{"id":47138,"date":"2022-04-03T16:02:31","date_gmt":"2022-04-03T10:32:31","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=47138"},"modified":"2022-04-07T11:10:57","modified_gmt":"2022-04-07T05:40:57","slug":"big-ideas-math-geometry-answers-chapter-8","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-geometry-answers-chapter-8\/","title":{"rendered":"Big Ideas Math Geometry Answers Chapter 8 Similarity"},"content":{"rendered":"<p><span style=\"font-size: 16px;\">Do you want a perfect guide for a better understanding of Similarity concepts in High School? Then, <\/span><span style=\"font-size: 16px;\"><strong>Big Ideas Math Geometry Answers Chapter 8 Similarity<\/strong> is the one-stop destination for all your requirements during preparation. Practicing and Solving no. of questions from chapter 8 similarity BIM Geometry Textbook Solutions is the best way to understand the concepts easily and gain more subject knowledge. Kickstart your preparation by taking the help of BigIdeas math geometry ch 8 similarity Answer key pdf and test your skills up-to-date for better scoring in the exams and become math proficient.\u00a0\u00a0<\/span><\/p>\n<h2>Big Ideas Math Book Geometry Answer Key Chapter 8 Similarity<\/h2>\n<p>Get the handy preparation material free of cost and enhance your math skills with ease. To make this possible, students have to access the given links below and download the <em><strong><a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-geometry-answers\/\">Big Ideas Math Geometry Textbook Answers<\/a> Ch 8 Similar<\/strong><strong>ity <\/strong><strong>in Pdf.<\/strong><\/em> In this guide, teachers, parents, and kids can find various questions from basic to complex levels. By solving the questions of chapter 8 similarity covered in BIM Geometry Ch 8 Answer key exercises, practice tests, chapter tests, cumulative assessments, etc. helps you to improve your skills &amp; knowledge.<\/p>\n<ul>\n<li><a href=\"#Similarity_Maintaining_Mathematical_Proficiency\">Similarity Maintaining Mathematical Proficiency &#8211; Page 415<\/a><\/li>\n<li><a href=\"#Similarity_Mathematical_Practices\">Similarity Mathematical Practices &#8211; Page 416<\/a><\/li>\n<li><a href=\"#8.1_Similar_Polygons\">8.1 Similar Polygons &#8211; Page 417<\/a><\/li>\n<li><a href=\"#Lesson_8.1_Similar_Polygons\">Lesson 8.1 Similar Polygons &#8211; Page (418-426)<\/a><\/li>\n<li><a href=\"#Exercise_8.1_Similar_Polygons\">Exercise 8.1 Similar Polygons &#8211; Page (423-426)<\/a><\/li>\n<li><a href=\"#8.2_Proving_Triangle_Similarity_by_AA\">8.2 Proving Triangle Similarity by AA &#8211; Page 427<\/a><\/li>\n<li><a href=\"#Lesson_8.2_Proving_Triangle_Similarity_by_AA\">Lesson 8.2 Proving Triangle Similarity by AA &#8211; Page (428-432)<\/a><\/li>\n<li><a href=\"#Exercise_8.2_Proving_Triangle_Similarity_by_AA\">Exercise 8.2 Proving Triangle Similarity by AA &#8211; Page (431-432)<\/a><\/li>\n<li><a href=\"#8.1_&amp;_8.2_Quiz\">8.1 &amp; 8.2 Quiz &#8211; Page 434<\/a><\/li>\n<li><a href=\"#8.3_Proving_Triangle_Similarity_by_SSS_and_SAS\">8.3 Proving Triangle Similarity by SSS and SAS &#8211; Page 435<\/a><\/li>\n<li><a href=\"#Lesson_8.3_Proving_Triangle_Similarity_by_SSS_and_SAS\">Lesson 8.3 Proving Triangle Similarity by SSS and SAS &#8211; Page (436-444)<\/a><\/li>\n<li><a href=\"#Exercise_8.3_Proving_Triangle_Similarity_by_SSS_and_SAS\">Exercise 8.3 Proving Triangle Similarity by SSS and SAS &#8211; Page (441-444)<\/a><\/li>\n<li><a href=\"#8.4_Proportionality_Theorems\">8.4 Proportionality Theorems &#8211; Page 445<\/a><\/li>\n<li><a href=\"#Lesson_8.4_Proportionality_Theorems\">Lesson 8.4 Proportionality Theorems &#8211; Page (446-452)<\/a><\/li>\n<li><a href=\"#Exercise_8.4_Proportionality_Theorems\">Exercise 8.4 Proportionality Theorems &#8211; Page (450-452)<\/a><\/li>\n<li><a href=\"#Similarity_Chapter_Review\">Similarity Chapter Review &#8211; Page (454-456)<\/a><\/li>\n<li><a href=\"#Similarity_Chapter_Test\">Similarity Chapter Test &#8211; Page 457<\/a><\/li>\n<li><a href=\"#Similarity_Cumulative_Assessment\">Similarity Cumulative Assessment &#8211; Page (458-459)<\/a><\/li>\n<\/ul>\n<h3><a id=\"Similarity_Maintaining_Mathematical_Proficiency\"><\/a>Similarity Maintaining Mathematical Proficiency<\/h3>\n<p>Tell whether the ratios form a proportion.<\/p>\n<p>Question 1.<br \/>\n\\(\\frac{5}{3}, \\frac{35}{21}\\)<\/p>\n<p>Answer:<br \/>\nYes, the ratios \\(\\frac{5}{3}, \\frac{35}{21}\\) form a proportion.<\/p>\n<p>Explanation:<br \/>\nA proportion means two ratios are equal.<br \/>\nSo, cross product of \\(\\frac{5}{3}, \\frac{35}{21}\\) is 21 x 5 = 105 = 35 x 3<br \/>\nTherefore, \\(\\frac{5}{3}, \\frac{35}{21}\\) form a proportion.<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{9}{24}, \\frac{24}{64}\\)<\/p>\n<p>Answer:<br \/>\nYes, the ratios \\(\\frac{9}{24}, \\frac{24}{64}\\) form a proportion.<\/p>\n<p>Explanation:<br \/>\nIf the cross product of two ratios is equal, then it forms a proportion.<br \/>\nSo, 24 x 24 = 576 = 64 x 9<br \/>\nTherefore, the ratios \\(\\frac{9}{24}, \\frac{24}{64}\\) form a proportion.<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{8}{56}, \\frac{6}{28}\\)<\/p>\n<p>Answer:<br \/>\nThe ratios \\(\\frac{8}{56}, \\frac{6}{28}\\) do not form a proportion.<\/p>\n<p>Explanation:<br \/>\nIf the cross product of two ratios is equal, then it forms a proportion.<br \/>\nSo, 56 x 6 = 336, 28 x 8 = 224<br \/>\nTherefore, the ratios \\(\\frac{8}{56}, \\frac{6}{28}\\) do not form a proportion.<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{18}{4}, \\frac{27}{9}\\)<\/p>\n<p>Answer:<br \/>\nThe ratios \\(\\frac{18}{4}, \\frac{27}{9}\\) do not form a proportion.<\/p>\n<p>Explanation:<br \/>\nIf the cross product of two ratios is equal, then it forms a proportion.<br \/>\nSo, 9 x 18 = 162, 27 x 4 = 108<br \/>\nTherefore, the ratios \\(\\frac{18}{4}, \\frac{27}{9}\\) do not form a proportion.<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{15}{21}, \\frac{55}{77}\\)<\/p>\n<p>Answer:<br \/>\nThe ratios \\(\\frac{15}{21}, \\frac{55}{77}\\) form a proportion.<\/p>\n<p>Explanation:<br \/>\nIf the cross product of two ratios is equal, then it forms a proportion.<br \/>\nSo, 15 x 77 = 1155, 55 x 21 = 1155<br \/>\nTherefore, the ratios \\(\\frac{15}{21}, \\frac{55}{77}\\) form a proportion.<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{26}{8}, \\frac{39}{12}\\)<\/p>\n<p>Answer:<br \/>\nThe ratios \\(\\frac{26}{8}, \\frac{39}{12}\\) form a proportion.<\/p>\n<p>Explanation:<br \/>\nIf the cross product of two ratios is equal, then it forms a proportion.<br \/>\nSo, 26 x 12 = 312, 39 x 8 = 312<br \/>\nTherefore, the ratios \\(\\frac{26}{8}, \\frac{39}{12}\\) form a proportion.<\/p>\n<p>Find the scale factor of the dilation.<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47143\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 1\" width=\"164\" height=\"111\" \/><\/p>\n<p>Answer:<br \/>\nk = \\(\\frac { 3 }{ 7 } \\)<\/p>\n<p>Explanation:<br \/>\nThe scale factor k = \\(\\frac { CP&#8217; }{ CP } \\)<br \/>\n= \\(\\frac { 6 }{ 14 } \\)<br \/>\n= \\(\\frac { 3 }{ 7 } \\)<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47142\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-2.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 2\" width=\"157\" height=\"108\" \/><\/p>\n<p>Answer:<br \/>\nk = \\(\\frac { 3 }{ 8 } \\)<\/p>\n<p>Explanation:<br \/>\nThe scale factor k = \\(\\frac { CP }{ CP&#8217; } \\)<br \/>\n= \\(\\frac { 9 }{ 24 } \\)<br \/>\n= \\(\\frac { 3 }{ 8 } \\)<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47141\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 3\" width=\"192\" height=\"108\" \/><\/p>\n<p>Answer:<br \/>\nk =\u00a0\\(\\frac { 1 }{ 2 } \\)<\/p>\n<p>Explanation:<br \/>\nThe scale factor k = \\(\\frac { MK }{ M&#8217;K&#8217; } \\)<br \/>\n= \\(\\frac { 14 }{ 28 } \\)<br \/>\n= \\(\\frac { 1 }{ 2 } \\)<\/p>\n<p>Question 10.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nIf ratio X and ratio Y form a proportion and ratio Y and ratio Z form a proportion, do ratio X and ratio Z form a proportion? Explain our reasoning.<\/p>\n<p>Answer:<br \/>\nYes, ratio X and ratio Z form a proportion.<\/p>\n<p>Explanation:<br \/>\nIf ratios are proportional means they are equal.<br \/>\nSo, ratio X and ratio Y form a proportion that means X = Y<br \/>\nratio Y and ratio Z form a proportion that means Y = Z<br \/>\nFrom the above two equations, we can say that X = Z<br \/>\nSo, ratio X and ratio Z also form a proportion.<\/p>\n<h3><a id=\"Similarity_Mathematical_Practices\"><\/a>Similarity Mathematical Practices<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nFind the perimeter and area of the image when the trapezoid is dilated by a scale factor of<br \/>\n(a) 2, (b) 3, and (c) 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47140\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-4.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 4\" width=\"216\" height=\"122\" \/><\/p>\n<p>Answer:<br \/>\n(a) Perimeter is 32 cm, area is 48 sq cm.<br \/>\n(b) Perimeter is 48 cm, the area is 108 sq cm.<br \/>\n(c) Perimeter is 64 cm, the area is 192 sq cm.<\/p>\n<p>Explanation:<br \/>\nThe perimeter of trapezoid P = 2 + 5 + 6 + 3 = 16 cm<br \/>\nArea of trapezoid A = \\(\\frac { (2 + 6)3 }{ 2 } \\)<br \/>\n= \\(\\frac { 3(8) }{ 2 } \\)<br \/>\n= \\(\\frac { 24 }{ 2 } \\)<br \/>\n= 12 sq cm<br \/>\n(a) If scale factor k = 2, then<br \/>\nPerimeter = kP<br \/>\n= 2 x 16 = 32<br \/>\nArea = k\u00b2A<br \/>\n= 2\u00b2 x 12<br \/>\n= 4 x 12<br \/>\n= 48<br \/>\n(b) If scale factor k = 3, then,<br \/>\nPerimeter = kP<br \/>\n= 3 x 16 = 48 cm<br \/>\nArea = k\u00b2A<br \/>\n= 3\u00b2 x 12 = 9 x 12 = 108<br \/>\n(c) If scale factor k = 4, then<br \/>\nPerimeter = kP<br \/>\n= 4 x 16 = 64<br \/>\nArea = k\u00b2A<br \/>\n= 4\u00b2 x 12 = 16 x 12 = 192<\/p>\n<p>Question 2.<br \/>\nFind the perimeter and area of the image when the parallelogram is dilated by a scale factor of<br \/>\n(a) 2, (b) 3, and (c) \\(\\frac{1}{2}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47139\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 5\" width=\"199\" height=\"156\" \/><\/p>\n<p>Answer:<br \/>\n(a) Perimeter is 28 ft, area is 32 sq ft<br \/>\n(b) Perimeter is 42 ft, area is 72 sq ft<br \/>\n(c) Perimeter is 7 ft, area is 2 sq ft<\/p>\n<p>Explanation:<br \/>\nPerimeter of parallelogram P = 2(2 + 5) = 7 x 2 = 14 ft<br \/>\nArea of the parallelogram = 2 x 4 = 8 sq ft<br \/>\n(a) If scale factor k = 2, then<br \/>\nPerimeter = kP<br \/>\n= 2 x 14 = 28<br \/>\nArea = k\u00b2A<br \/>\n= 2\u00b2 x 8 = 4 x 8 = 32<br \/>\n(b) If scale factor k = 3, then<br \/>\nPerimeter = kP<br \/>\n= 3 x 14 = 42<br \/>\nArea = k\u00b2A<br \/>\n= 3\u00b2 x 8 = 72<br \/>\n(c) If scale factor k = \\(\\frac{1}{2}\\), then<br \/>\nPerimeter = kP<br \/>\n= \\(\\frac{1}{2}\\) x 14 = 7<br \/>\nArea = k\u00b2A<br \/>\n= \\(\\frac{1}{2\u00b2}\\) x 8 = \\(\\frac{1}{4}\\) x 8 = 2<\/p>\n<p>Question 3.<br \/>\nA rectangular prism is 3 inches wide, 4 inches long, and 5 inches tall. Find the surface area and volume of the image of the prism when it is dilated by a scale factor of<br \/>\n(a) 2, (b) 3, and (c) 4.<\/p>\n<p>Answer:<br \/>\n(a) Surface area is 376 sq in, volume is 480 cubic in<br \/>\n(b) Surface area is 846 sq in, volume is 1620 cubic in<br \/>\n(c) Surface area is 1504 sq in, volume is 3840 cubic in<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism A = 2(3 x 4 + 4 x 5 + 5 x 3)<br \/>\n= 2(12 + 20 + 15) = 2(47) = 94 in<br \/>\nVolume of the rectangular prism V = 3 x 4 x 5 = 60 in\u00b3<br \/>\n(a) If the scale factor k = 2, then<br \/>\nSurface Area = k\u00b2A<br \/>\n= 2\u00b2 x 94 = 4 x 94 = 376 sq in<br \/>\nVolume = k\u00b3V<br \/>\n= 2\u00b3 x 60 = 8 x 60 = 480 cubic in<br \/>\n(b) If the scale factor k = 3, then<br \/>\nSurface Area = k\u00b2A<br \/>\n= 3\u00b2 x 94 = 9 x 94 = 846<br \/>\nVolume = k\u00b3V<br \/>\n= 3\u00b3 x 60 = 27 x 60 = 1620<br \/>\n(c) If the scale factor k = 4, then<br \/>\nSurface Area = k\u00b2A<br \/>\n= 4\u00b2 x 94 = 16 x 94 = 1504<br \/>\nVolume\u00a0= k\u00b3V<br \/>\n= 4\u00b3 x 60 = 64 x 60 = 3840<\/p>\n<h3><a id=\"8.1_Similar_Polygons\"><\/a>8.1 Similar Polygons<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Comparing Triangles after a Dilation<\/p>\n<p>Work with a partner: Use dynamic geometry software to draw any \u2206ABC. Dilate \u2206ABC to form a similar \u2206A&#8217;B&#8217;C&#8217; using an scale factor k and an center of dilation.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-47880\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-6.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 6\" width=\"304\" height=\"237\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-6.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-6-300x234.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><\/p>\n<p>a. Compare the corresponding angles of \u2206A&#8217;B&#8217;C and \u2206ABC.<br \/>\nAnswer:<\/p>\n<p>b. Find the ratios of the lengths of the sides of \u2206A&#8217;B&#8217;C&#8217; to the lengths of the corresponding sides of \u2206ABC. What do you observe?<br \/>\nAnswer:<\/p>\n<p>c. Repeat parts (a) and (b) for several other triangles, scale factors, and centers of dilation. Do you obtain similar results?<br \/>\nAnswer:<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Comparing Triangles after a Dilation<\/p>\n<p>Work with a partner: Use dynamic geometry Software to draw any \u2206ABC. Dilate \u2206ABC to form a similar \u2206A&#8217;B&#8217;C&#8217; using any scale factor k and any center of dilation.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-47879\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-7.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 7\" width=\"309\" height=\"237\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-7.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-7-300x230.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><\/p>\n<p>a. Compare the perimeters of \u2206A&#8217;B&#8217;C and \u2206ABC. What do you observe?<br \/>\nAnswer:<\/p>\n<p>b. Compare the areas of \u2206A&#8217;B&#8217;C&#8217; and \u2206ABC. What do you observe?<br \/>\nAnswer:<\/p>\n<p>c. Repeat parts (a) and (b) for several other triangles, scale factors, and centers of dilation. Do you obtain similar results?<br \/>\n<strong>LOOKING FOR STRUCTURE<\/strong><br \/>\nTo be proficient in math, you need to look closely to discern a pattern or structure.<br \/>\nAnswer:<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 3.<br \/>\nHow are similar polygons related?<\/p>\n<p>Answer:<br \/>\nif two polygons are similar means they have the same shape, corresponding angles are congruent and the ratios of lengths of their corresponding sides are equal. The common ratio is called the scale factor.<\/p>\n<p>Question 4.<br \/>\nA \u2206RST is dilated by a scale factor of 3 to form \u2206R&#8217;S&#8217;T&#8217;. The area of \u2206RST is 1 square inch. What is the area of \u2206R&#8217;S&#8217;T&#8217;?<\/p>\n<p>Answer:<br \/>\nArea of \u2206R&#8217;S&#8217;T&#8217; = 9 sq in<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nArea of \u2206RST = 1 sq inch<br \/>\nScale factor k = 3<br \/>\nArea of \u2206R&#8217;S&#8217;T&#8217; = k\u00b2 x Area of \u2206RST<br \/>\n= 3\u00b2 x 1 = 9 x 1 = 9<\/p>\n<h3><a id=\"Lesson_8.1_Similar_Polygons\"><\/a>Lesson 8.1 Similar Polygons<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nIn the diagram, \u2206JKL ~ \u2206PQR. Find the scale factor from \u2206JKL to \u2206PQR. Then list all pairs of congruent angles and write the ratios of the corresponding side lengths in a statement of proportionality.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47878\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8\" width=\"245\" height=\"134\" \/><\/p>\n<p>Answer:<br \/>\nThe pairs of congruent angles are \u2220K = \u2220Q, \u2220J = \u2220P, \u2220 L = \u2220R<br \/>\nThe scale factor is \\(\\frac { 3 }{ 2 } \\)<br \/>\nThe ratios of the corresponding side lengths in a statement of proportionality are \\(\\frac { PQ }{ JK } = \\frac { PR }{ JL } = \\frac { QR }{ LK } \\)<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\n\u2206JKL ~ \u2206PQR<br \/>\nThe pairs of congruent angles are \u2220K = \u2220Q, \u2220J = \u2220P, \u2220 L = \u2220R<br \/>\nTo find the scale factor,<br \/>\n\\(\\frac { PQ }{ JK } = \\frac { 9 }{ 6 } \\) = \\(\\frac { 3 }{ 2 } \\), \\(\\frac { PR }{ JL } = \\frac { 12 }{ 8 } \\) = \\(\\frac { 3 }{ 2 } \\), \\(\\frac { QR }{ LK } = \\frac { 6 }{ 4 } \\) = \\(\\frac { 3 }{ 2 } \\)<br \/>\nSo, the scale factor is \\(\\frac { 3 }{ 2 } \\)<\/p>\n<p>Question 2.<br \/>\nFind the value of x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47877\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-9.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 9\" width=\"200\" height=\"89\" \/><br \/>\nABCD ~ QRST<\/p>\n<p>Answer:<br \/>\nx = 2<\/p>\n<p>Explanation:<br \/>\nThe triangles are similar, so corresponding side lengths are proportional.<br \/>\n\\(\\frac { RS }{ BC } \\) = \\(\\frac { AB }{ QR } \\)<br \/>\n\\(\\frac { 4 }{ x } \\) = \\(\\frac { 12 }{ 6 } \\)<br \/>\n\\(\\frac { 4 }{ x } \\) = 2<br \/>\n4 = 2x<br \/>\nx = 2<\/p>\n<p>Question 3.<br \/>\nFind KM<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47876\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-10.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 10\" width=\"216\" height=\"80\" \/><br \/>\n\u2206JKL ~ \u2206EFG<\/p>\n<p>Answer:<br \/>\nKM = 42<\/p>\n<p>Explanation:<br \/>\nScale factor = \\(\\frac { JM }{ GH } \\)<br \/>\n= \\(\\frac { 48 }{ 40 } \\)<br \/>\n= \\(\\frac { 6 }{ 5 } \\)<br \/>\nBecause the ratio of the lengths of the altitudes in similar triangles is equal to the scale factor, you can write the following proportion<br \/>\n\\(\\frac { KM }{ HF } \\) = \\(\\frac { 6 }{ 5 } \\)<br \/>\n\\(\\frac { KM }{ 35 } \\) = \\(\\frac { 6 }{ 5 } \\)<br \/>\nKM = \\(\\frac { 6 }{ 5 } \\) x 35<br \/>\nKM = 42<\/p>\n<p>Question 4.<br \/>\nThe two gazebos shown are similar pentagons. Find the perimeter of Gazebo A.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47875\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-11.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 11\" width=\"246\" height=\"132\" \/><\/p>\n<p>Answer:<br \/>\nPerimeter of Gazebo A = 46 m<\/p>\n<p>Explanation:<br \/>\nScale factor = \\(\\frac { AB }{ FG } \\)<br \/>\n= \\(\\frac { 10 }{ 15 } \\)<br \/>\n= \\(\\frac { 2 }{ 3 } \\)<br \/>\nSo, \\(\\frac { AE }{ FK } \\) = \\(\\frac { 2 }{ 3 } \\)<br \/>\n\\(\\frac { x }{ 18 } \\) = \\(\\frac { 2 }{ 3 } \\)<br \/>\nx = 12<br \/>\n\\(\\frac { ED }{ KJ } \\) = \\(\\frac { 2 }{ 3 } \\)<br \/>\n\\(\\frac { ED }{ 15 } \\) = \\(\\frac { 2 }{ 3 } \\)<br \/>\nED = 10<br \/>\n\\(\\frac { DC }{ JH } \\) = \\(\\frac { 2 }{ 3 } \\)<br \/>\n\\(\\frac { DC }{ 12 } \\) = \\(\\frac { 2 }{ 3 } \\)<br \/>\nDC = 8<br \/>\n\\(\\frac { BC }{ GH } \\) = \\(\\frac { 2 }{ 3 } \\)<br \/>\n\\(\\frac { BC }{ 9 } \\) = \\(\\frac { 2 }{ 3 } \\)<br \/>\nBC = 6<br \/>\nTherefore, perimeter = 6 + 8 + 10 + 12 + 10 = 46<\/p>\n<p>Question 5.<br \/>\nIn the diagram, GHJK ~ LMNP. Find the area of LMNP.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47874\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-12.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 12\" width=\"346\" height=\"119\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-12.png 346w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-12-300x103.png 300w\" sizes=\"(max-width: 346px) 100vw, 346px\" \/><br \/>\nArea of GHJK = 84m<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\nArea of LMNP = 756 m<sup>2<\/sup><\/p>\n<p>Explanation:<br \/>\nAs shapes are similar, their corresponding side lengths are proportional.<br \/>\nScale Factor k = \\(\\frac { NP }{ JK } \\)<br \/>\n= \\(\\frac { 21 }{ 7 } \\)<br \/>\n= 3<br \/>\nArea of LMNP = k\u00b2 x Area of GHJK<br \/>\n= 3\u00b2 x 84<br \/>\n= 756 m<sup>2<\/sup><\/p>\n<p>Question 6.<br \/>\nDecide whether the hexagons in Tile Design 1 are similar. Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47873\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-13.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 13\" width=\"203\" height=\"219\" \/><\/p>\n<p>Answer:<\/p>\n<p>Question 7.<br \/>\nDecide whether the hexagons in Tile Design 2 are similar. Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47872\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-14.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 14\" width=\"200\" height=\"217\" \/><\/p>\n<p>Answer:<\/p>\n<h3><a id=\"Exercise_8.1_Similar_Polygons\"><\/a>Exercise 8.1 Similar Polygons<\/h3>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nFor two figures to be similar, the corresponding angles must be ____________ . and the corresponding side lengths must be _____________ .<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52852\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 1\" width=\"556\" height=\"84\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-1.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-1-300x45.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find \u201cboth\u201d answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47871\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-15.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 15\" width=\"272\" height=\"176\" \/><br \/>\nWhat is the scale factor?<br \/>\nAnswer:<br \/>\nScale Factor = \\(\\frac{image-length}{actual-length}\\)<br \/>\n= \\(\\frac{3}{12}\\)= \\(\\frac{4}{16}\\)= \\(\\frac{5}{20}\\)<br \/>\n= \\(\\frac{1}{4}\\)<\/p>\n<p>What is the ratio of their areas?<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-101572\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Exercise-8.1-Similar-Polygons-1.png\" alt=\"Big Ideas Math Geometry Answers Exercise 8.1 Similar Polygons 1\" width=\"487\" height=\"457\" \/><\/p>\n<p>What is the ratio of their corresponding side lengths?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-101573\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Exercise-8.1-Similar-Polygons-2.png\" alt=\"Big Ideas Math Geometry Answers Exercise 8.1 Similar Polygons 2\" width=\"162\" height=\"147\" \/><\/p>\n<p>What is the ratio of their perimeters?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-101574\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Exercise-8.1-Similar-Polygons-3.png\" alt=\"Big Ideas Math Geometry Answers Exercise 8.1 Similar Polygons 3\" width=\"476\" height=\"341\" \/><\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3 and 4, find the scale factor. Then list all pairs of congruent angles and write the ratios of the corresponding side lengths in a statement of proportionality.<\/p>\n<p>Question 3.<br \/>\n\u2206ABC ~ \u2206LMN<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47870\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-16.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 16\" width=\"286\" height=\"112\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52853\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 3\" width=\"550\" height=\"287\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-3.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-3-300x157.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 4.<br \/>\nDEFG ~ PQRS<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47869\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-17.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 17\" width=\"310\" height=\"105\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-17.png 310w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-17-300x102.png 300w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-101596\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Exercise-8.1-Similar-Polygons-5.png\" alt=\"Big Ideas Math Geometry Answers Exercise 8.1 Similar Polygons 5\" width=\"566\" height=\"589\" \/><\/p>\n<p>In Exercises 5-8, the polygons are similar. Find the value of x.<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47868\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-18.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 18\" width=\"227\" height=\"124\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52854\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 5\" width=\"173\" height=\"297\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47867\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-19.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 19\" width=\"224\" height=\"127\" \/><\/p>\n<p>Answer:<br \/>\nx = 20<\/p>\n<p>Explanation:<br \/>\n\\(\\frac { DF }{ GJ } \\) = \\(\\frac { DE }{ GH } \\)<br \/>\n\\(\\frac { 16 }{ 12 } \\) = \\(\\frac { x }{ 15 } \\)<br \/>\nx = \\(\\frac { 16 x 15 }{ 12 } \\) = \\(\\frac { 240 }{ 12 } \\)<br \/>\nx = 20<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47866\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-20.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 20\" width=\"254\" height=\"157\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52855\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-7.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 7\" width=\"124\" height=\"256\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47865\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-21.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 21\" width=\"251\" height=\"163\" \/><\/p>\n<p>Answer:<br \/>\nx = 12<\/p>\n<p>Explanation:<br \/>\n\\(\\frac { PN }{ KJ } \\) = \\(\\frac { MN }{ JH } \\)<br \/>\n\\(\\frac { x }{ 8 } \\) = \\(\\frac { 9 }{ 6 } \\)<br \/>\nx = \\(\\frac { 9 x 8 }{ 6 } \\) = \\(\\frac { 72 }{ 6 } \\)<br \/>\nx = 12<\/p>\n<p>In Exercises 9 and 10, the black triangles are similar. Identify the type of segment shown in blue and find the value of the variab1e.<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47864\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-22.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 22\" width=\"234\" height=\"123\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52856\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-9.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 9\" width=\"409\" height=\"223\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-9.png 409w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-9-300x164.png 300w\" sizes=\"(max-width: 409px) 100vw, 409px\" \/><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47863\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-23.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 23\" width=\"265\" height=\"135\" \/><\/p>\n<p>Answer:<\/p>\n<p>Explanation:<br \/>\n\\(\\frac { y }{ 18 } \\) = \\(\\frac { y &#8211; 1 }{ 16 } \\)<br \/>\n18(y &#8211; 1) = 16y<br \/>\n18y &#8211; 18 = 16y<br \/>\n18y &#8211; 16y = 18<br \/>\n2y = 18<br \/>\ny = 9<\/p>\n<p>In Exercises 11 and 12, RSTU ~ ABCD. Find the ratio of their perimeters.<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47862\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-24.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 24\" width=\"306\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-24.png 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-24-300x111.png 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52857\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-11.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 11\" width=\"392\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-11.png 392w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-11-300x82.png 300w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47861\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-25.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 25\" width=\"358\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-25.png 358w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-25-300x91.png 300w\" sizes=\"(max-width: 358px) 100vw, 358px\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac { RS + ST + TU + UR }{ AB + BC + CD + DA } \\) = \\(\\frac { RS }{ AB } \\) = \\(\\frac { 18 }{ 24 } \\)<br \/>\nThe ratio of perimeter is \\(\\frac { 3 }{ 4 } \\).<\/p>\n<p>In Exercises 13-16, two polygons are similar. The perimeter of one polygon and the ratio of the corresponding side lengths are given. Find the perimeter of the other polygon.<\/p>\n<p>Question 13.<br \/>\nperimeter of smaller polygon: 48 cm: ratio: \\(\\frac{2}{3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52858\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-13.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 13\" width=\"499\" height=\"192\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-13.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-13-300x115.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><\/p>\n<p>Question 14.<br \/>\nperimeter of smaller polygon: 66 ft: ratio: \\(\\frac{3}{4}\\)<\/p>\n<p>Answer:<br \/>\nThe perimeter of larger polygon is 88 ft.<\/p>\n<p>Explanation:<br \/>\n\\(\\frac { smaller }{ larger } \\) = \\(\\frac { 66 }{ x } \\) = \\(\\frac{3}{4}\\)<br \/>\n66 x 4 = 3x<br \/>\n3x = 264<br \/>\nx = \\(\\frac { 264 }{ 3 } \\) = 88<\/p>\n<p>Question 15.<br \/>\nperimeter of larger polygon: 120 yd: rttio: \\(\\frac{1}{6}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52859\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-15.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 15\" width=\"457\" height=\"194\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-15.png 457w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-15-300x127.png 300w\" sizes=\"(max-width: 457px) 100vw, 457px\" \/><\/p>\n<p>Question 16.<br \/>\nperimeter of larger polygon: 85 m; ratio: \\(\\frac{2}{5}\\)<\/p>\n<p>Answer:<br \/>\nThe perimeter of smaller polygon is 34 m.<\/p>\n<p>Explanation:<br \/>\n\\(\\frac { smaller }{ larger } \\) = \\(\\frac { x }{ 85 } \\) = \\(\\frac{2}{5}\\)<br \/>\n85 x 2 = 5x<br \/>\n5x = 170<br \/>\nx = \\(\\frac { 170 }{ 5 } \\) = 34<\/p>\n<p>Question 17.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA school gymnasium is being remodeled. The basketball court will be similar to an NCAA basketball court, which has a length of 94 feet and a width of 50 feet. The school plans to make the width of the new court 45 feet. Find the perimeters of ail NCAA court and of the new court in the school.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52860\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-17.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 17\" width=\"540\" height=\"258\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-17.png 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-17-300x143.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Question 18.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYour family has decided to put a rectangular patio in your backyard. similar to the shape of your backyard. Your backyard has a length of 45 feet and a width of 20 feet. The length of your new patio is 18 feet. Find the perimeters of your backyard and of the patio.<\/p>\n<p>Answer:<br \/>\nThe perimeter of the backyard is 130 ft.<br \/>\nPerimeter of patio is 52 ft<\/p>\n<p>Explanation:<br \/>\nDraw a rectangle to represent the patio and a larger rectangle to represent our backyard and its going to similar figures<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-101875\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/big-ideas-math-geometry-answers-chapter-8-1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 1\" width=\"392\" height=\"225\" \/><br \/>\nPerimeter of backyard = 2(45 + 20) = 2(65)<br \/>\n= 130 ft<br \/>\nScale factor = \\(\\frac { 18 }{ 45 } \\) = \\(\\frac { 2 }{ 5 } \\)<br \/>\nSo, \\(\\frac { perimeter of patio }{ perimeter of backyard } \\) = \\(\\frac { 2 }{ 5 } \\)<br \/>\n\\(\\frac { perimeter of patio }{ 130 } \\) = \\(\\frac { 2 }{ 5 } \\)<br \/>\nPerimeter of patio = \\(\\frac { 260 }{ 5 } \\) = 52 ft<\/p>\n<p>In Exercises 19-22, the polygons are similar. The area of one polygon is given. Find the area of the other polygon.<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47860\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-26.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 26\" width=\"328\" height=\"69\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-26.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-26-300x63.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52861\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-19.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 19\" width=\"500\" height=\"260\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-19.png 500w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-19-300x156.png 300w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47859\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-27.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 27\" width=\"258\" height=\"93\" \/><\/p>\n<p>Answer:<br \/>\nArea of the larger triangle is 90 cm\u00b2<\/p>\n<p>Explanation:<br \/>\n\\(\\frac { 10 }{ A } \\) = (\\(\\frac { 4 }{ 12 } \\))\u00b2<br \/>\n\\(\\frac { 10 }{ A } \\) = \\(\\frac { 1 }{ 9 } \\)<br \/>\nA = 10 x 9<br \/>\nA = 90<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47858\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-28.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 28\" width=\"351\" height=\"103\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-28.png 351w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-28-300x88.png 300w\" sizes=\"(max-width: 351px) 100vw, 351px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52862\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-21.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 21\" width=\"508\" height=\"276\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-21.png 508w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-21-300x163.png 300w\" sizes=\"(max-width: 508px) 100vw, 508px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47857\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-29.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 29\" width=\"182\" height=\"116\" \/><\/p>\n<p>Answer:<br \/>\nArea of smaller triangle = 6 sq cm<\/p>\n<p>Explanation:<br \/>\n\\(\\frac { A }{ 96 } \\) = (\\(\\frac { 3 }{ 12 } \\))\u00b2<br \/>\n\\(\\frac { A }{ 96 } \\) = \\(\\frac { 1 }{ 16 } \\)<br \/>\n16A = 96<br \/>\nA = \\(\\frac { 96 }{ 16 } \\)<br \/>\nA = 6<\/p>\n<p>Question 23.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in finding the perimeter of triangle B. The triangles are similar.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47856\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-30.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 30\" width=\"348\" height=\"134\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-30.png 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-30-300x116.png 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52863\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-23.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 23\" width=\"578\" height=\"202\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-23.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-23-300x105.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 24.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in finding the area of triangle B. The triangles are similar.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47855\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-31.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 31\" width=\"325\" height=\"145\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-31.png 325w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-31-300x134.png 300w\" sizes=\"(max-width: 325px) 100vw, 325px\" \/><\/p>\n<p>Answer:<br \/>\nBecause the first ratio has a side of A over the side length of B, the square of the second ratio should have the area of B over the area of A.<br \/>\n\\(\\frac { 24 }{ x } \\) = (\\(\\frac { 6 }{ 18 } \\))\u00b2<br \/>\n\\(\\frac { 24 }{ x } \\) = \\(\\frac { 1 }{ 9 } \\)<br \/>\nx = 24 x 9<br \/>\nx = 216<\/p>\n<p>In Exercises 25 and 26, decide whether the red and blue polygons are similar.<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47854\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-32.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 32\" width=\"163\" height=\"106\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52864\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-25.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 25\" width=\"582\" height=\"229\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-25.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-25-300x118.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47853\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-33.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 33\" width=\"214\" height=\"147\" \/><\/p>\n<p>Answer:<br \/>\nYes<br \/>\nBecause both shapes are apparent and their side lengths are proportional and their corresponding angles are congruent.<\/p>\n<p>Question 27.<br \/>\n<strong>REASONING<\/strong><br \/>\nTriangles ABC and DEF are similar. Which statement is correct? Select all that apply.<br \/>\n(A) \\(\\frac{B C}{E F}=\\frac{A C}{D F}\\)<br \/>\n(B) \\(\\frac{A B}{D E}=\\frac{C A}{F E}\\)<br \/>\n(C) \\(\\frac{A B}{E F}=\\frac{B C}{D E}\\)<br \/>\n(D) \\(\\frac{C A}{F D}=\\frac{B C}{E F}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52865\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-27.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 27\" width=\"553\" height=\"49\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-27.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-27-300x27.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p><strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nIn Exercises 28 &#8211; 34, JKLM ~ EFGH.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-47887\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-45.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 45\" width=\"245\" height=\"123\" \/><\/p>\n<p>Question 28.<br \/>\nFind the scale factor of JKLM to EFGH.<\/p>\n<p>Answer:<br \/>\nscale factor = \\(\\frac { EF }{ JK } \\) =\\(\\frac { 8 }{ 20 } \\)<br \/>\nk = \\(\\frac { 2 }{ 5 } \\)<\/p>\n<p>Question 29.<br \/>\nFind the scale factor of EFGH to JKLM.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52866\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-29.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 29\" width=\"385\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-29.png 385w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-29-300x84.png 300w\" sizes=\"(max-width: 385px) 100vw, 385px\" \/><\/p>\n<p>Question 30.<br \/>\nFind the values of x, y, and z.<\/p>\n<p>Answer:<br \/>\nx = \\(\\frac { 55 }{ 2 } \\)<br \/>\ny = 12<br \/>\nz = 65\u00b0<\/p>\n<p>Explanation:<br \/>\n\\(\\frac { KL }{ GF } \\) = \\(\\frac { x }{ 11 } \\) = \\(\\frac { 5 }{ 2 } \\)<br \/>\n2x = 55<br \/>\nx = \\(\\frac { 55 }{ 2 } \\)<br \/>\n\\(\\frac { MJ }{ HE } \\) = \\(\\frac { 30 }{ y } \\) = \\(\\frac { 5 }{ 2 } \\)<br \/>\n5y = 60<br \/>\ny = 12<\/p>\n<p>Question 31.<br \/>\nFind the perimeter of each polygon.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52867\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-31.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 31\" width=\"544\" height=\"190\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-31.png 544w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-31-300x105.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><\/p>\n<p>Question 32.<br \/>\nFind the ratio of the perimeters of JKLM to EFGH.<\/p>\n<p>Answer:<br \/>\nThe perimeter of JKLM : Perimeter of EFGH = 85 : 34<\/p>\n<p>Question 33.<br \/>\nFind the area of each polygon.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52868\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-33.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 33\" width=\"436\" height=\"321\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-33.png 436w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-33-300x221.png 300w\" sizes=\"(max-width: 436px) 100vw, 436px\" \/><\/p>\n<p>Question 34.<br \/>\nFind the ratio of the areas of JKLM to EFGH.<\/p>\n<p>Answer:<br \/>\nArea of JKLM : Area of EFGH = 378.125 : 60.5 = 25 : 4<\/p>\n<p>Question 35.<br \/>\n<strong>USING STRUCTURE<\/strong><br \/>\nRectangle A is similar to rectangle B. Rectangle A has side lengths of 6 and 12. Rectangle B has a side length of 18. What are the possible values for the length of the other side of rectangle B? Select all that apply.<br \/>\n(A) 6<br \/>\n(B) 9<br \/>\n(C) 24<br \/>\n(D) 36<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52869\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-35.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 35\" width=\"553\" height=\"379\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-35.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-35-300x206.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>DRAWING CONCLUSIONS<\/strong><br \/>\nIn table tennis, the table is a rectangle 9 feet long and 5 feet wide. A tennis Court is a rectangle 78 feet long and 36 feet wide. Are the two surfaces similar? Explain. If so, find the scale factor of the tennis court to the table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47852\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-34.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 34\" width=\"312\" height=\"150\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-34.png 312w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-34-300x144.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><\/p>\n<p>Answer:<br \/>\nThe tennis table and court are not similar<\/p>\n<p>Explanation:<br \/>\nIf two figures are similar then their angles are congruent and sides are proportional.<br \/>\nIf the tennis court and table are similar, then<br \/>\n\\(\\frac { length of table }{ length of court } \\) = \\(\\frac { width of table }{ width of court } \\)<br \/>\n\\(\\frac { 9 }{ 78 } \\) = \\(\\frac { 5 }{ 36 } \\)<br \/>\n9 \u2022 36 = 5 \u2022 78<br \/>\n324 = 390<br \/>\nSo, Table and court are not similar.<\/p>\n<p><strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nIn Exercises 37 and 38, the two polygons are similar. Find the values of x and y.<\/p>\n<p>Question 37.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47851\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-35.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 35\" width=\"238\" height=\"152\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52870\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-37.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 37\" width=\"285\" height=\"501\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-37.png 285w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-37-171x300.png 171w\" sizes=\"(max-width: 285px) 100vw, 285px\" \/><\/p>\n<p>Question 38.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47850\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-36.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 36\" width=\"334\" height=\"136\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-36.png 334w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-36-300x122.png 300w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><\/p>\n<p>Answer:<br \/>\nx = 7.5<\/p>\n<p>Explanation:<br \/>\n\\(\\frac { x }{ 5 } \\) = \\(\\frac { 6 }{ 4 } \\)<br \/>\nx = \\(\\frac { 15 }{ 2 } \\)<\/p>\n<p><strong>ATTENDING TO PRECISION<\/strong><br \/>\nIn Exercises 39 &#8211; 42. the figures are similar. Find the missing corresponding side length.<\/p>\n<p>Question 39.<br \/>\nFigure A has a pen meter of 72 meters and one of the side lengths is 18 meters. Figure B has a perimeter of 120 meters.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52871\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-39.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 39\" width=\"521\" height=\"301\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-39.png 521w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-39-300x173.png 300w\" sizes=\"(max-width: 521px) 100vw, 521px\" \/><\/p>\n<p>Question 40.<br \/>\nFigure A has a perimeter of 24 inches. Figure B has a perimeter of 36 inches and one of the side lengths is 12 inches.<\/p>\n<p>Answer:<br \/>\nThe corresponding side length of figure A is 8 in<\/p>\n<p>Explanation:<br \/>\n\\(\\frac { Perimeter of A }{ Perimeter of B } \\) = \\(\\frac { Side length of A }{ Side length of B } \\)<br \/>\n\\(\\frac { 24 }{ 36 } \\) = \\(\\frac { x }{ 12 } \\)<br \/>\n\\(\\frac { 2 }{ 3 } \\) = \\(\\frac { x }{ 12 } \\)<br \/>\n12 \u2022 2 = 3x<br \/>\nx = 8<\/p>\n<p>Question 41.<br \/>\nFigure A has an area of 48 square feet and one of the side lengths is 6 feet. Figure B has an area of 75 square feet.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52872\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-41.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 41\" width=\"495\" height=\"402\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-41.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-41-300x244.png 300w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><\/p>\n<p>Question 42.<br \/>\nFigure A has an area of 18 square feet. Figure B has an area of 98 square feet and one of the side lengths is 14 feet.<\/p>\n<p>Answer:<br \/>\nThe corresponding side length of figure A is 6 ft.<\/p>\n<p>Explanation:<br \/>\n\\(\\frac { Area of A }{ Area of B } \\) = (\\(\\frac { Side length of A }{ Side length of B } \\))\u00b2<br \/>\n\\(\\frac { 18 }{ 98 } \\) = (\\(\\frac { x }{ 14 } \\))\u00b2<br \/>\n\\(\\frac { 9 }{ 49 } \\) = \\(\\frac { x\u00b2 }{ 196 } \\)<br \/>\nx\u00b2 = 36<br \/>\nx = 6<\/p>\n<p><strong>CRITICAL THINKING<\/strong><br \/>\nIn Exercises 43-48, tell whether the polygons are always, sometimes, or never similar.<\/p>\n<p>Question 43.<br \/>\ntwo isosceles triangles<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52873\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-43.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 43\" width=\"419\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-43.png 419w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-43-300x24.png 300w\" sizes=\"(max-width: 419px) 100vw, 419px\" \/><\/p>\n<p>Question 44.<br \/>\ntwo isosceles trapezoids<\/p>\n<p>Answer:<br \/>\nTwo isosceles trapezoids are sometimes similar.<\/p>\n<p>Question 45.<br \/>\ntwo rhombuses<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52874\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-45.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 45\" width=\"360\" height=\"29\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-45.png 360w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-45-300x24.png 300w\" sizes=\"(max-width: 360px) 100vw, 360px\" \/><\/p>\n<p>Question 46.<br \/>\ntwo squares<\/p>\n<p>Answer:<br \/>\nTwo squares are always similar.<\/p>\n<p>Question 47.<br \/>\ntwo regular polygons<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52875\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-47.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 47\" width=\"424\" height=\"29\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-47.png 424w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-47-300x21.png 300w\" sizes=\"(max-width: 424px) 100vw, 424px\" \/><\/p>\n<p>Question 48.<br \/>\na right triangle and an equilateral triangle<\/p>\n<p>Answer:<br \/>\nA right triangle and an equilateral triangle are never similar.<\/p>\n<p>Question 49.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour sister claims that when the side lengths of two rectangles are proportional, the two rectangles must be similar. Is she correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52876\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-49.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 49\" width=\"574\" height=\"118\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-49.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-49-300x62.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 50.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nYou shine a flashlight directly on an object to project its image onto a parallel screen. Will the object and the image be similar? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47849\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-37.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 37\" width=\"292\" height=\"183\" \/><br \/>\nAnswer:<br \/>\nThe object and image are similar.<\/p>\n<p>Question 51.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nDuring a total eclipse of the Sun, the moon is directly in line with the Sun and blocks the Sun\u2019s rays. The distance DA between Earth and the Sun is 93,00,000 miles. the distance DE between Earth and the moon is 2,40,000 miles, and the radius AB of the Sun is 432,5000 miles. Use the diagram and the given measurements to estimate the radius EC of the moon.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47848\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-38.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 38\" width=\"370\" height=\"118\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-38.png 370w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-38-300x96.png 300w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52877\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-51.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 51\" width=\"484\" height=\"635\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-51.png 484w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-51-229x300.png 229w\" sizes=\"(max-width: 484px) 100vw, 484px\" \/><\/p>\n<p>Question 52.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nProve the Perimeters of Similar Polygons Theorem (Theorem 8.1) for similar rectangles. Include a diagram in your proof.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-101953\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/big-ideas-math-geometry-answers-chapter-8-2.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 2\" width=\"399\" height=\"186\" \/><br \/>\n\\(\\frac { PQ + QR + RS + SP }{ KL + LM + MN + NK } \\) = \\(\\frac { PQ }{ KL } \\) = \\(\\frac { QR }{ LM } \\) = \\(\\frac { RS }{ MN } \\) = \\(\\frac { SP }{ NK } \\)<\/p>\n<p>Question 53.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nProve the Areas of Similar Polygons Theorem (Theorem 8.2) for similar rectangles. Include a diagram in our proof.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52878\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-53.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 53\" width=\"562\" height=\"452\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-53.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-53-300x241.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 54.<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. A plane is the surface of the sphere. In spherical geometry, is it possible that two triangles are similar but not congruent? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nIn the diagram, PQRS is a square, and PLMS ~ LMRQ. Find the exact value of x. This value is called the golden ratio. Golden rectangles have their length and width in this ratio. Show that the similar rectangles in the diagram are golden rectangles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47847\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-39.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 39\" width=\"118\" height=\"112\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52879\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-55.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 55\" width=\"583\" height=\"633\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-55.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-55-276x300.png 276w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 56.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nThe equations of the lines shown are y = \\(\\frac{4}{3}\\)x + 4 and y = \\(\\frac{4}{3}\\)x &#8211; 8. Show that \u2206AOB ~ \u2206COD.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47846\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-40.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 40\" width=\"166\" height=\"162\" \/><br \/>\nAnswer:<br \/>\nThe two lines slopes are equal and triangles angles are congruent and side lengths are proportional. So, triangles are similar.<\/p>\n<p>Maintaining Mathematical proficiency<\/p>\n<p>Find the value of x.<\/p>\n<p>Question 57.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47844\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-41.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 41\" width=\"133\" height=\"97\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52880\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-57.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 57\" width=\"232\" height=\"96\" \/><\/p>\n<p>Question 58.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47842\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-42.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 42\" width=\"154\" height=\"65\" \/><\/p>\n<p>Answer:<br \/>\nx = 66\u00b0<\/p>\n<p>Explanation:<br \/>\nx + 24 + 90 = 180<br \/>\nx + 114 = 180<br \/>\nx = 180 &#8211; 114<br \/>\nx = 66<\/p>\n<p>Question 59.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47840\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-43.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 43\" width=\"117\" height=\"119\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52881\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-59.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 59\" width=\"222\" height=\"136\" \/><\/p>\n<p>Question 60.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47839\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-44.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 44\" width=\"135\" height=\"120\" \/><\/p>\n<p>Answer:<br \/>\nx = 60\u00b0<\/p>\n<p>Explanation:<br \/>\nx + x + x = 180<br \/>\n3x = 180<br \/>\nx = 60<\/p>\n<h3><a id=\"8.2_Proving_Triangle_Similarity_by_AA\"><\/a>8.2 Proving Triangle Similarity by AA<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Comparing Triangles<\/p>\n<p>Work with a partner. Use dynamic geometry software.<\/p>\n<p>a. Construct \u2206ABC and \u2206DEF So that m\u2220A = m\u2220D = 106\u00b0, m\u2220B = m\u2220E = 31\u00b0, and \u2206DEF is not congruent to \u2206ABC.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47948\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-46.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 46\" width=\"302\" height=\"236\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-46.png 302w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-46-300x234.png 300w\" sizes=\"(max-width: 302px) 100vw, 302px\" \/><br \/>\nAnswer:<br \/>\nm\u2220C \u2260 m\u2220F<\/p>\n<p>b. Find the third angle measure and the side lengths of each triangle. Copy the table below and record our results in column 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47947\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-47.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 47\" width=\"493\" height=\"291\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-47.png 493w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-47-300x177.png 300w\" sizes=\"(max-width: 493px) 100vw, 493px\" \/><br \/>\nAnswer:<\/p>\n<p>c. Are the two triangles similar? Explain.<br \/>\n<strong>CONSTRUCTING VIABLE ARGUMENTS<\/strong><br \/>\nTo be proficient in math, you need to understand and use stated assumptions, definitions, and previously established results in constructing arguments.<br \/>\nAnswer:<\/p>\n<p>d. Repeat parts (a) &#8211; (c) to complete columns 2 and 3 of the table for the given angle measures.<br \/>\nAnswer:<\/p>\n<p>e. Complete each remaining column of the table using your own choice of two pairs of equal corresponding angle measures. Can you construct two triangles in this way that are not similar?<br \/>\nAnswer:<\/p>\n<p>f. Make a conjecture about any two triangles with two pairs of congruent corresponding angles.<br \/>\nAnswer:<\/p>\n<p>Communicate Your Answer<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-47946\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-48.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 48\" width=\"150\" height=\"114\" \/><\/p>\n<p>Question 2.<br \/>\nWhat can you conclude about two triangles when you know that two pairs of corresponding angles are congruent?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nFind RS in the figure at the left.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_8.2_Proving_Triangle_Similarity_by_AA\"><\/a>Lesson 8.2 Proving Triangle Similarity by AA<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Show that the triangles are similar. Write a similarity statement.<\/p>\n<p>Question 1.<br \/>\n\u2206FGH and \u2206RQS<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47945\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-49.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 49\" width=\"182\" height=\"96\" \/><br \/>\nAnswer:<br \/>\n\u2206FGH and \u2206RQS are similar by the AA similarity theorem.<\/p>\n<p>Question 2.<br \/>\n\u2206CDF and \u2206DEF<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47944\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-50.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 50\" width=\"152\" height=\"91\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-50.png 152w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-50-150x91.png 150w\" sizes=\"(max-width: 152px) 100vw, 152px\" \/><\/p>\n<p>Answer:<\/p>\n<p>Question 3.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nSuppose that \\(\\overline{S R}\\) <img loading=\"lazy\" class=\"alignnone size-full wp-image-47943\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-51.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 51\" width=\"17\" height=\"26\" \/> \\(\\overline{T U}\\) in Example 2 part (b). Could the triangles still be similar? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nA child who is 58 inches tall is standing next to the woman in Example 3. How long is the child\u2019s shadow\u2019?<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nYou are standing outside, and you measure the lengths 0f the shadows cast by both you and a tree. Write a proportion showing how you could find the height of the tree.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Exercise_8.2_Proving_Triangle_Similarity_by_AA\"><\/a>Exercise 8.2 Proving Triangle Similarity by AA<\/h3>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nIf two angles of one triangle are congruent to two angles of another triangle. then the triangles are __________ .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52882\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 1\" width=\"552\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-1.png 552w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-1-300x32.png 300w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nCan you assume that corresponding sides and corresponding angles of any two similar triangles are congruent? Explain.<br \/>\nAnswer:<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3 &#8211; 6. determine whether the triangles are similar. If they are, write a similarity statement. Explain your reasoning.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47942\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-52.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 52\" width=\"184\" height=\"111\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52883\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 3\" width=\"646\" height=\"131\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-3.png 646w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-3-300x61.png 300w\" sizes=\"(max-width: 646px) 100vw, 646px\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47941\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-53.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 53\" width=\"199\" height=\"130\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47940\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-54.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 54\" width=\"144\" height=\"112\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52884\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 5\" width=\"538\" height=\"183\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-5.png 538w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-5-300x102.png 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47939\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-55.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 55\" width=\"137\" height=\"159\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 7 &#8211; 10. show that the two triangles are similar.<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47938\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-56.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 56\" width=\"117\" height=\"119\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52885\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-7.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 7\" width=\"569\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-7.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-7-300x46.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47937\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-57.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 57\" width=\"146\" height=\"109\" \/><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47936\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-58.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 58\" width=\"175\" height=\"101\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52886\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-9.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 9\" width=\"493\" height=\"114\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-9.png 493w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-9-300x69.png 300w\" sizes=\"(max-width: 493px) 100vw, 493px\" \/><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47935\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-59.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 59\" width=\"103\" height=\"105\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 11 &#8211; 18, use the diagram to copy and complete the statement.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-47934\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-60.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 60\" width=\"206\" height=\"169\" \/><\/p>\n<p>Question 11.<br \/>\n\u2206CAG ~ _________<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52887\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-11.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 11\" width=\"167\" height=\"29\" \/><\/p>\n<p>Question 12.<br \/>\n\u2206DCF ~ _________<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n\u2206ACB ~ _________<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52888\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-13.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 13\" width=\"163\" height=\"31\" \/><\/p>\n<p>Question 14.<br \/>\nm\u2220ECF = _________<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nm\u2220ECD = _________<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52889\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-15.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 15\" width=\"157\" height=\"30\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-15.png 157w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-15-150x30.png 150w\" sizes=\"(max-width: 157px) 100vw, 157px\" \/><\/p>\n<p>Question 16.<br \/>\nCF = _________<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\nBC = _________<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52890\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-17.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 17\" width=\"123\" height=\"34\" \/><\/p>\n<p>Question 18.<br \/>\nDE = _________<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in using the AA Similarity Theorem (Theorem 8.3).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47933\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-61.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 61\" width=\"332\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-61.png 332w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-61-300x145.png 300w\" sizes=\"(max-width: 332px) 100vw, 332px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52891\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-19.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 19\" width=\"561\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-19.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-19-300x47.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 20.<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-47932\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-62.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 62\" width=\"336\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-62.png 336w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-62-300x95.png 300w\" sizes=\"(max-width: 336px) 100vw, 336px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou can measure the width of the lake using a surveying technique, as shown in the diagram. Find the width of the lake, WX. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47931\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-63.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 63\" width=\"246\" height=\"142\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52892\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-21.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 21\" width=\"382\" height=\"265\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-21.png 382w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-21-300x208.png 300w\" sizes=\"(max-width: 382px) 100vw, 382px\" \/><\/p>\n<p>Question 22.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYou and your cousin are trying to determine the height of a telephone pole. Your cousin tells you to stand in the pole\u2019s shadow so that the tip of your shadow coincides with the tip of the pole\u2019s shadow. Your Cousin claims to be able to use the distance between the tips of the shadows and you, the distance between you and the pole, and your height to estimate the height of the telephone pole. Is this possible? Explain. Include a diagram in your answer.<br \/>\nAnswer:<\/p>\n<p><strong>REASONING<\/strong><br \/>\nIn Exercises 23 &#8211; 26, is it possible for \u2206JKL and \u2206XYZ to be similar? Explain your reasoning.<\/p>\n<p>Question 23.<br \/>\nm\u2220J = 71\u00b0, m\u2220K = 52\u00b0, m\u2220X = 71\u00b0, and m\u2220Z = 57\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52893\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-23.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 23\" width=\"380\" height=\"34\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-23.png 380w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-23-300x27.png 300w\" sizes=\"(max-width: 380px) 100vw, 380px\" \/><\/p>\n<p>Question 24.<br \/>\n\u2206JKL is a right triangle and m\u2220X + m\u2220Y= 150\u00b0.<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\nm\u2220L = 87\u00b0 and m\u2220Y = 94\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52894\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-25.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 25\" width=\"200\" height=\"33\" \/><\/p>\n<p>Question 26.<br \/>\nm\u2220J + m\u2220K = 85\u00b0 and m\u2220Y + m\u2220Z = 80\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nExplain how you can use similar triangles to show that any two points on a line can be used to find its slope.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47930\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-64.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 64\" width=\"228\" height=\"115\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52895\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-27.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 27\" width=\"580\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-27.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-27-300x29.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nIn the diagram, which triangles would you use to find the distance x between the shoreline and the buoy? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47929\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-65.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 65\" width=\"305\" height=\"172\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-65.png 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-65-300x169.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain why all equilateral triangles are similar.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52896\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-29.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 29\" width=\"590\" height=\"55\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-29.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-29-300x28.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nDecide whether each is a valid method of showing that two quadrilaterals are similar. Justify your answer.<br \/>\na. AAA<br \/>\nAnswer:<\/p>\n<p>b. AAAA<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<strong>PROOF<\/strong><br \/>\nWithout using corresponding lengths in similar polygons. prove that the ratio of two corresponding angle bisectors in similar triangles is equal to the scale factor.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52897\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-31.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 31\" width=\"598\" height=\"446\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-31.png 598w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-31-300x224.png 300w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>PROOF<\/strong><br \/>\nProve that if the lengths of two sides of a triangle are a and b, respectively, then the lengths of the corresponding altitudes to those sides are in the ratio \\(\\frac{b}{a}\\).<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA portion of an amusement park ride is shown. Find EF. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47928\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-66.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 66\" width=\"301\" height=\"147\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52898\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-33.1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 33.1\" width=\"583\" height=\"436\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-33.1.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-33.1-300x224.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52899\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-33.2.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 33.2\" width=\"273\" height=\"371\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-33.2.png 273w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-33.2-221x300.png 221w\" sizes=\"(max-width: 273px) 100vw, 273px\" \/><\/p>\n<p>Maintaining Mathematical Practices<\/p>\n<p>Determine whether there is enough information to prove that the triangles are congruent. Explain your reasoning.<\/p>\n<p>Question 34.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47927\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-67.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 67\" width=\"237\" height=\"96\" \/><br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47926\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-68.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 68\" width=\"145\" height=\"108\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52900\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-35.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 35\" width=\"521\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-35.png 521w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-35-300x35.png 300w\" sizes=\"(max-width: 521px) 100vw, 521px\" \/><\/p>\n<p>Question 36.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47925\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-69.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 69\" width=\"143\" height=\"100\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"8.1_&amp;_8.2_Quiz\"><\/a>8.1 &amp; 8.2 Quiz<\/h3>\n<p>List all pairs of congruent angles. Then write the ratios of the corresponding side lengths in a statement of proportionality.<\/p>\n<p>Question 1.<br \/>\n\u2206BDG ~ \u2206MPQ<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47982\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-70.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 70\" width=\"172\" height=\"90\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nDEFG ~ HJKL<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47981\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-71.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 71\" width=\"313\" height=\"99\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-71.png 313w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-71-300x95.png 300w\" sizes=\"(max-width: 313px) 100vw, 313px\" \/><br \/>\nAnswer:<\/p>\n<p>The polygons are similar. Find the value of x.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47980\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-72.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 72\" width=\"371\" height=\"98\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-72.png 371w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-72-300x79.png 300w\" sizes=\"(max-width: 371px) 100vw, 371px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47979\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-73.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 73\" width=\"348\" height=\"116\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-73.png 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-73-300x100.png 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><br \/>\nAnswer:<\/p>\n<p>Determine whether the polygons are similar. If they are, write a similarity statement. Explain your reasoning. (Section 8.1 and Section 8.2)<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47978\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-74.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 74\" width=\"194\" height=\"182\" \/><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47977\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-75.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 75\" width=\"202\" height=\"170\" \/><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47976\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-76.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 76\" width=\"192\" height=\"168\" \/><br \/>\nAnswer:<\/p>\n<p>Show that the two triangles are similar.<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47975\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-77.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 77\" width=\"202\" height=\"125\" \/><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47974\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-78.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 78\" width=\"155\" height=\"114\" \/><br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47973\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-79.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 79\" width=\"244\" height=\"105\" \/><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nThe dimensions of an official hockey rink used by the National Hockey League (NHL) are 200 feet by 85 feet. The dimensions of an air hockey table are 96 inches by 408 inches. Assume corresponding angles are congruent. (Section 8.1)<br \/>\na. Determine whether the two surfaces are similar.<br \/>\nAnswer:<\/p>\n<p>b. If the surfaces are similar, find the ratio of their perimeters and the ratio ol their areas. If not, find the dimensions of an air hockey table that are similar to an NHL hockey rink.<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nyou and a friend buy camping tents made by the same company but in different sizes and colors. Use the information given in the diagram to decide whether the triangular faces of the tents are similar. Explain your reasoning. (Section 8.2)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47972\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-80.png\" alt=\"Big Ideas Math Answers Geometry Chapter 8 Similarity 80\" width=\"370\" height=\"139\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-80.png 370w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-80-300x113.png 300w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"8.3_Proving_Triangle_Similarity_by_SSS_and_SAS\"><\/a>8.3 Proving Triangle Similarity by SSS and SAS<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Deciding Whether Triangles Are Similar<\/p>\n<p>Work with a partner: Use dynamic geometry software.<\/p>\n<p>a. Construct \u2206ABC and \u2206DEF with the side lengths given in column 1 of the table below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48466\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-81.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 81\" width=\"498\" height=\"332\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-81.png 498w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-81-300x200.png 300w\" sizes=\"(max-width: 498px) 100vw, 498px\" \/><br \/>\nAnswer:<\/p>\n<p>b. Copy the table and complete column 1.<br \/>\nAnswer:<\/p>\n<p>c. Are the triangles similar? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>d. Repeat parts (a) &#8211; (c) for columns 2 &#8211; 6 in the table.<br \/>\nAnswer:<\/p>\n<p>e. How are the corresponding side lengths related in each pair of triangles that are similar? Is this true for each pair of triangles that are not similar?<br \/>\nAnswer:<\/p>\n<p>f. Make a conjecture about the similarity of two triangles based on their corresponding side lengths.<br \/>\n<strong>CONSTRUCTING VIABLE ARGUMENTS<\/strong><br \/>\nTo be proficient in math, you need to analyze situations by breaking them into cases and recognize and use counter examples.<br \/>\nAnswer:<\/p>\n<p>g. Use your conjecture to write another set of side lengths of two similar triangles. Use the side lengths to complete column 7 of the table.<br \/>\nAnswer:<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Deciding Whether Triangles Are Similar<\/p>\n<p>Work with a partner: Use dynamic geometry software. Construct any \u2206ABC.<br \/>\na. Find AB, AC, and m\u2220A. Choose any positive rational number k and construct \u2206DEF so that DE = k \u2022 AB, DF = k \u2022 AC, and m\u2220D = m\u2220A.<br \/>\nAnswer:<\/p>\n<p>b. Is \u2206DEF similar to \u2206ABC? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>c. Repeat parts (a) and (b) several times by changing \u2206ABC and k. Describe your results.<br \/>\nAnswer:<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 3.<br \/>\nWhat are two ways to use corresponding sides of two triangles to determine that the triangles are similar?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_8.3_Proving_Triangle_Similarity_by_SSS_and_SAS\"><\/a>Lesson 8.3 Proving Triangle Similarity by SSS and SAS<\/h3>\n<p><strong>Monitoring progress<\/strong><\/p>\n<p>Use the diagram.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-48465\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-82.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 82\" width=\"260\" height=\"124\" \/><\/p>\n<p>Question 1.<br \/>\nWhich of the three triangles are similar? Write a similarity statement.<\/p>\n<p>Answer:<br \/>\nThe ratios are equal. So, \u25b3LMN, \u25b3XYZ are similar.<br \/>\nThe ratios are not equal. So \u25b3LMN, \u25b3RST are not similar.<\/p>\n<p>Explanation:<br \/>\nCompare \u25b3LMN, \u25b3XYZ by finding the ratios of corresponding side lengths<br \/>\nShortest sides: \\(\\frac { LM }{ YZ } \\) = \\(\\frac { 20 }{ 30 } \\) = \\(\\frac { 2 }{ 3 } \\)<br \/>\nLongest sides: \\(\\frac { LN }{ XY } \\) = \\(\\frac { 26 }{ 39 } \\) = \\(\\frac { 2 }{ 3 } \\)<br \/>\nRemaining sides: \\(\\frac { MN }{ ZX } \\) = \\(\\frac { 24 }{ 36 } \\) = \\(\\frac { 2 }{ 3 } \\)<br \/>\nThe ratios are equal. So, \u25b3LMN, \u25b3XYZ are similar.<br \/>\nCompare \u25b3LMN, \u25b3RST by finding the ratios of corresponding side lengths<br \/>\nShortest sides: \\(\\frac { LM }{ RS } \\) = \\(\\frac { 20 }{ 24 } \\) = \\(\\frac { 5 }{ 6 } \\)<br \/>\nLongest sides: \\(\\frac { LN }{ ST } \\) = \\(\\frac { 26 }{ 33 } \\)<br \/>\nRemaining sides: \\(\\frac { MN }{ RT } \\) = \\(\\frac { 24 }{ 30 } \\) = \\(\\frac { 4 }{ 5 } \\)<br \/>\nThe ratios are not equal. So \u25b3LMN, \u25b3RST are not similar.<\/p>\n<p>Question 2.<br \/>\nThe shortest side of a triangle similar to \u2206RST is 12 units long. Find the other side 1enths of the triangle.<\/p>\n<p>Answer:<br \/>\nThe other side lengths of the triangle are 15 units, 16.5 units.<\/p>\n<p>Explanation:<br \/>\nThe shortest side of a triangle similar to \u2206RST is 12 units<br \/>\nScale factor = \\(\\frac { 12 }{ 24 } \\) = \\(\\frac { 1 }{ 2 } \\)<br \/>\nSo, other sides are 33 x \\(\\frac { 12 }{ 2 } \\) = 16.5, 30 x \\(\\frac { 12 }{ 2 } \\) = 15.<\/p>\n<p>Explain how to show that the indicated triangles are similar.<\/p>\n<p>Question 3.<br \/>\n\u2206SRT ~ \u2206PNQ<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48464\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-83.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 83\" width=\"217\" height=\"107\" \/><\/p>\n<p>Answer:<br \/>\nThe shorter sides: \\(\\frac { 18 }{ 24 } \\) = \\(\\frac { 3 }{ 4 } \\)<br \/>\nLonger sides: \\(\\frac { 21 }{ 28 } \\) = \\(\\frac { 3 }{ 4 } \\)<br \/>\nThe side lengths are proportional. So \u2206SRT ~ \u2206PNQ<\/p>\n<p>Question 4.<br \/>\n\u2206XZW ~ \u2206YZX<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48463\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-84.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 84\" width=\"154\" height=\"99\" \/><\/p>\n<p>Answer:<br \/>\n\u2206XZW and \u2206YZX are not proportional.<\/p>\n<p>Explanation:<br \/>\nThe shorter sides: \\(\\frac { 9 }{ 16 } \\)<br \/>\nLonger sides: \\(\\frac { 15 }{ 20 } \\) = \\(\\frac { 3 }{ 4 } \\)<br \/>\nThe side lengths are not proportional. So \u2206XZW and \u2206YZX are not proportional.<\/p>\n<h3><a id=\"Exercise_8.3_Proving_Triangle_Similarity_by_SSS_and_SAS\"><\/a>Exercise 8.3 Proving Triangle Similarity by SSS and SAS<\/h3>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nYou plan to show that \u2206QRS is similar to \u2206XYZ by the SSS Similarity Theorem (Theorem 8.4). Copy and complete the proportion that you will use:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48462\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-85.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 85\" width=\"154\" height=\"60\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52901\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 1\" width=\"578\" height=\"83\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-1.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-1-300x43.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich triangle does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48461\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-86.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 86\" width=\"697\" height=\"80\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-86.png 697w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-86-300x34.png 300w\" sizes=\"(max-width: 697px) 100vw, 697px\" \/><br \/>\nAnswer:<\/p>\n<p>Monitoring progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3 and 4, determine whether \u2206JKL or \u2206RST is similar to \u2206ABC.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48460\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-87.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 87\" width=\"372\" height=\"116\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-87.png 372w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-87-300x94.png 300w\" sizes=\"(max-width: 372px) 100vw, 372px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52902\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 3\" width=\"439\" height=\"286\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-3.png 439w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-3-300x195.png 300w\" sizes=\"(max-width: 439px) 100vw, 439px\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48459\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-88.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 88\" width=\"377\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-88.png 377w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-88-300x88.png 300w\" sizes=\"(max-width: 377px) 100vw, 377px\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 5 and 6, find the value of x that makes \u2206DEF ~ \u2206XYZ.<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48458\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-89.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 89\" width=\"351\" height=\"83\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-89.png 351w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-89-300x71.png 300w\" sizes=\"(max-width: 351px) 100vw, 351px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52903\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 5\" width=\"215\" height=\"293\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48457\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-90.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 90\" width=\"258\" height=\"151\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 7 and 8, verify that \u2206ABC ~ \u2206DEF Find the scale factor of \u2206ABC to \u2206DEF<\/p>\n<p>Question 7.<br \/>\n\u2206ABC: BC = 18, AB = 15, AC = 12<br \/>\n\u2206DEF: EF = 12, DE = 10, DF = 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-7.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 7\" width=\"388\" height=\"203\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-7.png 388w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-7-300x157.png 300w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><\/p>\n<p>Question 8.<br \/>\n\u2206ABC: AB = 10, BC = 16, CA = 20<br \/>\n\u2206DEF: DE = 25, EF = 40, FD =50<br \/>\nAnswer:<\/p>\n<p>In Exercises 9 and 10. determine whether the two triangles are similar. If they are similar, write a similarity statement and find the scale factor of triangle B to triangle A.<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48456\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-91.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 91\" width=\"253\" height=\"138\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52905\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-9.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 9\" width=\"582\" height=\"225\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-9.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-9-300x116.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48455\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-92.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 92\" width=\"277\" height=\"117\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 11 and 12, sketch the triangles using the given description. Then determine whether the two triangles can be similar.<\/p>\n<p>Question 11.<br \/>\nIn \u2206RST, RS = 20, ST = 32, and m\u2220S = 16\u00b0. In \u2206FGH, GH = 30, HF = 48, and m\u2220H = 24\u00b0.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52906\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-11.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 11\" width=\"561\" height=\"261\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-11.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-11-300x140.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 12.<br \/>\nThe side lengths of \u2206ABC are 24, 8x, and 48, and the side lengths of \u2206DEF are 15, 25, and 6x.<\/p>\n<p>Answer:<br \/>\n\\(\\frac { AB }{ DE } \\) = \\(\\frac { AC }{ DF } \\) = \\(\\frac { BC }{ EF } \\)<br \/>\n\\(\\frac { 24 }{ 15 } \\) = \\(\\frac { 8x }{ 25 } \\)<br \/>\nx = 5<\/p>\n<p>In Exercises 13 &#8211; 16. show that the triangles are similar and write a similarity statement. Explain your reasoning.<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48454\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-93.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 93\" width=\"127\" height=\"120\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52907\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-13.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 13\" width=\"441\" height=\"275\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-13.png 441w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-13-300x187.png 300w\" sizes=\"(max-width: 441px) 100vw, 441px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48453\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-94.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 94\" width=\"182\" height=\"121\" \/><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48452\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-95.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 95\" width=\"310\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-95.png 310w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-95-300x108.png 300w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52908\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-15.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 15\" width=\"448\" height=\"201\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-15.png 448w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-15-300x135.png 300w\" sizes=\"(max-width: 448px) 100vw, 448px\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48451\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-96.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 96\" width=\"253\" height=\"129\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 17 and 18, use \u2206XYZ.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-48450\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-97.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 97\" width=\"128\" height=\"150\" \/><\/p>\n<p>Question 17.<br \/>\nThe shortest side of a triangle similar to \u2206XYZ is 20 units long. Find the other side lengths of the triangle.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52909\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-17.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 17\" width=\"566\" height=\"70\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-17.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-17-300x37.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 18.<br \/>\nThe longest side of a triangle similar to \u2206XYZ is 39 units long. Find the other side lengths of the triangle.<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in writing a similarity statement.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48449\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-98.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 98\" width=\"342\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-98.png 342w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-98-300x148.png 300w\" sizes=\"(max-width: 342px) 100vw, 342px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52910\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-19.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 19\" width=\"574\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-19.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-19-300x35.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 20.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nFind the value of n that makes \u2206DEF ~ \u2206XYZ when DE = 4, EF = 5, XY = 4(n + 1), YZ = 7n &#8211; 1, and \u2220E \u2245 \u2220Y. Include a sketch.<\/p>\n<p>Answer:<br \/>\n\\(\\frac { DE }{ XY } \\) = \\(\\frac { EF }{ YZ } \\)<br \/>\n\\(\\frac { 4 }{ 4(n + 1) } \\) = \\(\\frac { 5 }{ 7n &#8211; 1 } \\)<br \/>\ncross multiply the fractions<br \/>\n4(7n &#8211; 1) = 20(n + 1)<br \/>\n28n &#8211; 4 = 20n + 20<br \/>\n28n &#8211; 20n = 20 + 4<br \/>\n8n = 24<br \/>\nn = \\(\\frac { 24 }{ 8 } \\)<br \/>\nn = 3<\/p>\n<p><strong>ATTENDING TO PRECISION<\/strong><br \/>\nIn Exercises 21 &#8211; 26, use the diagram to copy and complete the statement.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-48448\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-99.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 99\" width=\"264\" height=\"189\" \/><\/p>\n<p>Question 21.<br \/>\nm\u2220LNS = ___________<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52911\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-21.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 21\" width=\"512\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-21.png 512w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-21-300x33.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/p>\n<p>Question 22.<br \/>\nm\u2220NRQ = ___________<br \/>\nAnswer:<br \/>\nm\u2220NRQ = m\u2220NRP = 91\u00b0 by the vertical congruence<\/p>\n<p>Question 23.<br \/>\nm\u2220NQR = ___________<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52912\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-23.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 23\" width=\"300\" height=\"127\" \/><\/p>\n<p>Question 24.<br \/>\nRQ = ___________<\/p>\n<p>Answer:<br \/>\nRQ = 4\u221a3<\/p>\n<p>Explanation:<br \/>\nUsing the pythogrean theorem<br \/>\nNQ\u00b2 = NR\u00b2 + RQ\u00b2<br \/>\n8\u00b2 = 4\u00b2 + RQ\u00b2<br \/>\n64 = 16 + RQ\u00b2<br \/>\n64 &#8211; 16 = RQ\u00b2<br \/>\n48 = RQ\u00b2<br \/>\nRQ = 4\u221a3<\/p>\n<p>Question 25.<br \/>\nm\u2220NSM = ___________<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52913\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-25.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 25\" width=\"283\" height=\"101\" \/><\/p>\n<p>Question 26.<br \/>\nm\u2220NPR = ___________<\/p>\n<p>Answer:<br \/>\nm\u2220NPR = 28\u00b0<\/p>\n<p>Explanation:<br \/>\nm\u2220NPR + m\u2220NRP +\u00a0m\u2220RNP = 180\u00b0<br \/>\nm\u2220NPR + 91\u00b0 + 61\u00b0 = 180\u00b0<br \/>\nm\u2220NPR + 152\u00b0 = 180\u00b0<br \/>\nm\u2220NPR = 180\u00b0 &#8211; 152\u00b0<br \/>\nm\u2220NPR = 28\u00b0<\/p>\n<p>Question 27.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims that \u2206JKL ~ \u2206MNO by the SAS Similarity Theorem (Theorem 8.5) when JK = 18, m\u2220K = 130\u00b0 KL = 16, MN = 9, m\u2220N = 65\u00b0, and NO = 8, Do you support your friend\u2019s claim? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52914\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-27.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 27\" width=\"558\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-27.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-27-300x32.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nCertain sections of stained glass are sold in triangular, beveled pieces. Which of the three beveled pieces, if any, are similar?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48447\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-100.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 100\" width=\"337\" height=\"175\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-100.png 337w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-100-300x156.png 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><br \/>\nAnswer:<br \/>\nOut of three triangles, violet and blue triangles are similar.<\/p>\n<p>Explanation:<br \/>\nCheck the similarity of maroon and violet triangles.<br \/>\nlongest sides: \\(\\frac { 5 }{ 7 } \\)<br \/>\nshortest sides: \\(\\frac { 3 }{ 4 } \\)<br \/>\nremaining sides: \\(\\frac { 3 }{ 4 } \\)<br \/>\nThe ratios are not equal. So those traingles are not similar.<br \/>\nCheck the similarity of blue and violet triangles.<br \/>\nlongest sides: \\(\\frac { 5 }{ 5.25 } \\) = 1<br \/>\nshortest sides: \\(\\frac { 3 }{ 3 } \\) = 1<br \/>\nremaining sides: \\(\\frac { 3 }{ 3 } \\) = 1<br \/>\nThe ratios are equal. So those traingles are similar.<\/p>\n<p>Question 29.<br \/>\n<strong>ATTENDING TO PRECISION<\/strong><br \/>\nIn the diagram, \\(\\frac{M N}{M R}=\\frac{M P}{M Q}\\) Which of the statements must be true?<br \/>\nSelect all that apply. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48446\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-101.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 101\" width=\"191\" height=\"106\" \/><br \/>\n(A) \u22201 \u2245\u22202<br \/>\n(B) \\(\\overline{Q R}\\) || \\(\\overline{N P}\\)<br \/>\n(C)\u22201 \u2245 \u22204<br \/>\n(D) \u2206MNP ~ \u2206MRQ<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52915\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-29.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 29\" width=\"529\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-29.png 529w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-29-300x50.png 300w\" sizes=\"(max-width: 529px) 100vw, 529px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>WRITING<\/strong><br \/>\nAre any two right triangles similar? Explain.<\/p>\n<p>Answer:<br \/>\nYes, any two right triangles can be similar. If two right triangles are similar, then the ratio of their longest, smallest and remaining side lengths must be equal and their angles must be congruent.<\/p>\n<p>Question 31.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nIn the portion of the shuffleboard court shown, \\(\\frac{B C}{A C}=\\frac{B D}{A E}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48445\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-102.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 102\" width=\"337\" height=\"199\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-102.png 337w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-102-300x177.png 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><br \/>\na. What additional information do you need to show that \u2206BED ~ \u2206ACE using the SSS Similarity Theorem (Theorem 8.4)?<br \/>\nb. What additional information do, you need to show that \u2206BCD ~ \u2206ACE using the SAS Similarity Theorem (Theorem 8.5)?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52916\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-31.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 31\" width=\"198\" height=\"84\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>PROOF<\/strong><br \/>\nGiven that \u2206BAC is a right triangle and D, E, and F are midpoints. prove that m\u2220DEF = 90\u00b0.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48444\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-103.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 103\" width=\"170\" height=\"89\" \/><\/p>\n<p>Answer:<br \/>\nBy observing the triangle ABC, m\u2220BAC = 90\u00b0<br \/>\nJoin the midpoints of the sides of the triangle.<br \/>\nm\u2220DEF = 90\u00b0<\/p>\n<p>Question 33.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nWrite a two-column proof of the SAS Similarity Theorem (Theorem 8.5).<br \/>\nGiven \u2220A \u2245 \u2220D, \\(\\frac{A B}{D E}=\\frac{A C}{D F}\\)<br \/>\nProve \u2206ABC ~ \u2206DEF<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48443\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-104.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 104\" width=\"284\" height=\"108\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52917\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-33.1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 33.1\" width=\"305\" height=\"210\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-33.1.png 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-33.1-300x207.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52918\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-33.2.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 33.2\" width=\"769\" height=\"516\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-33.2.png 769w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-33.2-300x201.png 300w\" sizes=\"(max-width: 769px) 100vw, 769px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52919\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-33.3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 33.3\" width=\"795\" height=\"440\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-33.3.png 795w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-33.3-300x166.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-33.3-768x425.png 768w\" sizes=\"(max-width: 795px) 100vw, 795px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nYou are given two right triangles with one pair of corresponding legs and the pair of hypotenuses having the same length ratios.<br \/>\na. The lengths of the given pair of corresponding legs are 6 and 18, and the lengths of the hypotenuses are 10 and 30. Use the Pythagorean Theorem to find the lengths of the other pair of corresponding legs. Draw a diagram.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-102097\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/big-ideas-math-geometry-answers-chapter-8-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 3\" width=\"624\" height=\"385\" \/><\/p>\n<p>b. Write the ratio of the lengths of the second pair of corresponding legs.<br \/>\nAnswer:<br \/>\nFirst find the length of AC using pythagorean theorem<br \/>\nAC\u00b2 + AB\u00b2 = BC\u00b2<br \/>\nAC\u00b2 + 36 = 100<br \/>\nAC\u00b2 = 64<br \/>\nAC = 8<br \/>\nFind the length of DF using pythagorean theorem<br \/>\nDF\u00b2 + DE\u00b2 = EF\u00b2<br \/>\nDF\u00b2 + 18\u00b2 = 30\u00b2<br \/>\nDF\u00b2 = 900 &#8211; 324<br \/>\nDF\u00b2 = 576<br \/>\nDF= 24<\/p>\n<p>c. Are these triangles similar? Does this suggest a Hypotenuse-Leg Similarity Theorem for right triangles? Explain.<br \/>\nAnswer:<br \/>\nk = \\(\\frac { AC }{ DF } \\) = \\(\\frac { 8 }{ 24 } \\) = \\(\\frac { 1 }{ 3 } \\)<br \/>\nk = \\(\\frac { AB }{ DE } \\) = \\(\\frac { 6 }{ 18 } \\) = \\(\\frac { 1 }{ 3 } \\)<br \/>\nSo, triangles are similar.<\/p>\n<p>Question 35.<br \/>\n<strong>WRITING<\/strong><br \/>\nCan two triangles have all three ratios of corresponding angle measures equal to a value greater than 1 ? less than 1 ? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52920\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-35.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 35\" width=\"574\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-35.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-35-300x57.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nWhich theorem could you use to show that \u2206OPQ ~ \u2206OMN in the portion of the Ferris wheel shown when PM = QN = 5 feet and MO = NO = 10 feet?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48442\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-105.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 105\" width=\"291\" height=\"203\" \/><br \/>\nAnswer:<br \/>\nThe corresponding angle theorem states that \u2206OPQ is similar to \u2206OMN.<\/p>\n<p>Question 37.<br \/>\n<strong>DRAWING CONCLUSIONS<\/strong><br \/>\nExplain why it is not necessary to have an Angle-Side-Angle Similarity Theorem.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52921\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-37.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 37\" width=\"518\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-37.png 518w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-37-300x35.png 300w\" sizes=\"(max-width: 518px) 100vw, 518px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nDecide whether each is a valid method of showing that two quadrilaterals are similar. Justify your answer.<br \/>\na. SASA<br \/>\nAnswer:<br \/>\nIf an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar.<\/p>\n<p>b. SASAS<br \/>\nAnswer:<br \/>\nIf two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.<\/p>\n<p>c. SSSS<br \/>\nAnswer:<br \/>\nIf the corresponding side lengths of two triangles are proportional, then the triangles are similar.<\/p>\n<p>d. SASSS<br \/>\nAnswer:<br \/>\nIf two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then those two triangles are similar.<\/p>\n<p>Question 39.<br \/>\n<strong>MULTIPLE REPRESENTATIONS<\/strong><br \/>\nUse a diagram to show why there is no Side-Side-Angle Similarity Theorem.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52922\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-39.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 39\" width=\"425\" height=\"157\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-39.png 425w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-39-300x111.png 300w\" sizes=\"(max-width: 425px) 100vw, 425px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe dimensions of an actual swing set are shown. You want to create a scale model of the swing set for a dollhouse using similar triangles. Sketch a drawing of your swing set and label each side length. Write a similarity statement for each pair of similar triangles. State the scale factor you used to create the scale model.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48441\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-106.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 106\" width=\"322\" height=\"266\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-106.png 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-106-300x248.png 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nAnswer:<br \/>\nHere we have to check the similarity statement for \u25b3ABC, \u25b3DEF.<br \/>\nThe scale factor k = \\(\\frac { AB }{ DE } \\) = \\(\\frac { 8 }{ 6 } \\) = \\(\\frac { 4 }{ 3 } \\)<\/p>\n<p>Question 41.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nCopy and complete the paragraph proot of the second part of the Slopes of Parallel Lines Theorem (Theorern 3. 13) from page 439.<br \/>\nGiven m<sub>l<\/sub> = m<sub>n<\/sub>, l and n are nonvertical.<br \/>\nProve l || n<br \/>\nYou are given that m<sub>l<\/sub> = m<sub>n<\/sub>. By the definition of slope. m<sub>l<\/sub> = \\(\\frac{B C}{A C}\\) and m<sub>n<\/sub> = \\(\\frac{E F}{D F}\\) By ____________, \\(\\frac{B C}{A C}=\\frac{E F}{D F}\\). Rewriting this proportion yields ___________,<\/p>\n<p>By the Right Angles Congruence Theorem (Thin. 2.3), ___________, So. \u2206ABC ~ \u2206DEF by ___________ . Because corresponding angles of similar triangles are congruent, \u2220BAC \u2245\u2220EDF. By ___________, l || n.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48440\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-107.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 107\" width=\"182\" height=\"157\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52923\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-41.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 41\" width=\"574\" height=\"381\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-41.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-41-300x199.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nCopy and complete the two-column proof 0f the second part of the Slopes of Perpendicular Lines Theorem (Theorem 3.14)<br \/>\nGiven m<sub>l<\/sub> m<sub>n<\/sub> = &#8211; 1, l and n are nonvertical.<br \/>\nProve l \u22a5 n<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48439\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-108.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 8 Similarity 108\" width=\"198\" height=\"153\" \/><\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"248\">Statements<\/td>\n<td style=\"text-align: center;\" width=\"279\">Reasons<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">1. m<sub>l<\/sub>m<sub>n<\/sub> = &#8211; 1<\/td>\n<td width=\"279\">1. Given<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">2. m<sub>l<\/sub> = \\(\\frac{D E}{A D}\\), m<sub>n<\/sub> = \\(\\frac{A B}{B C}\\)<\/td>\n<td width=\"279\">2. Definition of slope<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">3. \\(\\frac{D E}{A D} \\cdot-\\frac{A B}{B C}\\) = &#8211; 1<\/td>\n<td width=\"279\">3. ________________________________<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">4. \\(\\frac{D E}{A D}=\\frac{B C}{A B}\\)<\/td>\n<td width=\"279\">4. Multiply each side of statement 3 by &#8211;\\(\\frac{B C}{A B}\\).<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">5. \\(\\frac{D E}{B C}\\) = ____________<\/td>\n<td width=\"279\">5. Rewrite proportion.<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">6. ________________________________<\/td>\n<td width=\"279\">6. Right Angles Congruence Theorem (Thm. 2.3)<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">7. \u2206ABC ~ \u2206ADE<\/td>\n<td width=\"279\">7. ________________________________<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">8. \u2220BAC \u2245 \u2220DAE<\/td>\n<td width=\"279\">8. Corresponding angles of similar figures are congruent.<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">9. \u2220BCA \u2245 \u2220CAD<\/td>\n<td width=\"279\">9. Alternate Interior Angles Theorem (Thm. 3.2)<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">10. m\u2220BAC = m\u2220DAE, m\u2220BCA = m\u2220CAD<\/td>\n<td width=\"279\">10. ________________________________<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">11. m\u2220BAC + m\u2220BCA + 90\u00b0 = 180\u00b0<\/td>\n<td width=\"279\">11. ________________________________<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">12. ________________________________<\/td>\n<td width=\"279\">12. Subtraction Property of Equality<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">13. m\u2220CAD + m\u2220DAE = 90\u00b0<\/td>\n<td width=\"279\">13. Substitution Property of Equality<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">14. m\u2220CAE = m\u2220DAE + m\u2220CAD<\/td>\n<td width=\"279\">14. Angle Addition Postulate (Post. 1.4)<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">15. m\u2220CAE = 90\u00b0<\/td>\n<td width=\"279\">15. ________________________________<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">16. ________________________________<\/td>\n<td width=\"279\">16. Definition of perpendicular lines<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Answer:<\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"248\">Statements<\/td>\n<td style=\"text-align: center;\" width=\"279\">Reasons<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">1. m<sub>l<\/sub>m<sub>n<\/sub> = &#8211; 1<\/td>\n<td width=\"279\">1. Given<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">2. m<sub>l<\/sub> = \\(\\frac{D E}{A D}\\), m<sub>n<\/sub> = \\(\\frac{A B}{B C}\\)<\/td>\n<td width=\"279\">2. Definition of slope<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">3. \\(\\frac{D E}{A D} \\cdot-\\frac{A B}{B C}\\) = &#8211; 1<\/td>\n<td width=\"279\">3. Correspomsding sides are opposite<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">4. \\(\\frac{D E}{A D}=\\frac{B C}{A B}\\)<\/td>\n<td width=\"279\">4. Multiply each side of statement 3 by &#8211;\\(\\frac{B C}{A B}\\).<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">5. \\(\\frac{D E}{B C}\\) = \\(\\frac { AB }{ AD } \\)<\/td>\n<td width=\"279\">5. Rewrite proportion.<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">6. Two right-angled triangles are said to be congruent to each other if the hypotenuse and one side of the right triangle are equal to the hypotenuse and the corresponding side of the other right-angled triangle.<\/td>\n<td width=\"279\">6. Right Angles Congruence Theorem (Thm. 2.3)<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">7. \u2206ABC ~ \u2206ADE<\/td>\n<td width=\"279\">7. According to the side angle side theorem.<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">8. \u2220BAC \u2245 \u2220DAE<\/td>\n<td width=\"279\">8. Corresponding angles of similar figures are congruent.<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">9. \u2220BCA \u2245 \u2220CAD<\/td>\n<td width=\"279\">9. Alternate Interior Angles Theorem (Thm. 3.2)<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">10. m\u2220BAC = m\u2220DAE, m\u2220BCA = m\u2220CAD<\/td>\n<td width=\"279\">10. Congruent angles<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">11. m\u2220BAC + m\u2220BCA + 90\u00b0 = 180\u00b0<\/td>\n<td width=\"279\">11. \u25b3ABC is a right-angled triangle<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">12. m\u2220CAD + m\u2220DAE = 90\u00b0<\/td>\n<td width=\"279\">12. Subtraction Property of Equality<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">13. m\u2220CAD + m\u2220DAE = 90\u00b0<\/td>\n<td width=\"279\">13. Substitution Property of Equality<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">14. m\u2220CAE = m\u2220DAE + m\u2220CAD<\/td>\n<td width=\"279\">14. Angle Addition Postulate (Post. 1.4)<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">15. m\u2220CAE = 90\u00b0<\/td>\n<td width=\"279\">15. Right Angle<\/td>\n<\/tr>\n<tr>\n<td width=\"248\">16. If two lines meet each other a an angle of 90\u00b0, then they are called the perpendicular lines.<\/td>\n<td width=\"279\">16. Definition of perpendicular lines<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Maintaining Mathematical proficiency<\/p>\n<p>Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio.<\/p>\n<p>Question 43.<br \/>\nA(- 3, 6), B(2, 1); 3 to 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52924\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-43.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 43\" width=\"584\" height=\"355\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-43.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-43-300x182.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 44.<br \/>\nA(- 3, &#8211; 5), B(9, &#8211; 1); 1 to 3<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\nA(1, &#8211; 2), B(8, 12); 4 to 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52925\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-45.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 45\" width=\"580\" height=\"380\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-45.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-45-300x197.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<h3><a id=\"8.4_Proportionality_Theorems\"><\/a>8.4 Proportionality Theorems<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Discovering a Proportionality Relationship<\/p>\n<p>Work with a partner. Use dynamic geometry software to draw any \u2206ABC.<br \/>\na. Construct \\(\\overline{D E}\\) parallel to \\(\\overline{B C}\\) with endpoints on \\(\\overline{A B}\\) and \\(\\overline{A C}\\), respectively.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48928\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-109.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 109\" width=\"306\" height=\"242\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-109.png 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-109-300x237.png 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><br \/>\nAnswer:<\/p>\n<p>b. Compare the ratios of AD to BD and AE to CE.<br \/>\nAnswer:<\/p>\n<p>c. Move \\(\\overline{D E}\\) to other locations Parallel to \\(\\overline{B C}\\) with endpoints on \\(\\overline{A B}\\) and \\(\\overline{A C}\\), and repeat part (b).<br \/>\nAnswer:<\/p>\n<p>d. Change \u2206ABC and repeat parts (a) &#8211; (c) several times. Write a conjecture that summarizes your results.<br \/>\n<strong>LOOKING FOR STRUCTURE<\/strong><br \/>\nTo be proficient in math, you need to look closely to discern a pattern or structure.<br \/>\nAnswer:<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Discovering a Proportionality Relationship<\/p>\n<p>Work with a partner. Use dynamic geometry software to draw any AABC.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-48927\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-110.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 110\" width=\"304\" height=\"241\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-110.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-110-300x238.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><\/p>\n<p>a. Bisect \u2206B and plot point D at the intersection of the angle bisector and \\(\\overline{A C}\\).<br \/>\nAnswer:<\/p>\n<p>b. Compare the ratios of AD to DC and BA to BC.<br \/>\nAnswer:<\/p>\n<p>c. Change \u2206ABC and repeat parts (a) and (b) several times. Write a conjecture that summarizes your results.<br \/>\nAnswer:<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 3.<br \/>\nWhat proportionality relationships exist in a triangle intersected by an angle bisector or by a line parallel to one of the sides?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48926\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-111.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 111\" width=\"162\" height=\"139\" \/><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nUse the figure at the right to write a proportion.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48926\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-111.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 111\" width=\"162\" height=\"139\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_8.4_Proportionality_Theorems\"><\/a>Lesson 8.4 Proportionality Theorems<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nFind the length of \\(\\overline{Y Z}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48925\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-112.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 112\" width=\"203\" height=\"95\" \/><br \/>\nAnswer:<br \/>\nYZ = \\(\\frac { 315 }{ 11 } \\)<\/p>\n<p>Explanation:<br \/>\nTriangle property thorem is \\(\\frac { XW }{ WV } \\) = \\(\\frac { XY }{ YZ } \\)<br \/>\n\\(\\frac { 44 }{ 35 } \\) = \\(\\frac { 36 }{ YZ } \\)<br \/>\ncross multiply the fractions<br \/>\n44 \u2022 YZ = 36 \u2022 35<br \/>\n44 \u2022 YZ = 1260<br \/>\nYZ = \\(\\frac { 1260 }{ 44 } \\)<br \/>\nYZ = \\(\\frac { 315 }{ 11 } \\)<\/p>\n<p>Question 2.<br \/>\nDetermine whether \\(\\overline{P S}\\) || \\(\\overline{Q R}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48924\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-113.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 113\" width=\"184\" height=\"101\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac { PQ }{ PN } \\) = \\(\\frac { 50 }{ 90 } \\) = \\(\\frac { 5 }{ 9 } \\)<br \/>\n\\(\\frac { SR }{ SN } \\) = \\(\\frac { 40 }{ 72 } \\) = \\(\\frac { 5 }{ 9 } \\)<br \/>\n\\(\\frac { PQ }{ PN } \\) = \\(\\frac { SR }{ SN } \\) so PS is parallel to QR<\/p>\n<p>Find the length of the given line segment.<\/p>\n<p>Question 3.<br \/>\n\\(\\overline{B D}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48923\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-114.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 114\" width=\"133\" height=\"146\" \/><\/p>\n<p>Answer:<br \/>\n\\(\\overline{B D}\\) = 12<\/p>\n<p>Explanation:<br \/>\nAll the angles are congruent. So, \\(\\overline{A B}\\), \\(\\overline{C D}\\), \\(\\overline{E F}\\) are parallel.<br \/>\nusing the three parallel lines theorem<br \/>\n\\(\\frac { BD }{ DF } \\) = \\(\\frac { AC }{ CE } \\)<br \/>\n\\(\\frac { [latex]\\overline{B D}\\) }{ 30 } [\/latex] = \\(\\frac { 16 }{ 40 } \\)<br \/>\n\\(\\overline{B D}\\) = \\(\\frac { 16 }{ 40 } \\) \u2022 30<br \/>\n\\(\\overline{B D}\\) = 12<\/p>\n<p>Question 4.<br \/>\n\\(\\overline{J M}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48922\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-115.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 115\" width=\"216\" height=\"146\" \/><\/p>\n<p>Answer:<br \/>\n\\(\\overline{J M}\\) = \\(\\frac { 96 }{ 5 } \\)<\/p>\n<p>Explanation:<br \/>\nAll the angles are congruent. So, \\(\\overline{G H}\\), \\(\\overline{J K}\\), \\(\\overline{M N}\\) are parallel.<br \/>\nusing the three parallel lines theorem<br \/>\n\\(\\frac { HK }{ KN } \\) = \\(\\frac { GJ }{ JM } \\)<br \/>\n\\(\\frac { 15 }{ 18 } \\) = \\(\\frac { 16 }{ [latex]\\overline{J M}\\) } [\/latex]<br \/>\nCross multiply<br \/>\n15 \u2022 \\(\\overline{J M}\\) = 16 \u2022 18 = 288<br \/>\n\\(\\overline{J M}\\) = \\(\\frac { 288 }{ 15 } \\)<br \/>\n\\(\\overline{J M}\\) = \\(\\frac { 96 }{ 5 } \\)<\/p>\n<p>Find the value of the variable.<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48921\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-116.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 116\" width=\"181\" height=\"104\" \/><\/p>\n<p>Answer:<br \/>\nx = 28<\/p>\n<p>Explanation:<br \/>\n\\(\\overline{T V}\\) is the angle bisector<br \/>\nSo, \\(\\frac { ST }{ TU } \\) = \\(\\frac { SV }{ VU } \\)<br \/>\n\\(\\frac { 14 }{ x } \\) = \\(\\frac { 24 }{ 48 } \\)<br \/>\ncross multiply<br \/>\n24x = 14 \u2022 48 = 672<br \/>\nx = \\(\\frac { 672 }{ 24 } \\)<br \/>\nx = 28<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48920\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-117.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 117\" width=\"122\" height=\"111\" \/><\/p>\n<p>Answer:<br \/>\nx = 4\u221a2<\/p>\n<p>Explanation:<br \/>\n\\(\\overline{W Z}\\) is the angle bisector<br \/>\nSo, \\(\\frac { YZ }{ ZX } \\) = \\(\\frac { YW }{ WX } \\)<br \/>\n\\(\\frac { 4 }{ 4 } \\) = \\(\\frac { 4\u221a2 }{ x } \\)<br \/>\ncross multiply<br \/>\n4x = 4 \u2022 4\u221a2 = 16\u221a2<br \/>\nx = 4\u221a2<\/p>\n<h3><a id=\"Exercise_8.4_Proportionality_Theorems\"><\/a>Exercise 8.4 Proportionality Theorems<\/h3>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>COMPLETE THE STATEMENT<\/strong><br \/>\nIf a line divides two sides of a triangle proportionally, then it is ____________ to the third side. This theorem is knon as the ____________ .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52926\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 1\" width=\"584\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-1.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-1-300x45.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nIn \u2206ABC, point R lies on \\(\\overline{B C}\\) and \\(\\vec{A}\\)R bisects \u2206CAB. Write the proportionality statement for the triangle that is based on the Triangle Angle Bisector Theorem (Theorem 8.9).<\/p>\n<p>Answer:<br \/>\nAccording to the triangle angle bisector theorem \\(\\frac { CR }{ BR } \\) = \\(\\frac { AC }{ AB } \\)<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3 and 4, find the length of \\(\\overline{A B}\\) .<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48919\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-118.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 118\" width=\"155\" height=\"110\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52927\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 3\" width=\"262\" height=\"228\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48918\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-119.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 119\" width=\"187\" height=\"109\" \/><\/p>\n<p>Answer:<br \/>\n\\(\\frac { AE }{ ED } \\) = \\(\\frac { AB }{ BC } \\)<br \/>\n\\(\\frac { 14 }{ 12 } \\) = \\(\\frac { AB }{ 18 } \\)<br \/>\nAB = \\(\\frac { 14 }{ 12 } \\) \u2022 18<br \/>\nAB = 21 units.<\/p>\n<p>In Exercises 5 &#8211; 8, determine whether \\(\\overline{K M}\\) || \\(\\overline{J N}\\).<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48917\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-120.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 120\" width=\"148\" height=\"110\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52928\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 5\" width=\"307\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-5.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-5-300x206.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48916\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-121.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 121\" width=\"165\" height=\"108\" \/><br \/>\nAnswer:<br \/>\nIf \\(\\frac { JK }{ KL } \\) = \\(\\frac { NM }{ ML } \\), then KM || JN<br \/>\n\\(\\frac { JK }{ KL } \\) = latex]\\frac { 22.5 }{ 25 } [\/latex] = latex]\\frac { 9 }{ 10 } [\/latex]<br \/>\n\\(\\frac { NM }{ ML } \\) = \\(\\frac { 18 }{ 20 } \\) = latex]\\frac { 9 }{ 10 } [\/latex]<br \/>\n\\(\\frac { JK }{ KL } \\) = \\(\\frac { NM }{ ML } \\)<br \/>\nHence KM || JN<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48915\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-122.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 122\" width=\"171\" height=\"163\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52929\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-7.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 7\" width=\"388\" height=\"217\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-7.png 388w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-7-300x168.png 300w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48914\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-123.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 123\" width=\"115\" height=\"188\" \/><br \/>\nAnswer:<br \/>\nIf \\(\\frac { JK }{ KL } \\) = \\(\\frac { NM }{ ML } \\), then KM || JN<br \/>\n\\(\\frac { JK }{ KL } \\) = latex]\\frac {35 }{ 16 } [\/latex]<br \/>\n\\(\\frac { NM }{ ML } \\) = \\(\\frac { 34 }{ 15 } \\)<br \/>\n\\(\\frac { JK }{ KL } \\) \u2260 \\(\\frac { NM }{ ML } \\)<br \/>\nSo, KM is not parallel to JN<\/p>\n<p><strong>CONSTRUCTION<\/strong><br \/>\nIn Exercises 9 &#8211; 12, draw a segment with the given length. Construct the point that divides the segment in the given ratio.<br \/>\nQuestion 9.<br \/>\n3 in.; 1 to 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52930\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-9.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 9\" width=\"541\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-9.png 541w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-9-300x48.png 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Question 10.<br \/>\n2 in.; 2 to 3<\/p>\n<p>Answer:<br \/>\nConstruct a 2 inch segment and divide the segment into 2 + 3 or 5 congruent pieces. Point P is the point that is \\(\\frac { 1 }{ 5 } \\) of the way from point A to point B.<\/p>\n<p>Question 11.<br \/>\n12 cm; 1 to 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52931\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-11.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 11\" width=\"582\" height=\"248\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-11.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-11-300x128.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 12.<br \/>\n9 cm ; 2 to 5<br \/>\nAnswer:<br \/>\nConstruct a 9 cm segment and divide the segment into 2 + 5 or 7 congruent pieces. Point p is the point that is \\(\\frac { 1 }{ 7 } \\) of the way from point A to point B.<\/p>\n<p>In Exercises 13 &#8211; 16, use the diagram to complete the proportion.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-48913\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-124.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 124\" width=\"159\" height=\"91\" \/><\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48912\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-125.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 125\" width=\"83\" height=\"50\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52932\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-13.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 13\" width=\"115\" height=\"52\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48911\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-126.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 126\" width=\"83\" height=\"49\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac { CG }{ EG } \\) = \\(\\frac { BF }{ DF } \\)<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48910\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-127.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 127\" width=\"81\" height=\"54\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52933\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-15.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 15\" width=\"111\" height=\"55\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48909\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-128.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 128\" width=\"84\" height=\"52\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac { BF }{ BD } \\) = \\(\\frac { CG }{ CE } \\)<\/p>\n<p>In Exercises 17 and 18, find the length of the indicated line segment.<\/p>\n<p>Question 17.<br \/>\n\\(\\overline{V X}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48908\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-129.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 129\" width=\"159\" height=\"109\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52934\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-17.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 17\" width=\"271\" height=\"260\" \/><\/p>\n<p>Question 18.<br \/>\n\\(\\overline{S U}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48907\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-130.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 130\" width=\"147\" height=\"106\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac { SU }{ NS } \\) = \\(\\frac { RT }{ PR } \\)<br \/>\n\\(\\frac { SU }{ 10 } \\) = \\(\\frac { 12 }{ 8 } \\)<br \/>\nSU = \\(\\frac { 12 }{ 8 } \\) \u2022 10<br \/>\nSU = 10<\/p>\n<p>In Exercises 19 &#8211; 22, find the value of the variable.<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48906\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-131.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 131\" width=\"103\" height=\"96\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52935\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-19.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 19\" width=\"160\" height=\"152\" \/><\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48905\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-132.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 132\" width=\"154\" height=\"73\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac { z }{ 1.5 } \\) = \\(\\frac { 3 }{ 4.5 } \\)<br \/>\nz = \\(\\frac { 3 }{ 4.5 } \\) \u2022 1.5<br \/>\nz = 1<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-133.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 133\" width=\"147\" height=\"99\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52936\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-21.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 21\" width=\"211\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-21.png 211w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-21-150x150.png 150w\" sizes=\"(max-width: 211px) 100vw, 211px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48903\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-134.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 134\" width=\"162\" height=\"90\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac { q }{ 16 &#8211; q } \\) = \\(\\frac { 36 }{ 28 } \\)<br \/>\n28q = 36 (16 &#8211; q)<br \/>\n28q = 576 &#8211; 36q<br \/>\n28q + 36q = 576<br \/>\n64q = 576<br \/>\nq = 9<\/p>\n<p>Question 23.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in solving for x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48902\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-135.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 135\" width=\"345\" height=\"213\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-135.png 345w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-135-300x185.png 300w\" sizes=\"(max-width: 345px) 100vw, 345px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52937\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-23.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 23\" width=\"583\" height=\"218\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-23.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-23-300x112.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 24.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in the students reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48901\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-136.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 136\" width=\"329\" height=\"163\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-136.png 329w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-136-300x149.png 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac { BD }{ CD } \\) = \\(\\frac { AB }{ AC } \\)<br \/>\nBD = CD<br \/>\nSo, 1 = \\(\\frac { AB }{ AC } \\)<br \/>\nAC = AB<\/p>\n<p><strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nIn Exercises 25 and 26, find the value of x for which \\(\\overline{P Q}\\) || \\(\\overline{R S}\\).<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48900\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-137.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 137\" width=\"149\" height=\"104\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52938\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-25.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 25\" width=\"226\" height=\"220\" \/><\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48899\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-138.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 138\" width=\"157\" height=\"102\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac { PR }{ RT } \\) = \\(\\frac { QS }{ ST } \\)<br \/>\n\\(\\frac { 12 }{ 2x &#8211; 2 } \\) = \\(\\frac { 21 }{ 3x &#8211; 1 } \\)<br \/>\n12(3x &#8211; 1) = 21(2x &#8211; 2)<br \/>\n36x &#8211; 12 = 42x &#8211; 42<br \/>\n42x &#8211; 36x = 42 &#8211; 12<br \/>\n6x = 30<br \/>\nx = 5<\/p>\n<p>Question 27.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nProve the Triangle Proportionality Theorem (Theorem 8.6).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48898\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-139.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 139\" width=\"179\" height=\"87\" \/><br \/>\nGiven \\(\\overline{Q S}\\) || \\(\\overline{T U}\\)<br \/>\nProve \\(\\frac{Q T}{T R}=\\frac{S U}{U R}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52939\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-27.1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 27.1\" width=\"581\" height=\"499\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-27.1.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-27.1-300x258.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52940\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-27.2.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 27.2\" width=\"574\" height=\"255\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-27.2.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-27.2-300x133.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nProve the Converse of the Triangle Proportionality Theorem (Theorem 8.7).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48897\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-140.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 140\" width=\"115\" height=\"84\" \/><br \/>\nGiven \\(\\frac{Z Y}{Y W}=\\frac{Z X}{X V}\\)<br \/>\nProve \\(\\overline{Y X}\\) || \\(\\overline{W V}\\)<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe real estate term lake frontage refers to the distance along the edge of a piece of property that touches a lake.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48896\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-141.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 141\" width=\"305\" height=\"176\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-141.png 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-141-300x173.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><br \/>\na. Find the lake frontage (to the nearest tenth) of each lot shown.<br \/>\nb. In general, the more lake frontage a lot has, the higher its selling price. Which lot(s) should be listed for the highest price?<br \/>\nc. Suppose that low prices are in the same ratio as lake frontages. If the least expensive lot is $250,000, what are the prices of the other lots? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52941\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-29.1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 29.1\" width=\"409\" height=\"543\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-29.1.png 409w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-29.1-226x300.png 226w\" sizes=\"(max-width: 409px) 100vw, 409px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52942\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-29.2.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 29.2\" width=\"522\" height=\"256\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-29.2.png 522w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-29.2-300x147.png 300w\" sizes=\"(max-width: 522px) 100vw, 522px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>USING STRUCTURE<\/strong><br \/>\nUse the diagram to find the values of x and y.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48895\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-142.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 142\" width=\"132\" height=\"134\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac { 5 }{ 2 } \\) = \\(\\frac { x }{ 1.5 } \\)<br \/>\nx = \\(\\frac { 5 }{ 2 } \\) \u2022 1.5<br \/>\nx = 3.75<br \/>\n\\(\\frac { 3 }{ 7 } \\) = \\(\\frac { y }{ 5.25 } \\)<br \/>\ny = \\(\\frac { 3 }{ 7 } \\) \u2022 5.25<br \/>\ny = 2.25<\/p>\n<p>Question 31.<br \/>\n<strong>REASONING<\/strong><br \/>\nIn the construction on page 447, explain why you can apply the Triangle Proportionality Theorem (Theorem 86) in Step 3.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52943\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-31.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 31\" width=\"556\" height=\"130\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-31.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-31-300x70.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nUse the diagram with the auxiliary line drawn to write a paragraph proof of the Three Parallel Lines Theorem (Theorem 8.8).<br \/>\nGiven K<sub>1<\/sub> || K<sub>2<\/sub> || K<sub>3<\/sub><br \/>\nProve \\(\\frac{C B}{B A}=\\frac{D E}{E F}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48894\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-143.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 143\" width=\"203\" height=\"149\" \/><br \/>\nAnswer:<br \/>\nFrom the diagram, we can see that K\u2081 || K\u2082 || K\u2083<br \/>\nThose three parallel lines interest two traversals t\u2081, t\u2082<br \/>\nSo, \\(\\frac{C B}{B A}=\\frac{D E}{E F}\\)<\/p>\n<p>Question 33.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nIn \u2206LMN, the angle bisector of \u2220M also bisects \\(\\overline{L N}\\). Classify \u2206LMN as specifically as possible. Justify your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52944\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-33.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 33\" width=\"578\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-33.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-33-300x59.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nDuring a football game, the quarterback throws the ball to the receiver. The receiver is between two defensive players, as shown. If Player 1 is closer to the quarterback when the ball is thrown and both defensive players move at the same speed, which player will reach the receiver first? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48893\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-144.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 144\" width=\"330\" height=\"185\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-144.png 330w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-144-300x168.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><br \/>\nAnswer:<br \/>\nAs per the image, player 1 is closer to the receiver. So, player 1 will reach the receiver first.<\/p>\n<p>Question 35.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nUse the diagram with the auxiliary lines drawn to write a paragraph proof of the Triangle Angle Bisector Theorem (Theorem 8.9).<br \/>\nGiven \u2220YXW \u2245 \u2220WXZ<br \/>\nprove \\(\\frac{Y W}{W Z}=\\frac{X Y}{X Z}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48892\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-145.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 145\" width=\"213\" height=\"109\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52945\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-35.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 35\" width=\"566\" height=\"531\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-35.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-35-300x281.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nWrite the converse of the Triangle Angle Bisector Theorem (Theorem 8.9). Is the converse true? Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<strong>REASONING<\/strong><br \/>\nHow is the Triangle Midsegment Theorem (Theorem 6.8) related to the Triangle Proportionality Theorem (Theorem 8.6)? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52946\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-37.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 37\" width=\"587\" height=\"138\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-37.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-37-300x71.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nTwo people leave points A and B at the same time. They intend to meet at point C at the same time. The person who leaves point A walks at a speed of 3 miles per hour. You and a friend are trying to determine how fast the person who leaves point B must walk. Your friend claims you need to know the length of \\(\\overline{A C}\\). Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48891\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-146.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 146\" width=\"252\" height=\"139\" \/><br \/>\nAnswer:<br \/>\nMy self starts walking from point A with a speed of 3 miles per hour and reaches point C.<br \/>\nMy friend starts walking from point B with x speed and reaches point C.<br \/>\n\\(\\frac { AD }{ DC } \\) = \\(\\frac { BE }{ CE } \\)<br \/>\nI have to travel from A to C. So, I need to know distance between AC.<br \/>\nTherefore, my friend is correct.<\/p>\n<p>Question 39.<br \/>\n<strong>CONSTRUCTION<\/strong><br \/>\nGiven segments with lengths r, s, and t, construct a segment of length x, such that \\(\\frac{r}{s}=\\frac{t}{x}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48890\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-147.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 147\" width=\"140\" height=\"91\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52947\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-39.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 39\" width=\"548\" height=\"145\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-39.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-39-300x79.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>PROOF<\/strong><br \/>\nProve Ceva&#8217;s Theorem: If P is any point inside \u2206ABC, then \\(\\frac{A Y}{Y C} \\cdot \\frac{C X}{X B} \\cdot \\frac{B Z}{Z A}\\) = 1<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48889\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-148.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 148\" width=\"236\" height=\"131\" \/><br \/>\n(Hint: Draw segments parallel to \\(\\overline{B Y}\\) through A and C, as shown. Apply the Triangle Proportionality Theorem (Theorem 8.6) to \u2206ACM. Show that \u2206APN ~ \u2206MPC, \u2206CXM ~ \u2206BXP, and \u2206BZP ~ \u2206AZN.)<br \/>\nAnswer:<\/p>\n<p>Maintaining Mathematical Proficiency<\/p>\n<p>Use the triangle.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-48888\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-149.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 8 Similarity 149\" width=\"166\" height=\"78\" \/><\/p>\n<p>Question 41.<br \/>\nWhich sides are the legs?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52948\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-41.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 41\" width=\"381\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-41.png 381w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-41-300x26.png 300w\" sizes=\"(max-width: 381px) 100vw, 381px\" \/><\/p>\n<p>Question 42.<br \/>\nWhich side is the hypotenuse?<br \/>\nAnswer:<br \/>\nThe leg c is the hypotenuse.<\/p>\n<p>Solve the equation.<\/p>\n<p>Question 43.<br \/>\nx<sup>2<\/sup>\u00a0= 121<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52949\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-43.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 43\" width=\"144\" height=\"99\" \/><\/p>\n<p>Question 44.<br \/>\nx<sup>2<\/sup> + 16 = 25<br \/>\nAnswer:<br \/>\nx\u00b2 + 16 = 25<br \/>\nx\u00b2 = 25 &#8211; 16<br \/>\nx\u00b2 = 9<br \/>\nx = <a id=\"emoji-info-url\" href=\"https:\/\/coolsymbol.com\/copy\/Minus-or-Plus_Sign_Symbol_%E2%88%93\"><span id=\"emoji-info-value\">\u2213<\/span><\/a>3<\/p>\n<p>Question 45.<br \/>\n36 + x<sup>2<\/sup> = 85<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52950\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-45.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 45\" width=\"163\" height=\"135\" \/><\/p>\n<h3><a id=\"Similarity_Chapter_Review\"><\/a>Similarity Review<\/h3>\n<h3>8.1 Similar Polygons<\/h3>\n<p>Find the scale factor. Then list all pairs of congruent angles and write the ratios of the corresponding side lengths in a statement of proportionality.<\/p>\n<p>Question 1.<br \/>\nABCD ~ EFGH<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49103\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-150.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 8 Similarity 150\" width=\"264\" height=\"121\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac { BC }{ CD } \\) = \\(\\frac { 8 }{ 12 } \\) = \\(\\frac { 2 }{ 3 } \\)<br \/>\n\\(\\frac { EH }{ GH } \\) = \\(\\frac { 6 }{ 9 } \\) = \\(\\frac { 2 }{ 3 } \\)<br \/>\nSo, scale factor = \\(\\frac { 2 }{ 3 } \\)<\/p>\n<p>Question 2.<br \/>\n\u2206XYZ ~ \u2206RPQ<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49102\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-151.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 8 Similarity 151\" width=\"248\" height=\"120\" \/><br \/>\nAnswer:<br \/>\nlonger sides: \\(\\frac { 10 }{ 25 } \\) = \\(\\frac { 2 }{ 5 } \\)<br \/>\nshorter sides: \\(\\frac { 6 }{ 15 } \\) = \\(\\frac { 2 }{ 5 } \\)<br \/>\nremaining sides: \\(\\frac { 8 }{ 20 } \\) = \\(\\frac { 2 }{ 5 } \\)<br \/>\nSo, scale factor = \\(\\frac { 2 }{ 5 } \\)<\/p>\n<p>Question 3.<br \/>\nTwo similar triangles have a scale factor of 3 : 5. The altitude of the larger triangle is 24 inches. What is the altitude of the smaller triangle?<br \/>\nAnswer:<br \/>\nScale factor of smaller triangle to larger traingle is \\(\\frac { 3 }{ 5 } \\) and larger traingle altitude is 24 inches<br \/>\nLet x be the smaller triangle altitude<br \/>\n\\(\\frac { altitude of smaller triangle }{ altitude of larger traingle } \\) = scale factor<br \/>\n\\(\\frac { x }{ 24 } \\) = \\(\\frac { 3 }{ 5 } \\)<br \/>\nx = \\(\\frac { 3 }{ 5 } \\) \u2022 24<br \/>\nx = 14.4<\/p>\n<p>Question 4.<br \/>\nTwo similar triangles have a pair of corresponding sides of length 12 meters and 8 meters. The larger triangle has a perimeter of 48 meters and an area of 180 square meters. Find the perimeter and area of the smaller triangle.<br \/>\nAnswer:<br \/>\nScale factor = \\(\\frac { 2 }{ 3 } \\)<br \/>\nperimeter of smaller triangle = 32<br \/>\nArea of smaller triangle = 80<\/p>\n<p>Explanation:<br \/>\nThe scale factor of smaller to larger traingle = \\(\\frac { 8 }{ 12 } \\) = \\(\\frac { 2 }{ 3 } \\)<br \/>\n\\(\\frac { perimeter of smaller triangle }{ perimeter of larger triangle } \\) = scale factor\\(\\frac { perimeter of smaller triangle }{ 48 } \\) = \\(\\frac { 2 }{ 3 } \\)<br \/>\nperimeter of smaller triangle = \\(\\frac { 2 }{ 3 } \\) \u2022 48<br \/>\nperimeter of smaller triangle = 32<br \/>\n\\(\\frac { Area of smaller triangle }{ Area of larger triangle } \\) = (scale factor)\u00b2<br \/>\n\\(\\frac { Area of smaller triangle }{ 180 } \\) = ( \\(\\frac { 2 }{ 3 } \\))\u00b2<br \/>\nArea of smaller triangle = \\(\\frac { 4 }{ 9 } \\) \u2022 180<br \/>\n= 80<\/p>\n<h3>8.2 Proving Triangle Similarity by AA<\/h3>\n<p>Show that the triangles are similar. Write a similarity statement.<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49101\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-152.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 8 Similarity 152\" width=\"221\" height=\"111\" \/><br \/>\nAnswer:<br \/>\nm\u2220RQS = m\u2220UTS = 30\u00b0.<br \/>\n\u25b3QRS and \u25b3STU are similar as per the AA similarity theorem.<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49100\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-153.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 8 Similarity 153\" width=\"226\" height=\"103\" \/><br \/>\nAnswer:<br \/>\nm\u2220CAB = 60\u00b0, m\u2220DEF = 30\u00b0<br \/>\n\u25b3ABC and \u25b3DEF are not similar as per the AA similarity theorem.<\/p>\n<p>Question 7.<br \/>\nA cellular telephone tower casts a shadow that is 72 feet long, while a nearby tree that is 27 feet tall casts a shadow that is 6 feet long. How tall is the tower?<br \/>\nAnswer:<br \/>\n\\(\\frac { shadow of tree }{ shadow of tower } \\) = \\(\\frac { height of tree }{ height of tower } \\)<br \/>\n\\(\\frac { 6 }{ 72 } \\) = \\(\\frac { 27 }{ x } \\)<br \/>\n6x = 1944<br \/>\nx = 324 ft<br \/>\nThe height of the tower is 324 ft.<\/p>\n<h3>8.3 Proving Triangle Similarity by SSS and SAS<\/h3>\n<p>Use the SSS Similarity Theorem (Theorem 8.4) or the SAS Similarity Theorem (Theorem 8.5) to show that the triangles are similar.<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49099\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-154.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 8 Similarity 154\" width=\"279\" height=\"121\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac { DE }{ CD } \\) = \\(\\frac { 7 }{ 3.5 } \\) = 2<br \/>\n\\(\\frac { AB }{ BC } \\) = \\(\\frac { 8 }{ 4 } \\) = 2<br \/>\n\\(\\frac { DE }{ CD } \\) = \\(\\frac { AB }{ BC } \\)<br \/>\nSo, BD is parallel to AE.<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49098\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-155.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 8 Similarity 155\" width=\"226\" height=\"129\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac { QU }{ TU } \\) = \\(\\frac { 9 }{ 4.5 } \\) = 2<br \/>\n\\(\\frac { QR }{ SR } \\) = \\(\\frac { 14 }{ 7 } \\) = 2<br \/>\n\\(\\frac { QU }{ TU } \\) = \\(\\frac { QR }{ SR } \\)<br \/>\nSo, ST is parallel to RU.<\/p>\n<p>Question 10.<br \/>\nFind the value of x that makes \u2206ABC ~ \u2206DEF<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49097\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-156.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 8 Similarity 156\" width=\"246\" height=\"109\" \/><\/p>\n<p>Answer:<br \/>\n\\(\\frac { 24 }{ 6 } \\) = 4<br \/>\n\\(\\frac { 32 }{ 2x } \\) = 4<br \/>\n32 = 8x<br \/>\nx = \\(\\frac { 32 }{ 8 } \\)<br \/>\nx = 4<\/p>\n<h3>8.4 Proportionality Theorems<\/h3>\n<p>Determine whether \\(\\overline{A B}\\) || \\(\\overline{C D}\\)<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49096\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-157.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 8 Similarity 157\" width=\"225\" height=\"92\" \/><\/p>\n<p>Answer:<br \/>\n\\(\\frac { DB }{ BE } \\) = \\(\\frac { 10 }{ 16 } \\) = \\(\\frac { 5 }{ 8 } \\)<br \/>\n\\(\\frac { CA }{ AE } \\) = \\(\\frac { 20 }{ 28 } \\) = \\(\\frac { 5 }{ 7 } \\)<br \/>\n\\(\\frac { DB }{ BE } \\) \u2260 \\(\\frac { CA }{ AE } \\)<br \/>\nSo, CD and AB are not parallel.<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49095\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-158.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 8 Similarity 158\" width=\"236\" height=\"112\" \/><\/p>\n<p>Answer:<br \/>\n\\(\\frac { DB }{ BE } \\) = \\(\\frac { 12 }{ 20 } \\) = \\(\\frac { 3 }{ 5 } \\)<br \/>\n\\(\\frac { CA }{ AE } \\) = \\(\\frac { 13.5 }{ 22.5 } \\) = \\(\\frac { 3 }{ 5 } \\)<br \/>\n\\(\\frac { DB }{ BE } \\) = \\(\\frac { CA }{ AE } \\)<br \/>\nSo, AB and CD are parallel.<\/p>\n<p>Question 13.<br \/>\nFind the length of \\(\\overline{Y B}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49094\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-159.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 8 Similarity 159\" width=\"215\" height=\"130\" \/><\/p>\n<p>Answer:<br \/>\n\\(\\frac { ZC }{ AZ } \\) = \\(\\frac { 24 }{ 15 } \\) = \\(\\frac { 8 }{ 5 } \\)<br \/>\n\\(\\frac { YB }{ AY } \\) = \\(\\frac { ZC }{ AZ } \\)<br \/>\n\\(\\frac { YB }{ 7 } \\) = \\(\\frac { 8 }{ 5 } \\)<br \/>\nYB = \\(\\frac { 8 }{ 5 } \\) \u2022 7<br \/>\nYB = \\(\\frac { 56 }{ 5 } \\)<br \/>\nThe length of \\(\\overline{Y B}\\) is \\(\\frac { 56 }{ 5 } \\)<\/p>\n<p>Find the length of \\(\\overline{A B}\\).<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49093\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-160.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 8 Similarity 160\" width=\"233\" height=\"112\" \/><\/p>\n<p>Answer:<br \/>\n\\(\\frac { AB }{ 7 } \\) = \\(\\frac { 6 }{ 4 } \\)<br \/>\n\\(\\overline{A B}\\) = \\(\\frac { 6 }{ 4 } \\) \u2022 7<br \/>\n\\(\\overline{A B}\\) = \\(\\frac { 42 }{ 4 } \\)<br \/>\n\\(\\overline{A B}\\) = \\(\\frac { 21 }{ 2 } \\)<br \/>\nThe length of \\(\\overline{A B}\\) is \\(\\frac { 21 }{ 2 } \\).<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49092\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-161.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 8 Similarity 161\" width=\"276\" height=\"110\" \/><\/p>\n<p>Answer:<br \/>\n\\(\\frac { DB }{ CD } \\) = \\(\\frac { AB }{ AC } \\)<br \/>\n\\(\\frac { 4 }{ 10 } \\) = \\(\\frac { AB }{ 18 } \\)<br \/>\n\\(\\frac { 2 }{ 5 } \\) = \\(\\frac { AB }{ 18 } \\)<br \/>\nAB = \\(\\frac { 36 }{ 5 } \\)<\/p>\n<h3><a id=\"Similarity_Chapter_Test\"><\/a>Similarity Test<\/h3>\n<p>Determine whether the triangles are similar. If they are, write a similarity statement. Explain your reasoning.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49116\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-162.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 8 Similarity 162\" width=\"206\" height=\"107\" \/><\/p>\n<p>Answer:<br \/>\nLonger sides: \\(\\frac { 32 }{ 24 } \\) = \\(\\frac { 4 }{ 3 } \\)<br \/>\nshorter sides: \\(\\frac { 18 }{ 14 } \\) = \\(\\frac { 9 }{ 7 } \\)<br \/>\nremaining sides: \\(\\frac { 20 }{ 15 } \\) = \\(\\frac { 4 }{ 3 } \\)<br \/>\nThose are not equal.<br \/>\nSo, triangles are not similar.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49115\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-163.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 8 Similarity 163\" width=\"219\" height=\"114\" \/><\/p>\n<p>Answer:<br \/>\n\\(\\frac { AC }{ KJ } \\) = \\(\\frac { 6 }{ 8 } \\) = \\(\\frac { 3 }{ 4 } \\)<br \/>\n\\(\\frac { BC }{ JL } \\) = \\(\\frac { 8 }{ [latex]\\frac { 32 }{ 3 } \\) } [\/latex] = \\(\\frac { 3 }{ 4 } \\)<br \/>\n\\(\\frac { AC }{ KJ } \\) = \\(\\frac { BC }{ JL } \\)<br \/>\n\u2220C = \u2220J<br \/>\nSo, \u25b3ABC and \u25b3JLK are similar.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49114\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-164.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 8 Similarity 164\" width=\"166\" height=\"100\" \/><\/p>\n<p>Answer:<br \/>\n\\(\\frac { XY }{ XW } \\) = \\(\\frac { PZ }{ PW } \\)<\/p>\n<p>Find the value of the variable.<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49113\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-165.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 8 Similarity 165\" width=\"220\" height=\"103\" \/><\/p>\n<p>Answer:<br \/>\n\\(\\frac { 9 }{ w } \\) = \\(\\frac { 15 }{ 5 } \\)<br \/>\n\\(\\frac { 9 }{ w } \\) = 3<br \/>\n9 = 3w<br \/>\nw = 3<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49112\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-166.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 8 Similarity 166\" width=\"105\" height=\"99\" \/><\/p>\n<p>Answer:<br \/>\n\\(\\frac { 17.5 }{ 21 } \\) = \\(\\frac { q }{ 33 } \\)<br \/>\nq = \\(\\frac { 17.5 }{ 21 } \\) \u2022 33<br \/>\nq = \\(\\frac { 55 }{ 2 } \\)<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49111\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-167.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 8 Similarity 167\" width=\"192\" height=\"129\" \/><\/p>\n<p>Answer:<br \/>\n\\(\\frac { 21 &#8211; p }{ p } \\) = \\(\\frac { 12 }{ 24 } \\)<br \/>\n\\(\\frac { 21 &#8211; p }{ p } \\) = \\(\\frac { 1 }{ 2 } \\)<br \/>\ncross multiply<br \/>\n2(21 &#8211; p) = p<br \/>\n42 &#8211; 2p = p<br \/>\n42 = p + 2p<br \/>\n42 = 3p<br \/>\np = 14<\/p>\n<p>Question 7.<br \/>\nGiven \u2206QRS ~ \u2206MNP, list all pairs of congruent angles, Then write the ratios of the corresponding side lengths in a statement of proportionality.<\/p>\n<p>Answer:<br \/>\nThe pairs of congruent anglres are m\u2220QRS, m\u2220RSQ, m\u2220SQR, m\u2220MNP, m\u2220NPM, m\u2220PMN.<br \/>\nThe ratios of side lengths are \\(\\frac { RQ }{ MN } \\), \\(\\frac { QS }{ MP } \\), \\(\\frac { RS }{ NP } \\)<\/p>\n<p>Use the diagram.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-49110\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-168.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 8 Similarity 168\" width=\"225\" height=\"139\" \/><\/p>\n<p>Question 8.<br \/>\nFind the length of \\(\\overline{E F}\\).<\/p>\n<p>Answer:<br \/>\n\\(\\frac { DE }{ EF } \\) = \\(\\frac { CD }{ BC } \\)<br \/>\n\\(\\frac { 3.2 }{ EF } \\) = \\(\\frac { 2.8 }{ 1.4 } \\)<br \/>\nEF = 1.6<br \/>\nThe length of \\(\\overline{E F}\\) is 1.6<\/p>\n<p>Question 9.<br \/>\nFind the length of \\(\\overline{F G}\\).<\/p>\n<p>Answer:<br \/>\n\\(\\frac { EF }{ FG } \\) = \\(\\frac { BC }{ AB } \\)<br \/>\n\\(\\frac { 1.6 }{ FG } \\) = \\(\\frac { 1.4 }{ 4.2 } \\)<br \/>\nFG = 4.8<br \/>\nThe length of \\(\\overline{F G}\\) is 4.8<\/p>\n<p>Question 10.<br \/>\nIs quadrilateral FECB similar to quadrilateral GFBA? If so, what is the scale factor of the dilation that maps quadrilateral FECB to quadrilateral GFBA?<\/p>\n<p>Answer:<br \/>\nThe scale factor of dilation from quadrilateral FECB to quadrilateral GFBA is \\(\\frac { GF }{ FE } \\)<\/p>\n<p>Question 11.<br \/>\nYou are visiting the Unisphere at Flushing Meadows Corona Park in New York. To estimate the height of the stainless steel model of Earth. you place a mirror on the ground and stand where you can see the top of the model in the mirror. Use the diagram to estimate the height of the model. Explain why this method works.<\/p>\n<p>Answer:<\/p>\n<p>Question 12.<br \/>\nYou are making a scale model of a rectangular park for a school project. Your model has a length of 2 feet and a width of 1.4 feet. The actual park is 800 yards long. What are the perimeter and area of the actual park?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49109\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-169.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 8 Similarity 169\" width=\"326\" height=\"216\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-169.png 326w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-169-300x199.png 300w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><\/p>\n<p>Answer:<br \/>\nwe know that 1 yard = ft<br \/>\nAs per the similarity theorem<br \/>\n\\(\\frac { AD }{ EH } \\) = \\(\\frac { AB }{ EF } \\)<br \/>\n\\(\\frac { 2 }{ 800.3 } \\) = \\(\\frac { 1.4 }{ EF } \\)<br \/>\nEF = 1200 \u2022 1 \u2022 4<br \/>\nEF = 1680<br \/>\nPerimete of the park P = 2(1680 + 2400)<br \/>\n= 2(4080) = 8160 ft<br \/>\nArea of the actual park = 1680 \u2022 2400 = 4,032,000 sq ft<br \/>\nTherefore, perimeter of the actual park = 8160 ft<br \/>\narea of the actual park is 4,032,000 sq ft.<\/p>\n<p>Question 13.<br \/>\nIn a Perspective drawing, lines that are parallel in real life must meet at a vanishing point on the horizon. To make the train cars in the drawing appear equal in length, they are drawn so that the lines connecting the opposite corners of each car are parallel. Use the dimensions given and the yellow parallel lines to find the length of the bottom edge of the drawing of Car 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49108\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-170.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 8 Similarity 170\" width=\"355\" height=\"222\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-170.png 355w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-170-300x188.png 300w\" sizes=\"(max-width: 355px) 100vw, 355px\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac { 5.4 }{ 10.6 } \\) = \\(\\frac { 5.4 + C }{ 19 } \\)<br \/>\nC = \\(\\frac { 45.36 }{ 10.6 } \\)<br \/>\n\\(\\frac { (19 &#8211; x &#8211; 8.4) }{ (19 &#8211; 8.4) } \\) = \\(\\frac { 5.4 }{ 5.4 + c } \\)<br \/>\n\\(\\frac { 19 &#8211; 8.4 }{ 19 } \\) = \\(\\frac { c2 + 5.4 }{ c1 + c2 + 5.4 } \\)<br \/>\n\\(\\frac { 19 &#8211; 8.4 }{ 19 } \\) = \\(\\frac { 5.4 }{ 5.4 + c2 } \\)<br \/>\nc1 = 7.6, c2 = 4.2, x = 4.6<br \/>\nThe length of car 2 is 4.2 cm.<\/p>\n<h3><a id=\"Similarity_Cumulative_Assessment\"><\/a>Similarity Cumulative Assessment<\/h3>\n<p>Question 1.<br \/>\nUse the graph of quadrilaterals ABCD and QRST.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49294\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-171.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 171\" width=\"209\" height=\"207\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-171.png 209w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-171-150x150.png 150w\" sizes=\"(max-width: 209px) 100vw, 209px\" \/><br \/>\na. Write a composition of transformations that maps quadrilateral ABCD to quadrilateral QRST.<br \/>\nAnswer:<br \/>\nThe scale factor = \\(\\frac { AD }{ QT } \\) = \\(\\frac { 2 }{ 1.5 } \\)<\/p>\n<p>b. Are the quadrilaterals similar? Explain your reasoning.<br \/>\nAnswer:<br \/>\nNo.<br \/>\n\\(\\frac { AD }{ QT } \\) = \\(\\frac { 2 }{ 1.5 } \\)<br \/>\n\\(\\frac { CD }{ TS } \\) = \\(\\frac { 2.8 }{ 1.4 } \\) = 2<br \/>\nSo, quadrilaterals are not similar.<\/p>\n<p>Question 2.<br \/>\nIn the diagram. ABCD is a parallelogram. Which congruence theorem(s) could you Use to show that \u2206AED \u2245 \u2206CEB? Select all that apply.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49293\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-172.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 172\" width=\"235\" height=\"124\" \/><br \/>\nSAS Congruence Theorem (Theorem 5.5)<br \/>\nAnswer:<br \/>\nIt states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.<\/p>\n<p>SSS Congruence Theorem (Theorem 5.8)<br \/>\nAnswer:<br \/>\nIf all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.<\/p>\n<p>HL Congruence Theorem (Theorem 5.9)<br \/>\nAnswer:<br \/>\nA given set of triangles are congruent if the corresponding lengths of their hypotenuse and one leg are equal.<\/p>\n<p>ASA Congruence Theorem (Theorem 5. 10)<br \/>\nAnswer:<br \/>\nIf any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule<\/p>\n<p>AAS Congruence Theorem (Theorem 5. 11)<br \/>\nAnswer:<br \/>\nAAS stands for Angle-angle-side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.<\/p>\n<p>Question 3.<br \/>\nBy the Triangle Proportionality Theorem (Theorem 8.6), \\(\\frac{V W}{W Y}=\\frac{V X}{X Z}\\) In the diagram, VX &gt; VW and XZ &gt; WY. List three possible values for VX and XZ.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49292\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-173.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 173\" width=\"190\" height=\"137\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac{V W}{W Y}=\\frac{V X}{X Z}\\)<br \/>\n\\(\\frac{ 4 }{6}=\\frac{V X}{X Z}\\)<br \/>\nThe possible values of VX are greater than 4 means 5, 6, 7, . . .<br \/>\nThe possible values of XZ are greater than 6 means 7, 8, 9, . .<\/p>\n<p>Question 4.<br \/>\nThe slope of line l is &#8211; \\(\\frac{3}{4}\\). The slope of line n is \\(\\frac{4}{3}\\) What must be true about lines l and n ?<br \/>\n(A) Lines l and n are parallel.<br \/>\n(B) Lines l and n arc perpendicular.<br \/>\n(C) Lines l and n are skew.<br \/>\n(D) Lines l and n are the same line.<br \/>\nAnswer:<br \/>\nThe slope of l = &#8211; \\(\\frac{3}{4}\\)<br \/>\nSlope of n = \\(\\frac{4}{3}\\)<br \/>\nlines slopes are reciprocal and opposite. So, they are perpendicular.<\/p>\n<p>Question 5.<br \/>\nEnter a statement or reason in each blank to complete the two-column proof.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49291\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-174.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 174\" width=\"348\" height=\"128\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-174.png 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-174-300x110.png 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><br \/>\nGiven \\(\\frac{K J}{K L}=\\frac{K H}{K M}\\)<br \/>\nProve \u2220LMN \u2245 \u2220JHG<\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"204\">Statements<\/td>\n<td style=\"text-align: center;\" width=\"222\">Reasons<\/td>\n<\/tr>\n<tr>\n<td width=\"204\">1. \\(\\frac{K J}{K L}=\\frac{K H}{K M}\\)<\/td>\n<td width=\"222\">1. Given<\/td>\n<\/tr>\n<tr>\n<td width=\"204\">2. \u2220JKH \u2245 \u2220LKM<\/td>\n<td width=\"222\">2. ________________________<\/td>\n<\/tr>\n<tr>\n<td width=\"204\">3. \u2206JKH ~ \u2206LKM<\/td>\n<td width=\"222\">3. ________________________<\/td>\n<\/tr>\n<tr>\n<td width=\"204\">4. \u2220KHJ \u2245\u2220KML<\/td>\n<td width=\"222\">4. ________________________<\/td>\n<\/tr>\n<tr>\n<td width=\"204\">5. _______________________<\/td>\n<td width=\"222\">5. Definition of congruent angles<\/td>\n<\/tr>\n<tr>\n<td width=\"204\">6. m\u2220KHJ + m\u2220JHG = 180\u00b0<\/td>\n<td width=\"222\">6. Linear Pair Postulate (Post. 18)<\/td>\n<\/tr>\n<tr>\n<td width=\"204\">7. m\u2220JHG = 180\u00b0 &#8211; m\u2220KHJ<\/td>\n<td width=\"222\">7. ________________________<\/td>\n<\/tr>\n<tr>\n<td width=\"204\">8. m\u2220KML + m\u2220LMN = 180\u00b0<\/td>\n<td width=\"222\">8. ________________________<\/td>\n<\/tr>\n<tr>\n<td width=\"204\">9. ________________________<\/td>\n<td width=\"222\">9. Subtraction Property of Equality<\/td>\n<\/tr>\n<tr>\n<td width=\"204\">10. m\u2220LMN = 180\u00b0 &#8211; m\u2220KHJ<\/td>\n<td width=\"222\">10. ________________________<\/td>\n<\/tr>\n<tr>\n<td width=\"204\">11. ________________________<\/td>\n<td width=\"222\">11. Transitive Property of Equality<\/td>\n<\/tr>\n<tr>\n<td width=\"204\">12. \u2220LMN \u2245 \u2220JHG<\/td>\n<td width=\"222\">12. ________________________<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Answer:<\/p>\n<p>Question 6.<br \/>\nThe coordinates of the vertices of \u2206DEF are D(- 8, 5), E(- 5, 8), and F(- 1, 4), The coordinates of the vertices of \u2206JKL are J(16, &#8211; 10), K(10, &#8211; 16), and L(2, &#8211; 8), \u2220D \u2245 \u2220J. Can you show that \u2206DEF \u2206JKL by using the AA Similarity Theorem (Theorem 8.3)? If so, do so by listing the congruent corresponding angles and writing a similarity transformation that maps \u2206DEF to \u2206JKL. If not, explain why not.<br \/>\nAnswer:<br \/>\nAA similarity theorem states that \u2220D = \u2220J. So, \u2206DEF and \u2206JKL are similar.<\/p>\n<p>Question 7.<br \/>\nClassify the quadrilateral using the most specific name.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49290\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-175.png\" alt=\"Big Ideas Math Geometry Answers Chapter 8 Similarity 175\" width=\"199\" height=\"88\" \/><br \/>\nrectangle\u00a0 \u00a0 \u00a0square\u00a0 \u00a0 parallelogram\u00a0 \u00a0 rhombus<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n\u2018Your friend makes the statement \u201cQuadrilateral PQRS is similar to quadrilateral WXYZ.\u201d Describe the relationships between corresponding angles and between corresponding sides that make this statement true.<\/p>\n<p>Answer:<br \/>\nWhen 2 figures are similar, then their corresponding angles are congruent and their corresponding lengths are proportional. hence if PQRS is similar to wxyZ, then the following statements are true.<br \/>\n\u2220P = \u2220W, \u2220Q = \u2220X, \u2220R = \u2220Y and \u2220S = \u2220Z and<br \/>\n\\(\\frac { PQ }{ WX } \\) = \\(\\frac { QR }{ XY } \\) = \\(\\frac { RS }{ YZ } \\) = \\(\\frac { PS }{ WZ } \\) = k<br \/>\nHere is a constant of proportionality.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Do you want a perfect guide for a better understanding of Similarity concepts in High School? Then, Big Ideas Math Geometry Answers Chapter 8 Similarity is the one-stop destination for all your requirements during preparation. Practicing and Solving no. of questions from chapter 8 similarity BIM Geometry Textbook Solutions is the best way to understand &#8230; <a title=\"Big Ideas Math Geometry Answers Chapter 8 Similarity\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-geometry-answers-chapter-8\/\" aria-label=\"More on Big Ideas Math Geometry Answers Chapter 8 Similarity\">Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":89452,"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-8-Similarity-46.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/47138"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=47138"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/47138\/revisions"}],"predecessor-version":[{"id":90288,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/47138\/revisions\/90288"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89452"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=47138"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=47138"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=47138"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}