enough information is given to prove that the triangles are congruent using the SSS Congruence Theorem (Theorem 5.8). Explain.<\/p>\n<p>Question 3.<br \/>\n\u2206ABC, \u2206DBE<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40439\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-141.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 141\" width=\"134\" height=\"113\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48803\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-3.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 5.5 a 3\" width=\"349\" height=\"41\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-3.png 349w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-3-300x35.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/><\/p>\n<p>Question 4.<br \/>\n\u2206PQS, \u2206RQS<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40437\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-143.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 143\" width=\"107\" height=\"115\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 5 and 6, decide whether enough information is given to prove that the triangles are congruent using the HL Congruence Theorem (Theorem 5.9). Explain.<\/p>\n<p>Question 5.<br \/>\n\u2206ABC, \u2206FED<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40436\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-144.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 144\" width=\"128\" height=\"116\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48804\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-5.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 5.5 a 5\" width=\"528\" height=\"42\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-5.png 528w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-5-300x24.png 300w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><\/p>\n<p>Question 6.<br \/>\n\u2206PQT, \u2206SRT<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40435\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-145.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 145\" width=\"136\" height=\"105\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 7-10. decide whether the congruence statement is true. Explain your reasoning.<\/p>\n<p>Question 7.<br \/>\n\u2206RST \u2245 \u2206TQP<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40434\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-146.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 146\" width=\"181\" height=\"73\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48805\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-7.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 5.5 a 7\" width=\"546\" height=\"91\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-7.png 546w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-7-300x50.png 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p>Question 8.<br \/>\n\u2206ABD \u2245 \u2206CDB<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40433\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-147.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 147\" width=\"162\" height=\"74\" \/><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n\u2206DEF \u2245 \u2206DGF<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40432\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-148.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 148\" width=\"134\" height=\"107\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48806\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-9.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 5.5 a 9\" width=\"539\" height=\"118\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-9.png 539w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-9-300x66.png 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/p>\n<p>Question 10.<br \/>\n\u2206JKL \u2245 \u2206LJM<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40431\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-149.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 149\" width=\"121\" height=\"126\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 11 and 12, determine whether the figure is stable. Explain your reasoning.<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40430\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-150.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 150\" width=\"134\" height=\"94\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48807\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-11.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 5.5 a 11\" width=\"578\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-11.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-11-300x57.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40429\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-151.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 151\" width=\"150\" height=\"94\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 13 and 14, redraw the triangles so they are side by side with corresponding parts in the same position. Then write a proof.<\/p>\n<p>Question 13.<br \/>\nGiven \\(\\overline{A C}\\) \u2245 \\(\\overline{B D}\\)<br \/>\n\\(\\overline{A B}\\) \u22a5 \\(\\overline{A D}\\)<br \/>\n\\(\\overline{C D}\\) \u22a5 \\(\\overline{A D}\\)<br \/>\nProve \u2206BAD \u2245 \u2206CDA<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40428\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-152.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 152\" width=\"168\" height=\"123\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48808\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-13.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 5.5 a 13\" width=\"560\" height=\"764\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-13.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-13-220x300.png 220w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 14.<br \/>\nGiven G is the midpoint of \\(\\overline{E H}\\), \\(\\overline{F G}\\) \u2245 \\(\\overline{G I}\\), \u2220E and \u2220H are right angles.<br \/>\nProve \u2206EFG \u2245 \u2206HIG<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40427\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-153.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 153\" width=\"230\" height=\"192\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 15 and 16. write a proof.<\/p>\n<p>Question 15.<br \/>\nGiven \\(\\overline{L M}\\) \u2245 \\(\\overline{J K}\\), \\(\\overline{M J}\\) \u2245 \\(\\overline{K L}\\)<br \/>\nProve \u2206LMJ \u2245 \u2206JKL<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40426\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-154.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 154\" width=\"238\" height=\"98\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48809\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-15.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 5.5 a 15\" width=\"553\" height=\"388\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-15.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-15-300x210.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 16.<br \/>\nGiven \\(\\overline{W X}\\) \u2245 \\(\\overline{V Z}\\), \\(\\overline{W Y}\\) \u2245 \\(\\overline{V Y}\\), \\(\\overline{Y Z}\\) \u2245 \\(\\overline{Y X}\\)<br \/>\nProve \u2206VWX \u2245 \u2206WVZ<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40425\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-155.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 155\" width=\"243\" height=\"103\" \/><br \/>\nAnswer:<\/p>\n<p><strong>CONSTRUCTION<\/strong><br \/>\nIn Exercises 17 and 18, construct a triangle that is congruent to \u2206QRS using the SSS Congruence Theorem Theorem 5.8).<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40424\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-156.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 156\" width=\"112\" height=\"84\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48810\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-17.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 5.5 a 17\" width=\"556\" height=\"301\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-17.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-17-300x162.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40423\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-157.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 157\" width=\"111\" height=\"82\" \/><br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in identifying congruent triangles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40422\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-158.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 158\" width=\"355\" height=\"142\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-158.png 355w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-158-300x120.png 300w\" sizes=\"(max-width: 355px) 100vw, 355px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48811\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-19.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 5.5 a 19\" width=\"556\" height=\"118\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-19.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-19-300x64.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 20.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in determining the value of x that makes the triangles congruent.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40421\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-159.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 159\" width=\"344\" height=\"163\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-159.png 344w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-159-300x142.png 300w\" sizes=\"(max-width: 344px) 100vw, 344px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims that in order to use the SSS Congruence Theorem (Theorem 5.8) Lo prove that two triangles are congruent, both triangles must be equilateral triangles. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48812\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-21.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 5.5 a 21\" width=\"579\" height=\"89\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-21.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-21-300x46.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 22.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe distances between consecutive bases on a softball field are the same. The distance from home plate to second base is the same as the distance from first base to third base. The angles created at each base are 90\u00b0. Prove<br \/>\n\u2206HFS \u2245 \u2206FST \u2245 \u2206STH<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40420\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-160.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 160\" width=\"264\" height=\"197\" \/><br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n<strong>REASONING<\/strong><br \/>\nTo support a tree you attach wires from the trunk of the tree to stakes in the ground, as shown in the diagram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40419\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-161.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 161\" width=\"291\" height=\"217\" \/><br \/>\na. What additional information do you need to use the HL Congruence Theorem (Theorem 5.9) to prove that \u2206JKL \u2245 \u2206MKL?<br \/>\nb. Suppose K is the midpoint of JM. Name a theorem you could use to prove that \u2206JKL \u2245 \u2206MKL. Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48813\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-23.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 5.5 a 23\" width=\"568\" height=\"174\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-23.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-23-300x92.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 24.<br \/>\n<strong>REASONING<\/strong><br \/>\nUse the photo of the Navajo rug, where \\(\\overline{B C}\\) \u2245 \\(\\overline{D E}\\) and \\(\\overline{A C}\\) \u2245 \\(\\overline{C E}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40418\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-162.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 162\" width=\"274\" height=\"110\" \/><br \/>\na. What additional intormation do you need to use the SSS Congruence Theorem (Theorem 5.8) to prove that \u2206ABC \u2245 \u2206CDE?<br \/>\nb. What additional information do you need to use the HL Congruence Theorem (Theorem 5.9) to prove that \u2206ABC \u2245 \u2206CDE?<br \/>\nAnswer:<\/p>\n<p>In Exercises 25-28. use the given coordinates to determine whether \u2206ABC \u2245 \u2206DEF.<\/p>\n<p>Question 25.<br \/>\nA(- 2, &#8211; 2), B(4, &#8211; 2), C(4, 6), D(5, 7), E(5, 1), F(13, 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48814\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-25.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 5.5 a 25\" width=\"554\" height=\"430\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-25.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-25-300x233.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 26.<br \/>\nA(- 2, 1), B(3, &#8211; 3), C(7, 5), D(3, 6), E(S, 2), F( 10, 11)<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\nA(0, 0), B(6, 5), C(9, 0), D(0, &#8211; 1), E(6, &#8211; 6), F(9, &#8211; 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48815\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-27.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 5.5 a 27\" width=\"546\" height=\"447\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-27.png 546w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-27-300x246.png 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p>Question 28.<br \/>\nA(- 5, 7), B(- 5, 2), C(0, 2), D(0, 6), E(o, 1), F(4, 1)<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nYou notice two triangles in the tile floor of a hotel lobby. You want to determine whether the triangles are congruent. but you only have a piece of string. Can you determine whether the triangles are congruent? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48816\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-29.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 5.5 a 29\" width=\"571\" height=\"114\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-29.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-29-300x60.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThere are several theorems you can use to show that the triangles in the \u201csquare\u201d pattern are congruent. Name two of them.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40417\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-163.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 163\" width=\"204\" height=\"207\" \/><br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour cousin says that \u2206JKL is congruent to \u2206LMJ by the SSS Congruence Theorem (Thm. 5.8). Your friend says that \u2206JKL is congruent to \u2206LMJ by the HL Congruence Theorem (Thm. 5.9). Who is correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40416\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-164.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 164\" width=\"116\" height=\"114\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48817\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-31.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 5.5 a 31\" width=\"578\" height=\"172\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-31.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-31-300x89.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nThe postulates and theorems in this book represent Euclidean geometry. In spherical geometry. all points are points on the surface of a sphere. A line is a circle on the sphere whose diameter is equal to the diameter of the sphere. In spherical geometry. do you think that two triangles are congruent if their corresponding sides are congruent? Justify your answer.<br \/>\nAnswer:<\/p>\n<p><strong>USING TOOLS<\/strong><br \/>\nIn Exercises 33 and 34, use the given information to sketch \u2206LMN and \u2206STU. Mark the triangles with the given information.<\/p>\n<p>Question 33.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40415\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-165.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 165\" width=\"307\" height=\"28\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-165.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-165-300x27.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48818\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-33.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 5.5 a 33\" width=\"359\" height=\"184\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-33.png 359w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-33-300x154.png 300w\" sizes=\"(max-width: 359px) 100vw, 359px\" \/><\/p>\n<p>Question 34.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40414\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-166.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 166\" width=\"297\" height=\"28\" \/><br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nThe diagram shows the light created by two spotlights, Both spotlights are the same distance from the stage.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40413\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-167.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 167\" width=\"271\" height=\"179\" \/><br \/>\nAnswer:<br \/>\na. Show that \u2206ABD \u2245 \u2206CBD. State which theorem or postulate you used and explain your reasoning.<br \/>\nb. Are all four right triangles shown in the diagram Congruent? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48819\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-35.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 5.5 a 35\" width=\"572\" height=\"258\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-35.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-35-300x135.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nFind all values of x that make the triangles congruent. Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40412\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-168.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 168\" width=\"297\" height=\"87\" \/><br \/>\nAnswer:<\/p>\n<p>Maintaining Mathematical proficiency<\/p>\n<p>Use the congruent triangles.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40411\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-169.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 169\" width=\"382\" height=\"130\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-169.png 382w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-169-300x102.png 300w\" sizes=\"(max-width: 382px) 100vw, 382px\" \/><\/p>\n<p>Question 37.<br \/>\nName the Segment in \u2206DEF that is congruent to \\(\\overline{A C}\\).<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48820\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-37.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 5.5 a 37\" width=\"374\" height=\"38\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-37.png 374w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-37-300x30.png 300w\" sizes=\"(max-width: 374px) 100vw, 374px\" \/><\/p>\n<p>Question 38.<br \/>\nName the segment in \u2206ABC that is congruent to \\(\\overline{E F}\\).<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\nName the angle in \u2206DEF that is congruent to \u2220B.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48821\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-39.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 5.5 a 39\" width=\"384\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-39.png 384w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-5.5-a-39-300x26.png 300w\" sizes=\"(max-width: 384px) 100vw, 384px\" \/><\/p>\n<p>Question 40.<br \/>\nName the angle in \u2206ABC that is congruent to \u2220F.<br \/>\nAnswer:<\/p>\n<h3><a id=\"5.6_Proving_Triangle_Congruence_by_ASA_and_AAS\"><\/a>5.6 Proving Triangle Congruence by ASA and AAS<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Determining Whether SSA Is Sufficient<\/p>\n<p>Work with a partner.<br \/>\na. Use dynamic geometry software to construct \u2206ABC. Construct the triangle so that vertex B is at the origin. \\(\\overline{A B}\\) has a length of 3 units. and \\(\\overline{B C}\\) has a length of 2 units.<br \/>\nAnswer:<\/p>\n<p>b. Construct a circle with a radius of 2 units centered at the origin. Locate point D where the circle intersects \\(\\overline{A C}\\). Draw \\(\\overline{B D}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40917\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-170.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 170\" width=\"430\" height=\"260\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-170.png 430w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-170-300x181.png 300w\" sizes=\"(max-width: 430px) 100vw, 430px\" \/><br \/>\nAnswer:<\/p>\n<p>c. \u2206ABC and \u2206ABD have two congruent sides and a non included congruent angle.<br \/>\nName them.<br \/>\nAnswer:<\/p>\n<p>d. Is \u2206ABC \u2245 \u2206ABD? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>e. Is SSA sufficient to determine whether two triangles are congruent? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Determining Valid Congruence Theorems<\/p>\n<p>Work with a partner. Use dynamic geometry software to determine which of the following are valid triangle congruence theorems. For those that are not valid. write a counter example. Explain your reasoning.<br \/>\n<strong>CONSTRUCTING VIABLE ARGUMENTS<\/strong><br \/>\nTo be proficient in math, you need to recognize and use counterexamples.<\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td width=\"198\">Possible Congruence Theorem<\/td>\n<td width=\"132\">Valid or not valid?<\/td>\n<\/tr>\n<tr>\n<td width=\"198\">SSS<\/td>\n<td width=\"132\"><\/td>\n<\/tr>\n<tr>\n<td width=\"198\">SSA<\/td>\n<td width=\"132\"><\/td>\n<\/tr>\n<tr>\n<td width=\"198\">SAS<\/td>\n<td width=\"132\"><\/td>\n<\/tr>\n<tr>\n<td width=\"198\">AAS<\/td>\n<td width=\"132\"><\/td>\n<\/tr>\n<tr>\n<td width=\"198\">ASA<\/td>\n<td width=\"132\"><\/td>\n<\/tr>\n<tr>\n<td width=\"198\">AAA<\/td>\n<td width=\"132\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Answer:<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 3.<br \/>\nWhat information is sufficient to determine whether two triangles are congruent?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nIs it possible to show that two triangles are congruent using more than one congruence theorem? If so, give an example.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_5.6_Proving_Triangle_Congruence_by_ASA_and_AAS\"><\/a>Lesson 5.6 Proving Triangle Congruence by ASA and AAS<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nCan the triangles be proven congruent with the information given in the diagram? If so, state the theorem you would use.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40644\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-171.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 171\" width=\"122\" height=\"94\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nIn the diagram, \\(\\overline{A B}\\) \u22a5 \\(\\overline{A D}\\), \\(\\overline{D E}\\) \u22a5 \\(\\overline{A D}\\), and \\(\\overline{A C}\\) \u2245 \\(\\overline{D C}\\) . Prove \u2206ABC \u2245 \u2206DEF.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40643\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-172.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 172\" width=\"213\" height=\"124\" \/><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nIn the diagram, \u2220S \u2245 \u2220U and \\(\\overline{B D}\\)\\(\\overline{B D}\\) . Prove that \u2206RST \u2245 \u2206VYT<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40642\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-173.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 173\" width=\"139\" height=\"113\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_5.6_Proving_Triangle_Congruence_by_ASA_and_AAS\"><\/a>Lesson 5.6 Proving Triangle Congruence by ASA and AAS<\/h3>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nHow arc the AAS Congruence Theorem (Theorem 5. 11) and the ASA Congruence<br \/>\nTheorem (Theorem 5.10) similar? How are they different?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48824\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-1.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 1\" width=\"585\" height=\"206\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-1.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-1-300x106.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nYou know that a pair of triangles has two pairs of congruent corresponding angles. What other information do you need to show that the triangles are congruent?<br \/>\nAnswer:<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3-6, decide whether enough information is given to prove that the triangles are congruent. If so, state the theorem you would use.<\/p>\n<p>Question 3.<br \/>\n\u2206ABC, \u2206QRS<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40641\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-174.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 174\" width=\"145\" height=\"125\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48825\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-3.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 3\" width=\"590\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-3.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-3-300x31.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p>Question 4.<br \/>\n\u2206ABC, \u2206DBC<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40640\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-175.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 175\" width=\"151\" height=\"129\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n\u2206XYZ, \u2206JKL<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40639\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-176.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 176\" width=\"188\" height=\"123\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48826\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-5.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 5\" width=\"543\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-5.png 543w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-5-300x32.png 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/p>\n<p>Question 6.<br \/>\n\u2206RSV, \u2206UTV<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40638\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-177.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 177\" width=\"150\" height=\"117\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 7 and 8, state the third congruence statement that is needed to prove that \u2206FGH \u2245 \u2206LMN the given theorem.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40637\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-178.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 178\" width=\"212\" height=\"151\" \/><br \/>\nQuestion 7.<br \/>\nGiven \\(\\overline{G H}\\) \u2245 \\(\\overline{M N}\\), \u2220G \u2245 \u2220M, _______ = ________<br \/>\nUse the AAS Congruence Theorem (Thm. 5.11).<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48827\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-7.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 7\" width=\"402\" height=\"37\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-7.png 402w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-7-300x28.png 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><\/p>\n<p>Question 8.<br \/>\nGiven \\(\\overline{F G}\\) \u2245 \\(\\overline{L M}\\), \u2220G \u2245 \u2220M, _______ = ________<br \/>\nUse the ASA Congruence Theorem (Thm. 5.10).<br \/>\nAnswer:<\/p>\n<p>In Exercises 9 &#8211; 12. decide whether you can use the given information to prove that \u2206ABC \u2245 \u2206DEF Explain your reasoning.<\/p>\n<p>Question 9.<br \/>\n\u2220A \u2245 \u2220G, \u2220C \u2245\u2220F, \\(\\overline{A C}\\) \u2245 \\(\\overline{D F}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48828\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-9.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 9\" width=\"526\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-9.png 526w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-9-300x33.png 300w\" sizes=\"(max-width: 526px) 100vw, 526px\" \/><\/p>\n<p>Question 10.<br \/>\n\u2220C \u2245 \u2220F, \\(\\overline{A B}\\) \u2245 \\(\\overline{D E}\\), \\(\\overline{B C}\\) \u2245 \\(\\overline{E F}\\)<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n\u2220B \u2245 \u2220E, \u2220C \u2245\u2220F, \\(\\overline{A C}\\) \u2245 \\(\\overline{D E}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48829\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-11.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 11\" width=\"411\" height=\"41\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-11.png 411w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-11-300x30.png 300w\" sizes=\"(max-width: 411px) 100vw, 411px\" \/><\/p>\n<p>Question 12.<br \/>\n\u2220A \u2245 \u2220D, \u2220B \u2245\u2220E, \\(\\overline{B C}\\) \u2245 \\(\\overline{E F}\\)<br \/>\nAnswer:<\/p>\n<p><strong>CONSTRUCTION<\/strong><br \/>\nIn Exercises 13 and 14, construct a triangle that is congruent to the given triangle using the ASA Congruence Theorem (Theorem 5.10). Use a compass and straightedge.<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40636\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-179.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 179\" width=\"136\" height=\"93\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48830\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-13.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 13\" width=\"577\" height=\"233\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-13.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-13-300x121.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40635\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-180.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 180\" width=\"143\" height=\"96\" \/><br \/>\nAnswer:<\/p>\n<p><strong>ERROR ANALYSIS<\/strong><br \/>\nIn Exercises 15 and 16, describe and correct the error.<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40634\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-181.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 181\" width=\"345\" height=\"120\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-181.png 345w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-181-300x104.png 300w\" sizes=\"(max-width: 345px) 100vw, 345px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48831\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-15.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 15\" width=\"499\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-15.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-15-300x52.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40633\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-182.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 182\" width=\"349\" height=\"105\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-182.png 349w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-182-300x90.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>PROOF<\/strong><br \/>\nIn Exercises 17 and 18, prove that the triangles are congruent using the ASA Congruence Theorem (Theorem 5.10).<\/p>\n<p>Question 17.<br \/>\nGiven M is the midpoint of \\(\\overline{N L}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40632\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-183.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 183\" width=\"214\" height=\"27\" \/><br \/>\nProve \u2206NQM \u2245 \u2206MPL<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40631\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-184.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 184\" width=\"266\" height=\"122\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48832\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-17.1.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 17.1\" width=\"562\" height=\"595\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-17.1.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-17.1-283x300.png 283w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48833\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-17.2.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 17.2\" width=\"550\" height=\"187\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-17.2.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-17.2-300x102.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 18.<br \/>\nGiven \\(\\overline{A J}\\) \u2245 \\(\\overline{K C}\\) \u2220BJK \u2245 \u2220BKJ, \u2220A \u2245 \u2220C<br \/>\nProve \u2206ABK \u2245 \u2206CBJ<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40630\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-185.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 185\" width=\"247\" height=\"98\" \/><br \/>\nAnswer:<\/p>\n<p><strong>PROOF<\/strong><br \/>\nIn Exercises 19 and 20, prove that the triangles are congruent using the AAS Congruence Theorem (Theorem 5.11).<\/p>\n<p>Question 19.<br \/>\nGiven \\(\\overline{V W}\\) \u2245 \\(\\overline{U W}\\), \u2220X \u2245 \u2220Z<br \/>\nProve \u2206XWV \u2245 \u2206ZWU<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40629\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-186.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 186\" width=\"240\" height=\"103\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48834\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-19.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 19\" width=\"565\" height=\"403\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-19.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-19-300x214.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 20.<br \/>\nGiven \u2220NKM \u2245\u2220LMK, \u2220L \u2245\u2220N<br \/>\nProve \u2206NMK \u2245 \u2206LKM<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40628\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-187.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 187\" width=\"238\" height=\"98\" \/><br \/>\nAnswer:<\/p>\n<p><strong>PROOF<\/strong><br \/>\nIn Exercises 21-23, write a paragraph proof for the theorem about right triangles.<\/p>\n<p>Question 21.<br \/>\nHypotenuse-Angle (HA) Congruence Theorem<br \/>\nIf an angle and the hypotenuse of a right triangle are congruent to an angle and the hypotenuse of a second right triangle, then the triangles are congruent.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48835\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-21.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 21\" width=\"575\" height=\"165\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-21.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-21-300x86.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 22.<br \/>\nLeg-Leg (LL) Congruence Theorem<br \/>\nIf the legs of a right triangle are congruent to the legs of a second right triangle, then the triangles are congruent.<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\nAngle-Leg (AL) Congruence Theorem<br \/>\nIf an angle and a leg of a right triangle are congruent to an angle and a leg of a second right triangle, then the triangles are Congruent.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48836\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-23.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 23\" width=\"567\" height=\"247\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-23.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-23-300x131.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 24.<br \/>\n<strong>REASONING<\/strong><br \/>\nWhat additional in information do you need to prove \u2206JKL \u2245 \u2206MNL by the ASA Congruence Theorem (Theorem 5. 10)?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40627\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-188.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 188\" width=\"136\" height=\"138\" \/><br \/>\n(A) \\(\\overline{K M}\\) \u2245 \\(\\overline{K J}\\)<br \/>\n(B) \\(\\overline{K H}\\) \u2245 \\(\\overline{N H}\\)<br \/>\n(C) \u2220M \u2245 \u2220J<br \/>\n(D) \u2220LKJ \u2245 \u2220LNM<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nThis toy contains \u25b3ABC and \u25b3DBC. Can you conclude that \u25b3ABC \u2245 \u25b3DBC from the given angle measures? Explain<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40626\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-189.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 189\" width=\"135\" height=\"104\" \/><br \/>\nm\u2220ABC = (8x &#8211; 32)\u00b0<br \/>\nm\u2220DBC = (4y &#8211; 24)\u00b0<br \/>\nm\u2220BCA = (5x + 10)\u00b0<br \/>\nm\u2220BCD = (3y + 2)\u00b0<br \/>\nm\u2220CAB = (2x &#8211; 8)\u00b0<br \/>\nm\u2220CDB = (y &#8211; 6)\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48837\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-25.1.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 25.1\" width=\"577\" height=\"552\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-25.1.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-25.1-300x287.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48838\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-25.2.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 25.2\" width=\"525\" height=\"411\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-25.2.png 525w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-25.2-300x235.png 300w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>REASONING<\/strong><br \/>\nWhich of the following congruence statements are true? Select all that apply.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40625\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-190.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 190\" width=\"133\" height=\"135\" \/><br \/>\n(A) \\(\\overline{B D}\\) \u2245 \\(\\overline{B D}\\)<br \/>\n(B) \u2206STV \u2245 \u2206XVW<br \/>\n(C) \u2206TVS \u2245 \u2206VWU<br \/>\n(D) \u2206VST \u2245 \u2206VUW<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nProve the Converse of the Base Angles Theorem (Theorem 5.7). (Hint: Draw an auxiliary line inside the triangle.)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48839\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-27.1.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 27.1\" width=\"568\" height=\"602\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-27.1.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-27.1-283x300.png 283w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48840\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-27.2.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 27.2\" width=\"574\" height=\"180\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-27.2.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-27.2-300x94.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims to be able Lo rewrite any proof that uses the AAS Congruence Theorem (Thin. 5. 11) as a proof that uses the ASA Congruence Theorem (Thin. 5.10). Is this possible? Explain our reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nWhen a light ray from an object meets a mirror, it is reflected back to your eye. For example, in the diagram, a light ray from point C is reflected at point D and travels back to point A. The law of reflection states that the angle of incidence, \u2220CDB. is congruent to the angle of reflection. \u2220ADB.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40624\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-191.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 191\" width=\"154\" height=\"319\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-191.png 154w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-191-145x300.png 145w\" sizes=\"(max-width: 154px) 100vw, 154px\" \/><br \/>\na. Prove that \u2206ABD is Congruent to \u2206CBD.<br \/>\nGiven \u2220CBD \u2245\u2220ABD<br \/>\nDB \u22a5 AC<br \/>\nProve \u2206ABD \u2245 \u2206CBD<br \/>\nb. Verify that \u2206ACD is isosceles.<br \/>\nc. Does moving away from the mirror have an effect on the amount of his or her reflection a person sees? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48841\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-29.1.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 29.1\" width=\"566\" height=\"524\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-29.1.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-29.1-300x278.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48842\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-29.2.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 29.2\" width=\"589\" height=\"213\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-29.2.png 589w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-29.2-300x108.png 300w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nName as man pairs of congruent triangles as you can from the diagram. Explain how you know that each pair of triangles is congruent.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40623\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-192.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 192\" width=\"200\" height=\"128\" \/><br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<strong>CONSTRUCTION<\/strong><br \/>\nConstruct a triangle. Show that there is no AAA congruence rule by constructing a second triangle that has the same angle measures but is not congruent.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48843\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-31.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 31\" width=\"559\" height=\"329\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-31.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-31-300x177.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nGraph theory is a branch of mathematics that studies vertices and the way they are connected. In graph theory. two polygons are isomorphic if there is a one-to-one mapping from one polygon\u2019s vertices to the other polygon\u2019s vertices that preserves adjacent vertices. In graph theory, are any two triangles isomorphic? Explain your reasoning. second triangle that has the same angle measures but is not congruent.<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\nMathematical Connections<br \/>\nSix statements are given about \u2206TUV and \u2206XYZ<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40622\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-193.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 193\" width=\"322\" height=\"185\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-193.png 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-193-300x172.png 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\na. List all combinations of three given statements that could provide enough information to prove that \u2206TUV is congruent to \u2206XYZ.<br \/>\nb. You choose three statements at random. What is the probability that the statements you choose provide enough information to prove that the triangles are congruent?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48844\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-33.1.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 33.1\" width=\"559\" height=\"594\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-33.1.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-33.1-282x300.png 282w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48845\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-33.2.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 33.2\" width=\"578\" height=\"256\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-33.2.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-33.2-300x133.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Maintaining Mathematical proficiency<\/p>\n<p>Find the coordinates of the midpoint of the line segment with the given endpoints.<\/p>\n<p>Question 34.<br \/>\nC(1, 0) and D(5, 4)<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\nJ(- 2, 3) and K(4, &#8211; 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48846\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-35.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 35\" width=\"488\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-35.png 488w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-35-300x34.png 300w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><\/p>\n<p>Question 36.<br \/>\nR(- 5, &#8211; 7) and S(2, &#8211; 4)<br \/>\nAnswer:<\/p>\n<p>Copy and angle using a compass and straightedge.<\/p>\n<p>Question 37.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40621\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-194.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 194\" width=\"208\" height=\"135\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48847\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-37.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 5.6 a 37\" width=\"573\" height=\"253\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-37.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-5.6-a-37-300x132.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 38.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40620\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-195.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 195\" width=\"167\" height=\"144\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"5.7_Using_Congruent_Triangles\"><\/a>5.7 Using Congruent Triangles<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Measuring the Width of a River<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40918\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-219.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 219\" width=\"295\" height=\"239\" \/><\/p>\n<p>Work with a partner:<br \/>\nThe figure shows how a surveyor can measure the width of a river by making measurements on only one side of the river.<\/p>\n<p>a. Study the figure. Then explain how the surveyor can find the width of the river.<br \/>\nAnswer:<\/p>\n<p>b. Write a proof to verify that the method you described in part (a) is valid.<br \/>\nGiven \u2220A is a right angle, \u2220D is a right angle, \\(\\overline{A C}\\) \u2245 \\(\\overline{C D}\\)<br \/>\nAnswer:<\/p>\n<p>c. Exchange Proofs with your partner and discuss the reasoning used.<br \/>\n<strong>CRITIQUING THE REASONING OF OTHERS<\/strong><br \/>\nTo be proficient in math, you need to listen to or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.<br \/>\nAnswer:<\/p>\n<p>Exploration 2<\/p>\n<p>Measuring the Width of a River<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40915\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-196.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 196\" width=\"275\" height=\"164\" \/><\/p>\n<p>Work with a partner. It was reported that one of Napoleon\u2019s offers estimated the width of a river as follows. The officer stood on the hank of the river and lowered the visor on his cap until the farthest thin visible was the edge of the bank on the other side. He then turned and rioted the point on his side that was in line with the tip of his visor and his eye. The officer then paced the distance to this point and concluded that distance was the width of the river.<\/p>\n<p>a. Study the figure. Then explain how the officer concluded that the width of the river is EG.<br \/>\nAnswer:<\/p>\n<p>b. Write a proof to verify that the conclusion the officer made is correct.<br \/>\nGiven \u2220DEG is a right angle, \u2220DEF is a right angle, \u2220EDG \u2245 \u2220EDF<br \/>\nAnswer:<\/p>\n<p>c. Exchange proofs with your partner and discuss the reasoning used.<br \/>\nAnswer:<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 3.<br \/>\nHow can you use congruent triangles to make an indirect measurement?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nWhy do you think the types of measurements described in Explorations 1 and 2 are called indirect measurements?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_5.7_Using_Congruent_Triangles\"><\/a>Lesson 5.7 Using Congruent Triangles<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nExplain how you can prove that \u2220A \u2245 \u2220C.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40914\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-197.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 197\" width=\"171\" height=\"108\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nIn Example 2, does it mailer how far from point N you place a stake at point K? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nWrite a plan to prove that \u2206PTU \u2245 \u2206UQP.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40913\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-198.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 198\" width=\"182\" height=\"110\" \/><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nUse the construction of an angle bisector on page 42. What segments can you assume are congruent?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Exercise_5.7_Using_Congruent_Triangles\"><\/a>Exercise 5.7 Using Congruent Triangles<\/h3>\n<p>Vocabulary and core concept check<\/p>\n<p>Question 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\n_____________ parts of congruent triangle are congruent.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48848\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-1.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.7 a 1\" width=\"545\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-1.png 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-1-300x18.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nDescribe a situation in which you might choose to use indirect measurement with<br \/>\ncongruent triangles to find a measure rather than measuring directly.<br \/>\nAnswer:<\/p>\n<p>Monitoring Progress and Modeling With Mathematics<\/p>\n<p>In Exercise 3-8, explain how to prove that the statement is true.<\/p>\n<p>Question 3.<br \/>\n\u2220A \u2245 \u2220D<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40912\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-199.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 199\" width=\"189\" height=\"85\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48849\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-3.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.7 a 3\" width=\"573\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-3.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-3-300x59.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 4.<br \/>\n\u2220Q \u2245\u2220T<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40911\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-200.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 200\" width=\"185\" height=\"96\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n\\(\\overline{J M}\\) \u2245 \\(\\overline{L M}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40910\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-201.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 201\" width=\"171\" height=\"91\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48850\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-5.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.7 a 5\" width=\"593\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-5.png 593w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-5-300x57.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><\/p>\n<p>Question 6.<br \/>\n\\(\\overline{A C}\\) \u2245 \\(\\overline{D B}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40909\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-202.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 202\" width=\"184\" height=\"92\" \/><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n\\(\\overline{G K}\\) \u2245 \\(\\overline{H J}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40908\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-203.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 203\" width=\"187\" height=\"90\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48851\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-7.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.7 a 7\" width=\"584\" height=\"116\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-7.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-7-300x60.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 8.<br \/>\n\\(\\overline{Q W}\\) \u2245 \\(\\overline{V T}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40907\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-204.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 204\" width=\"168\" height=\"116\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 9-12, write a plan to prove that \u22201 \u2245\u22202.<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40906\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-205.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 205\" width=\"169\" height=\"99\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48852\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-9.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.7 a 9\" width=\"596\" height=\"125\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-9.png 596w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-9-300x63.png 300w\" sizes=\"(max-width: 596px) 100vw, 596px\" \/><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40905\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-206.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 206\" width=\"200\" height=\"95\" \/><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-207.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 207\" width=\"166\" height=\"98\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48853\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-11.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.7 a 11\" width=\"587\" height=\"141\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-11.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-11-300x72.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40903\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-208.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 208\" width=\"181\" height=\"104\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 13 and 14. write a proof to verify that the construction is valid.<\/p>\n<p>Question 13.<br \/>\nLine perpendicular to a line through a point not on the line<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40902\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-209.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 209\" width=\"156\" height=\"157\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-209.png 156w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-209-150x150.png 150w\" sizes=\"(max-width: 156px) 100vw, 156px\" \/><br \/>\nPlan for proof \u2206APQ \u2245 \u2206BPQ by the congruence Theorem (Theorem 5.8). Then show the \u2206APM \u2245 \u2206BPM using the SAS Congruence Theorem (Theorem 5.5). Use corresponding parts of congruent triangles to show that \u2220AMP and \u2220BMP are right angles.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48854\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-13.1.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.7 a 13.1\" width=\"556\" height=\"582\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-13.1.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-13.1-287x300.png 287w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48855\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-13.2.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.7 a 13.2\" width=\"545\" height=\"394\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-13.2.png 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-13.2-300x217.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Question 14.<br \/>\nLine perpendicular to a line through a p0int on the line<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40901\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-210.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 210\" width=\"149\" height=\"158\" \/><br \/>\nPlan for Proof Show that \u2206APQ \u2245 \u2206BPQ by the SSS Congruence Theorem (Theorem 5.8) Use corresponding parts of congruent triangles to show that \u2220QPA and \u2220QPB are right angles.<br \/>\nAnswer:<\/p>\n<p>In Exercises 15 and 16, use the information given in the diagram to write a proof.<\/p>\n<p>Question 15.<br \/>\nProve \\(\\overline{F L}\\) \u2245 \\(\\overline{H N}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40900\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-211.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 211\" width=\"188\" height=\"158\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48856\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-15.1.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.7 a 15.1\" width=\"563\" height=\"601\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-15.1.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-15.1-281x300.png 281w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48857\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-15.2.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.7 a 15.2\" width=\"543\" height=\"541\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-15.2.png 543w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-15.2-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-15.2-150x150.png 150w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/p>\n<p>Question 16.<br \/>\nProve \u2206PUX \u2245 \u2206QSY<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40899\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-212.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 212\" width=\"253\" height=\"145\" \/><br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nExplain how to find the distance across the canyon.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40898\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-213.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 213\" width=\"361\" height=\"162\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-213.png 361w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-213-300x135.png 300w\" sizes=\"(max-width: 361px) 100vw, 361px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48858\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-17.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.7 a 17\" width=\"581\" height=\"203\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-17.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-17-300x105.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 18.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nUse the tangram puzzle.<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40897\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-214.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 214\" width=\"162\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-214.png 162w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-214-150x150.png 150w\" sizes=\"(max-width: 162px) 100vw, 162px\" \/><\/p>\n<p>a. Which triangle(s) have an area that is twice the area of the purple triangle?<br \/>\nb. How man times greater is the area of the orange triangle than the area of the purple triangle?<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<strong>PROOF<\/strong><br \/>\nProve that the green triangles in the Jamaican flag congruent if \\(\\overline{A D}\\) || \\(\\overline{B C}\\) and E is the midpoint of \\(\\overline{A C}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40896\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-215.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 215\" width=\"290\" height=\"183\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48859\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-19.1.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.7 a 19.1\" width=\"541\" height=\"644\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-19.1.png 541w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-19.1-252x300.png 252w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48860\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-19.2.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.7 a 19.2\" width=\"571\" height=\"242\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-19.2.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-19.2-300x127.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 20.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nThe Bermuda Triangle is a region in the Atlantic Ocean in which many ships and planes have mysteriously disappeared. The vertices are Miami. San Juan. and Bermuda. Use the Internet or some other resource to find the side lengths. the perimeter, and the area of this triangle (in miles). Then create a congruent triangle on land using cities as vertices.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40895\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-216.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 216\" width=\"322\" height=\"223\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-216.png 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-216-300x208.png 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims that \u2206WZY can be proven congruent to \u2206YXW using the HL Congruence Theorem (Thm. 5.9). Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40894\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-217.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 217\" width=\"201\" height=\"109\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48861\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-21.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.7 a 21\" width=\"584\" height=\"179\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-21.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-21-300x92.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 22.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nDetermine whether each conditional statement is true or false. If the statement is false, rewrite it as a true statement using the converse, inverse, or contrapositive.<br \/>\na. If two triangles have the same perimeter, then they are congruent.<br \/>\nb. If two triangles are congruent. then they have the same area.<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n<strong>ATTENDING TO PRECISION<\/strong><br \/>\nWhich triangles are congruent to \u2206ABC? Select all that apply.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40893\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-218.png\" alt=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles 218\" width=\"378\" height=\"201\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-218.png 378w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-5-Congruent-Triangles-218-300x160.png 300w\" sizes=\"(max-width: 378px) 100vw, 378px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48862\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-23.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.7 a 23\" width=\"585\" height=\"193\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-23.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-23-300x99.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Maintaining Mathematical Proficiency<\/p>\n<p>Find the perimeter of the polygon with the given vertices.<\/p>\n<p>Question 24.<br \/>\nA(- 1, 1), B(4, 1), C(4, &#8211; 2), D(- 1, &#8211; 2)<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\nJ(- 5, 3), K(- 2, 1), L(3, 4)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48863\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-25.png\" alt=\"Big Ideas Math Answers Geometry Chapter 5 Congruent Triangles 5.7 a 25\" width=\"505\" height=\"373\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-25.png 505w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-5-Congruent-Triangles-5.7-a-25-300x222.png 300w\" sizes=\"(max-width: 505px) 100vw, 505px\" \/><\/p>\n<h3><a id=\"5.8_Coordinate_Proofs\"><\/a>5.8 Coordinate Proofs<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Writing a coordinate Proof<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40964\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-218.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 218\" width=\"387\" height=\"240\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-218.png 387w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-218-300x186.png 300w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><\/p>\n<p>Work with a partner.<\/p>\n<p>a. Use dynamic geometry software to draw \\(\\overline{A B}\\) with endpoints A(0, 0) and B(6, 0).<br \/>\nAnswer:<\/p>\n<p>b. Draw the vertical line x = 3.<br \/>\nAnswer:<\/p>\n<p>c. Draw \u2206ABC so that C lies on the line x = 3.<br \/>\nAnswer:<\/p>\n<p>d. Use your drawing to prove that \u2206ABC is an isosceles triangle.<br \/>\nAnswer:<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Writing a Coordinate proof<\/p>\n<p>Work with a partner.<\/p>\n<p>a. Use dynamic geometry software to draw \\(\\overline{A B}\\) with endpoints A(0, 0) and B(6, 0).<\/p>\n<p>b. Draw the vertical line x = 3.<\/p>\n<p>c. Plot the point C(3, 3) and draw \u2206ABC. Then use your drawing to prove that \u2206ABC is an isosceles right triangle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40963\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-219.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 219\" width=\"402\" height=\"245\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-219.png 402w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-219-300x183.png 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><\/p>\n<p>d. Change the coordinates of C so that C lies below the x-axis and \u2206ABC is an isosceles right triangle.<br \/>\nAnswer:<\/p>\n<p>e. Write a coordinate proof to show that if C lies on the line x = 3 and \u2206ABC is an isosceles right triangle. then C must be the point (3, 3) or the point found in part (d).<br \/>\n<strong>CRITIQUING THE REASONING OF OTHERS<\/strong><br \/>\nTo be proficient in math, you need to understand and use stated assumptions, definitions, and previously established results.<br \/>\nAnswer:<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 3.<br \/>\nHow can you use a coordinate plane to write a proof?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nWrite a coordinate proof to prove that \u2206ABC with vertices A(0, 0), 8(6, 0), and C(3, 3\u221a3) is an equilateral triangle.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_5.8_Coordinate_Proofs\"><\/a>Lesson 5.8 Coordinate Proofs<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nShow another way to place the rectangle in Example 1 part (a) that is convenient<br \/>\nfor finding side lengths. Assign new coordinates.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nA square has vertices (0, 0), (m, 0), and (0, m), Find the fourth vertex.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nWrite a plan for the proof.<br \/>\nGiven \\(\\vec{G}\\)J bisects \u2220OGH.<br \/>\nProof \u2206GJO \u2245 \u2206GJH<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40962\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-220.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 220\" width=\"175\" height=\"157\" \/><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nGraph the points 0(0, 0), H(m, n), and J(m, 0). Is \u2206OHJ a right triangle? Find the side lengths and the coordinates of the midpoint of each side.<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nWrite a coordinate proof.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40961\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-221.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 221\" width=\"244\" height=\"167\" \/><br \/>\nGiven Coordinates of vertices of \u2206NPO and \u2206NMO<br \/>\nProve \u2206NPO \u2245 \u2206NMO<br \/>\nAnswer:<\/p>\n<h3><a id=\"Exercise_5.8_Coordinate_Proofs\"><\/a>Exercise 5.8 Coordinate Proofs<\/h3>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nHow is a coordinate proof different from other types of proofs you have studied?<br \/>\nHow is it the same?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48864\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-1.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.8 a 1\" width=\"589\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-1.png 589w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-1-300x90.png 300w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain why it is convenient to place a right triangle on the grid as shown when writing a coordinate proof.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40960\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-222.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 222\" width=\"168\" height=\"117\" \/><br \/>\nAnswer:<\/p>\n<p>Maintaining Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3-6, place (he figure in a coordinate plane in a convenient way. Assign coordinates to each vertex. Explain the advantages of your placement.<\/p>\n<p>Question 3.<br \/>\na right triangle with leg lengths of 3 units and 2 units<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48865\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-3.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.8 a 3\" width=\"512\" height=\"340\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-3.png 512w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-3-300x199.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/p>\n<p>Question 4.<br \/>\na square with a side length of 3 units<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nan isosceles right triangle with leg length p<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48866\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-5.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.8 a 5\" width=\"515\" height=\"339\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-5.png 515w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-5-300x197.png 300w\" sizes=\"(max-width: 515px) 100vw, 515px\" \/><\/p>\n<p>Question 6.<br \/>\na scalene triangle with one side length of 2m<br \/>\nAnswer:<\/p>\n<p>In Exercises 7 and 8, write a plan for the proof.<\/p>\n<p>Question 7.<br \/>\nGiven Coordinates of vertices of \u2206OPM and \u2206ONM Prove \u2206OPM and \u2206ONM are isosceles triangles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40959\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-223.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 223\" width=\"176\" height=\"144\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48867\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-7.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.8 a 7\" width=\"501\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-7.png 501w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-7-300x36.png 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><\/p>\n<p>Question 8.<br \/>\nGiven G is the midpoint of \\(\\overline{H F}\\).<br \/>\nProve \u2206GHJ \u2245 \u2206GFO<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40958\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-224.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 224\" width=\"191\" height=\"141\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 9-12, place the figure in a coordinate plane and find the indicated length.<\/p>\n<p>Question 9.<br \/>\na right triangle with leg lengths of 7 and 9 units; Find the length of the hypotenuse.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48868\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-9.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.8 a 9\" width=\"466\" height=\"369\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-9.png 466w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-9-300x238.png 300w\" sizes=\"(max-width: 466px) 100vw, 466px\" \/><\/p>\n<p>Question 10.<br \/>\nan isosceles triangle with a base length of 60 units and a height of 50 units: Find the length of one of the legs.<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\na rectangle with a length o! 5 units and a width of 4 units: Find the length of the diagonal.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48869\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-11.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.8 a 11\" width=\"446\" height=\"324\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-11.png 446w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-11-300x218.png 300w\" sizes=\"(max-width: 446px) 100vw, 446px\" \/><\/p>\n<p>Question 12.<br \/>\na square with side length n: Find the length of the diagonal.<br \/>\nAnswer:<\/p>\n<p>In Exercises 13 and 14, graph the triangle with the given vertices. Find the length and the slope of each side of the triangle. Then find the coordinates of the midpoint of each side. Is the triangle a right triangle? isosceles? Explain. Assume all variables are positive and in m \u2260 n.)<\/p>\n<p>Question 13.<br \/>\nA(0, 0), B(h, h), C(2h, 0)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48870\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-13.1.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.8 a 13.1\" width=\"584\" height=\"558\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-13.1.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-13.1-300x287.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48871\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-13.2.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.8 a 13.2\" width=\"574\" height=\"329\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-13.2.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-13.2-300x172.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 14.<br \/>\nD(0, n), E(m, n), F(m, 0)<br \/>\nAnswer:<\/p>\n<p>In Exercises 15 and 16, find the coordinates of any unlabeled vertices. Then find the indicated length(s).<\/p>\n<p>Question 15.<br \/>\nFind ON and MN.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40957\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-225.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 225\" width=\"189\" height=\"114\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48872\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-15.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.8 a 15\" width=\"550\" height=\"118\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-15.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-15-300x64.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 16.<br \/>\nFind OT.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40956\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-226.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 226\" width=\"179\" height=\"120\" \/><br \/>\nAnswer:<\/p>\n<p><strong>PROOF<\/strong><br \/>\nIn Exercises 17 and 18, rite a coordinate proof.<\/p>\n<p>Question 17.<br \/>\nGiven Coordinates of vertices of \u2206DEC and \u2206BOC<br \/>\nProve \u2206DEC \u2245 \u2206BOC<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40955\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-227.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 227\" width=\"213\" height=\"142\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48873\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-17.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.8 a 17\" width=\"580\" height=\"452\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-17.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-17-300x234.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 18.<br \/>\nGiven Coordinates of \u2206DEA, H is the midpoint of \\(\\overline{D A}\\), G is the mid point of \\(\\overline{E A}\\)<br \/>\nProve \\(\\overline{D G}\\) \u2245 \\(\\overline{E H}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40954\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-228.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 228\" width=\"204\" height=\"126\" \/><br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou and your cousin are camping in the woods. You hike to a point that is 500 meters cast and 1200 meters north of the Campsite. Your cousin hikes to a point that is 1000 meters cast of the campsite. Use a coordinate proof to prove that the triangle formed by your Position, your Cousin\u2019s position. and the campsite is isosceles. (See Example 5.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40953\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-229.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 229\" width=\"204\" height=\"123\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48874\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-19.1.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.8 a 19.1\" width=\"548\" height=\"611\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-19.1.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-19.1-269x300.png 269w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48875\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-19.2.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.8 a 19.2\" width=\"571\" height=\"565\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-19.2.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-19.2-300x297.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 20.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nTwo friends see a drawing of quadrilateral PQRS with vertices P(0, 2), Q(3, &#8211; 4), R(1, &#8211; 5), and S(- 2, 1). One friend says the quadrilateral is a parallelogram but not a rectangle. The other friend says the quadrilateral is a rectangle. Which friend is correct? Use a coordinate proof to support your answer.<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nWrite an algebraic expression for the coordinates of each endpoint of a line segment whose midpoint is the origin.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48876\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-21.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.8 a 21\" width=\"582\" height=\"119\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-21.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-21-300x61.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 22.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe vertices of a parallelogram are (w, 0), (o, v), (- w, 0), and (0, &#8211; v). What is the midpoint of the side in Quadrant III?<br \/>\n(a) \\(\\left(\\frac{w}{2}, \\frac{v}{2}\\right)\\)<br \/>\n(b) \\(\\left(-\\frac{w}{2},-\\frac{v}{2}\\right)\\)<br \/>\n(c) \\(\\left(-\\frac{w}{2}, \\frac{v}{2}\\right)\\)<br \/>\n(d) \\(\\left(\\frac{w}{2},-\\frac{v}{2}\\right)\\)<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n<strong>REASONING<\/strong><br \/>\nA rectangle with a length of 3h and a width of k has a vertex at (- h, k), Which point cannot be a vertex of the rectangle?<br \/>\n(A) (h, k)<br \/>\n(B) (- h, 0)<br \/>\n(c) (2h, 0)<br \/>\n(D) (2h, k)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48877\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-23.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.8 a 23\" width=\"297\" height=\"273\" \/><\/p>\n<p>Question 24.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nChoose one of the theorems you have encountered up to this point that you think would be easier to prove with a coordinate proof than with another type of proof. Explain your reasoning. Then write a coordinate proof.<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nThe coordinates of a triangle are (5d &#8211; 5d), (0, &#8211; 5d), and (5d, 0). How sh<br \/>\nwould the coordinates be changed to make a coordinate proof easier to complete?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48878\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-25.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.8 a 25\" width=\"571\" height=\"163\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-25.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-25-300x86.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nwithout performing any calculations, how do you know that the diagonals of square TUVW are perpendicular to each oilier? How can you use a similar diagram to show that the diagonals of any square are perpendicular to each other?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40952\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-230.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 230\" width=\"210\" height=\"143\" \/><br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<strong>PROOF<\/strong><br \/>\nWrite a coordinate proof for each statement.<br \/>\na. The midpoint o! the hypotenuse of a right triangle is the same distance from each vertex of the triangle.<br \/>\nb. Any two congruent right isosceles triangles can be combined to form a single isosceles triangle.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48879\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-27.1.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.8 a 27.1\" width=\"574\" height=\"639\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-27.1.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-27.1-269x300.png 269w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48880\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-27.2.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.8 a 27.2\" width=\"578\" height=\"196\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-27.2.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-27.2-300x102.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Maintaining Mathematical proficiency<\/p>\n<p>\\(\\vec{Y}\\)W bisects \u2220XYZ such that m\u2220XYW = (3x &#8211; 7)\u00b0 and m\u2220WYZ = (2x + 1)\u00b0.<\/p>\n<p>Question 28.<br \/>\nFind the value of x.<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\nFind m\u2220XYZ<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48881\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-29.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 5 Congruent Triangles 5.8 a 29\" width=\"425\" height=\"147\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-29.png 425w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-5-Congruent-Triangles-5.8-a-29-300x104.png 300w\" sizes=\"(max-width: 425px) 100vw, 425px\" \/><\/p>\n<h3><a id=\"Congruent_Triangles_Chapter_Review\"><\/a>Congruent Triangles Chapter Review<\/h3>\n<h3>5.1 Angles of Triangles<\/h3>\n<p>Question 1.<br \/>\nClassify the triangle at the right by its sides and by measuring its angles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41004\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-231.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 231\" width=\"102\" height=\"98\" \/><br \/>\nAnswer:<\/p>\n<p>Find the measure of the exterior angle.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41003\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-232.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 232\" width=\"163\" height=\"75\" \/><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41001\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-234.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 234\" width=\"128\" height=\"88\" \/><br \/>\nAnswer:<\/p>\n<p>Find the measure of each acute angle.<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41000\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-235.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 235\" width=\"98\" height=\"90\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40999\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-236.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 236\" width=\"181\" height=\"85\" \/><br \/>\nAnswer:<\/p>\n<h3>5.2 Congruent Polygons<\/h3>\n<p>Question 6.<br \/>\nIn the diagram. GHJK \u2245 LMNP. Identify all pairs of congruent corresponding parts. Then write another congruence statement for the quadrilaterals.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40998\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-237.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 237\" width=\"280\" height=\"144\" \/><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nFind m \u2220 V.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40997\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-238.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 238\" width=\"296\" height=\"97\" \/><br \/>\nAnswer:<\/p>\n<h3>5.3 Proving Triangle Congruence by SAS<\/h3>\n<p>Decide whether enough information is given to prove that \u2206WXZ \u2245 \u2206YZX using the SAS Congruence Theorem (Theorem 5.5). If so, write a proof. If not, explain why.<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40996\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-239.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 239\" width=\"145\" height=\"173\" \/><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40995\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-240.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 240\" width=\"150\" height=\"170\" \/><br \/>\nAnswer:<\/p>\n<h3>5.4 Equilateral and Isosceles Triangles<\/h3>\n<p>Copy and Complete the statement.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40994\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-241.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 241\" width=\"219\" height=\"108\" \/><\/p>\n<p>Question 10.<br \/>\nIf \\(\\overline{Q P}\\) \u2245 \\(\\overline{Q R}\\), then \u2220 ______ \u2245 \u2220 ______ .<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nIf \u2220TRV \u2245 \u2220TVR, then ______ \u2245 ______ .<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nIf \\(\\overline{R Q} \\cong \\overline{R S}\\), then \u2220 ______ \u2245 \u2220 ______ .<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nIf \u2220SRV \u2245 \u2220SVR, then ______ \u2245 ______ .<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nFind the values of x and y in the diagram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40993\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-242.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 242\" width=\"200\" height=\"92\" \/><br \/>\nAnswer:<\/p>\n<h3>5.5 Proving Triangle Congruence by SSS<\/h3>\n<p>Question 15.<br \/>\nDecide whether enough information is given to prose that \u2206LMP \u2245 \u2206NPM using the SSS Congruence Theorem (Thin. 5.8). If so, write a proof. If not, explain why.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40992\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-243.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 243\" width=\"215\" height=\"116\" \/><br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\nDecide whether enough information is given to prove that \u2206WXZ \u2245 \u2206YZX using the HL Congruence Theorem (Thm. 5.9). If so, write a proof. If not, explain why.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40991\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-244.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 244\" width=\"139\" height=\"106\" \/><br \/>\nAnswer:<\/p>\n<h3>5.6 Proving Triangle Congruence by ASA and AAS<\/h3>\n<p>Question 17.<br \/>\n\u2206EFG, \u2206HJK<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40990\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-245.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 245\" width=\"234\" height=\"100\" \/><br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\n\u2206TUS, \u2206QRS<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40989\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-246.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 246\" width=\"304\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-246.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-246-300x109.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><br \/>\nAnswer:<\/p>\n<p>Decide whether enough information is given to prove that the triangles are congruent using the ASA Congruence Theorem (Thm. 5.10). If so, write a proof, If not, explain why.<\/p>\n<p>Question 19.<br \/>\n\u2206LPN, \u2206LMN<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40988\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-247.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 247\" width=\"182\" height=\"136\" \/><br \/>\nAnswer:<\/p>\n<p>Question 20.<br \/>\n\u2206WXZ, \u2206YZX<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40987\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-248.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 248\" width=\"142\" height=\"132\" \/><br \/>\nAnswer:<\/p>\n<h3>5.7 Using Congruent Triangles<\/h3>\n<p>Question 21.<br \/>\nExplain how to prove that \u2220K \u2245\u2220N.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40986\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-249.png\" alt=\"\" width=\"265\" height=\"134\" \/><br \/>\nAnswer:<\/p>\n<p>Question 22.<br \/>\nWrite a plan to prkove that \u22201 \u2245 \u22202<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40985\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-250.png\" alt=\"\" width=\"167\" height=\"108\" \/><br \/>\nAnswer:<\/p>\n<h3>5.8 Coordinate Proofs<\/h3>\n<p>Question 23.<br \/>\nWrite a coordinate proof.<br \/>\nGiven Coordinates of vertices of quadrilateral OPQR<br \/>\nProve \u2206OPQ \u2245 \u2206QRO<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40984\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-251.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 251\" width=\"199\" height=\"176\" \/><br \/>\nAnswer:<\/p>\n<p>Question 24.<br \/>\nPlace an isosceles triangle in a coordinate plane in a way that is convenient for finding side lengths. Assign coordinates to each vertex.<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\nA rectangle has vertices (0, 0), (2k, 0), and (0, k), Find the fourth vertex.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Congruent_Triangles_Test\"><\/a>Congruent Triangles Test<\/h3>\n<p>Write a Proof.<\/p>\n<p>Question 1.<br \/>\nGiven \\(\\overline{C A} \\cong \\overline{C B} \\cong \\overline{C D} \\cong \\overline{C E}\\)<br \/>\nProve \u2206ABC \u2245 \u2206EDC<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41023\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-252.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 252\" width=\"168\" height=\"123\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nGiven \\(\\overline{J K}\\|\\overline{M L}, \\overline{M J}\\| \\overline{K L}\\)<br \/>\nProve \u2206MJK \u2245 \u2206KLM<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41022\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-253.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 253\" width=\"198\" height=\"110\" \/><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nGven \\overline{Q R} \\cong \\overrightarrow{R S}\\(\\), \u2220P \u2245 \u2220T<br \/>\nProve \u2206SRP \u2245 \u2206QRT<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41021\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-254.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 254\" width=\"195\" height=\"121\" \/><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nFind the measure of each acute angle in the figure at the right.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41020\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-255.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 255\" width=\"137\" height=\"103\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nIs it possible to draw an equilateral triangle that is not equiangular? If so, provide an example. If not, explain why.<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nCan you use the Third Angles Theorem (Theorem 5.4) to prove that two triangles are congruent? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Write a plan through that \u22201 \u2245\u22202<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41019\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-256.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 256\" width=\"117\" height=\"130\" \/><br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41018\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-257.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 257\" width=\"155\" height=\"140\" \/><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nIs there more than one theorem that could be used to prove that \u2206ABD \u2245 \u2206CDB? If so, list all possible theorems.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41017\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-258.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 258\" width=\"176\" height=\"132\" \/><br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nWrite a coordinate proof t0 show that the triangles created b the keyboard stand are congruent.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41016\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-259.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 259\" width=\"207\" height=\"224\" \/><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nThe picture shows the Pyramid of Cestius. which is located in Rome, Italy. The measure of the base for the triangle shown is 100 Roman feet. The measures of the other two sides of the triangle are both 144 Roman feet.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41014\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-5-Congruent-Triangles-260.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles 260\" width=\"252\" height=\"246\" \/><br \/>\na. Classify the triangle shown by its sides.<br \/>\nAnswer:<\/p>\n<p>b. The measure of \u22203 is 40\u00b0 What are the measures of \u22201 and \u22202? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Congruent_Triangles_Cumulative_Assessment\"><\/a>Congruent Triangles Cumulative Assessment<\/h3>\n<p>Question 1.<br \/>\nYour friend claims that the Exterior Angle Theorem (Theorem 5.2) can be used to prove the Triangle Sum Theorem (Theorem 5, 1). Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nUse the steps in the construction to explain how you know that the line through point P is parallel to line m.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41038\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-261.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 261\" width=\"684\" height=\"255\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-261.png 684w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-261-300x112.png 300w\" sizes=\"(max-width: 684px) 100vw, 684px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nThe coordinate plane shows \u2206JKL and \u2206XYZ<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41037\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-262.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 262\" width=\"210\" height=\"208\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-262.png 210w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-262-150x150.png 150w\" sizes=\"(max-width: 210px) 100vw, 210px\" \/><br \/>\na. Write a composition of transformations that maps \u2206JKL to \u2206XYZ<br \/>\nAnswer:<\/p>\n<p>b. Is the composition a congruence transformation? If so, identify all congruent corresponding parts.<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nThe directed line segment RS is shown. Point Q is located along \\(\\overline{R S}\\) so that the ratio of RQ to QS is 2 to 3. What are the coordinates of point Q?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41036\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-263.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 263\" width=\"246\" height=\"208\" \/><br \/>\n(A) Q(1, 2, 3)<br \/>\n(B) Q(4, 2)<br \/>\n(C) Q(2, 3)<br \/>\n(D) Q(-6, 7)<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nThe coordinate plane shows that \u2206ABC and \u2206DEF<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41035\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-264.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 264\" width=\"211\" height=\"208\" \/><br \/>\na. Prove \u2206ABC \u2245 \u2206DEF using the given information.<br \/>\nAnswer:<\/p>\n<p>b. Describe the composition of rigid motions that maps \u2206ABC to \u2206DEF<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nThe vertices of a quadrilateral are W(0, 0), X(- 1, 3), )(2, 7), and Z(4, 2). Your friend claims that point W will not change after dilatinig quadrilateral WXYZ by a scale factor of 2. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nWhich figure(s) have rotational symmetry? Select all that apply.<br \/>\n(A) <img loading=\"lazy\" class=\"alignnone size-full wp-image-41034\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-265.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 265\" width=\"114\" height=\"113\" \/><br \/>\n(B) <img loading=\"lazy\" class=\"alignnone size-full wp-image-41033\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-266.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 266\" width=\"111\" height=\"109\" \/><br \/>\n(C) <img loading=\"lazy\" class=\"alignnone size-full wp-image-41032\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-267.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 267\" width=\"78\" height=\"111\" \/><br \/>\n(D) <img loading=\"lazy\" class=\"alignnone size-full wp-image-41031\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-268.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 268\" width=\"103\" height=\"102\" \/><br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nWrite a coordinate proof.<br \/>\nGiven Coordinates of vertices of quadrilateral ABCD<br \/>\nProve Quadrilateral ABCD is a rectangle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41030\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-269.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 269\" width=\"207\" height=\"206\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-269.png 207w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-269-150x150.png 150w\" sizes=\"(max-width: 207px) 100vw, 207px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nWrite a proof to verify that the construction of the equilateral triangle shown below is valid.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41029\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-270.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 5 Congruent Triangles 270\" width=\"705\" height=\"171\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-270.png 705w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-5-Congruent-Triangles-270-300x73.png 300w\" sizes=\"(max-width: 705px) 100vw, 705px\" \/><br \/>\nAnswer:<\/p>\n","protected":false},"excerpt":{"rendered":"<p>If you are looking across the web for better preparation resources regarding the Big Ideas Math Geometry Ch 5 Congruent Triangles then this is the one stop destination for all your needs. For better understanding of the concepts we have compiled all the Big Ideas Math Geometry Answers Ch 5 Congruent Triangles in a simple &#8230; <a title=\"Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-geometry-answers-chapter-5\/\" aria-label=\"More on Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles\">Read more<\/a><\/p>\n","protected":false},"author":7,"featured_media":89480,"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-5.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/39742"}],"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\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=39742"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/39742\/revisions"}],"predecessor-version":[{"id":90292,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/39742\/revisions\/90292"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89480"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=39742"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=39742"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=39742"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}