{"id":5993,"date":"2022-03-26T18:57:42","date_gmt":"2022-03-26T13:27:42","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=5993"},"modified":"2022-04-07T12:56:11","modified_gmt":"2022-04-07T07:26:11","slug":"go-math-grade-7-answer-key-chapter-8-modeling-geometric-figures","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/go-math-grade-7-answer-key-chapter-8-modeling-geometric-figures\/","title":{"rendered":"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures"},"content":{"rendered":"<p>Students of 7th grade can get a detailed explanation for all the problems in Go Math Answer Key Chapter 8 Modeling Geometric Figures. Redefine yourself by practicing problems from <a href=\"https:\/\/ccssmathanswers.com\/go-math-grade-7-answer-key\/\" target=\"_blank\" rel=\"noopener noreferrer\">Go Math Grade 7 Answer Key<\/a> Chapter 8 Modeling Geometric Figures. We have given the pdf to Download HMH Go Math Answer Key of Grade 7 Chapter 8 Modeling Geometric Figures. So, refer to Go Math 7th Grade Answer Key Chapter 8 Modeling Geometric Figures to secure the highest score in exams.<\/p>\n<h2>Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures<\/h2>\n<p>Get access to Download HMH Go Math Grade 7 Key Chapter 8 Modeling Geometric Figures here. Start preparing for your exams by using the Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures pdf. In this article, you can check the answers to review questions in addition to the exercise and homework questions. So, make use of the below links and learn the problems according to the topics.<\/p>\n<p><strong>Chapter 8 &#8211; Modeling Geometric Figures &#8211; Lesson: 1<\/strong><\/p>\n<ul>\n<li><a href=\"#Guided_Practice_Page_No_240\">Guided Practice &#8211; Page No. 240<\/a><\/li>\n<li><a href=\"#Independent_Practice_Page_No_241\">Independent Practice &#8211; Page No. 241<\/a><\/li>\n<li><a href=\"#Page_No_242\">Page No. 242<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 8 &#8211; Modeling Geometric Figures &#8211; Lesson: 2<\/strong><\/p>\n<ul>\n<li><a href=\"#Guided_Practice_Page_No_245\">Guided Practice &#8211; Page No. 245<\/a><\/li>\n<li><a href=\"#Independent_Practice_Page_No_246\">Independent Practice &#8211; Page No. 246<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 8 &#8211; Modeling Geometric Figures &#8211; Lesson: 3<\/strong><\/p>\n<ul>\n<li><a href=\"#Guided_Practice_Page_No_249\">Guided Practice &#8211; Page No. 249<\/a><\/li>\n<li><a href=\"#Page_No_250\">Page No. 250<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 8 &#8211; Modeling Geometric Figures &#8211; Lesson: 4<\/strong><\/p>\n<ul>\n<li><a href=\"#Guided_Practice_Page_No_256\">Guided Practice &#8211; Page No. 256<\/a><\/li>\n<li><a href=\"#Independent_Practice_Page_No_257\">Independent Practice &#8211; Page No. 257<\/a><\/li>\n<li><a href=\"#Page_No_258\">Page No. 258<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 8 &#8211; Modeling Geometric Figures<\/strong><\/p>\n<ul>\n<li><a href=\"#8.1_Similar_Shapes_and_Scale_Drawings_Page_No_259\">8.1 Similar Shapes and Scale Drawings &#8211; Page No. 259<\/a><\/li>\n<li><a href=\"#Selected_Response_Page_No_260\">Selected Response &#8211; Page No. 260<\/a><\/li>\n<\/ul>\n<h3><a id=\"Guided_Practice_Page_No_240\"><\/a>Guided Practice &#8211; Page No. 240<\/h3>\n<p>Question 1.<br \/>\nThe scale of a room in a blueprint is 3 in : 5 ft. A wall in the same blueprint is 18 in. Complete the table.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-1.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 1\" width=\"509\" height=\"94\" \/><br \/>\na. How long is the actual wall?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-2.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 2\" width=\"352\" height=\"84\" \/><br \/>\n______ feet<\/p>\n<p>Answer: 30 feet<\/p>\n<p>Explanation:<br \/>\nWe complete the table using the direct proportionality<br \/>\n3 in : 5 ft.<br \/>\nA wall in the same blueprint is 18 in. is 30 feet.<\/p>\n<p>Question 1.<br \/>\nb. A window in the room has an actual width of 2.5 feet. Find the width of the window in the blueprint.<br \/>\n______ inches<\/p>\n<p>Answer: 1.5 inches<\/p>\n<p>Explanation:<br \/>\nWe determine the number of inches corresponding to 1 foot on the actual window<br \/>\n3 in \/5 in.<br \/>\nMultiply and divide by 5<br \/>\n(3 in \u00f7 5)\/(5 ft \u00f7 5) = 0.6\/1 ft<br \/>\nThus 1 foot corresponds to 0.6 inches, so the width of the window in the table is<br \/>\n2.5 \u00d7 0.6 = 1.5 inches<\/p>\n<p>Question 2.<br \/>\nThe scale in the drawing is 2 in. : 4 ft. What are the length and width of the actual room? Find the area of the actual room.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-3.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 3\" width=\"281\" height=\"149\" \/><br \/>\nWidth: _________ feet<br \/>\nLength: _________ feet<br \/>\nArea: _________ sq ft<\/p>\n<p>Answer:<br \/>\nWidth: 28 feet<br \/>\nLength: 14 feet<br \/>\nArea: 392 sq ft<\/p>\n<p>Explanation:<br \/>\nWe determine the number of feet corresponding to 1 inch in the drawing<br \/>\n2 in\/4 in = (2 in. \u00f7 2)\/(4 in \u00f7 2) = 1\/2<br \/>\nThus 1 inch corresponds to 2 feet on the actual dimensions of the room.<br \/>\nWe determine the actual length of the room, labeled 14 inches in the drawing.<br \/>\n14 \u00d7 2 = 28 feet<br \/>\nWe determine the actual width of the room, labeled 7 inches in the drawing.<br \/>\n7 \u00d7 = 14 feet<br \/>\nWe compute the area of the actual room:<br \/>\n28 \u00d7 14 = 392 square feet.<\/p>\n<p>Question 3.<br \/>\nThe scale in the drawing is 2 cm: 5 m. What are the length and width of the actual room? Find the area of the actual room.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-4.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 4\" width=\"220\" height=\"129\" \/><br \/>\nWidth: _________ m<br \/>\nLength: _________ m<br \/>\nArea: _________ sq meters<\/p>\n<p>Answer:<br \/>\nWidth: 25 m<br \/>\nLength: 15 m<br \/>\nArea: 375 sq meters<\/p>\n<p>Explanation:<br \/>\nWe determine the number of meters corresponding to 1 centimeter in the drawing:<br \/>\n2 cm\/5 cm = (2 cm \u00f7 2)\/(5 cm \u00f7 2) = 1 cm\/ 2.5 m<br \/>\nWe determine the actual length of the room, labeled 10 cm in the drawing:<br \/>\n10 \u00d7 2.5 = 25 m<br \/>\nWe determine the actual width of the room, labeled 6 cm in the drawing:<br \/>\n6 \u00d7 2.5 = 15 m<br \/>\nWe compute the area of the room:<br \/>\n25 \u00d7 15 = 375 square feet.<\/p>\n<p>Question 4.<br \/>\nA scale drawing of a cafeteria is drawn on centimeter grid paper as shown. The scale is 1 cm: 4 m.<br \/>\na. Redraw the rectangle on centimeter grid paper using a scale of 1 cm:6 m.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-5.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 5\" width=\"285\" height=\"165\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-7836\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Chapter-8-Answer-Key-solution-img-1.jpg\" alt=\"Go Math Grade 7 Chapter 8 Answer Key solution img-1\" width=\"187\" height=\"137\" \/><\/p>\n<p>Question 4.<br \/>\nb. What is the actual length and width of the cafeteria using the original scale? What are the actual dimensions of the cafeteria using the new scale?<br \/>\nLength: _________ m<br \/>\nWidth: _________ m<\/p>\n<p>Answer:<br \/>\nIn the original scale, the dimensions on the drawing are<br \/>\nl1 = 9 cm<br \/>\nw1 = 6\u00a0 cm<br \/>\nWe determine the actual length using the original scale:<br \/>\n9 \u00d7 4 = 36<br \/>\nWe determine the actual width using the original scale:<br \/>\n6 \u00d7 4 = 24<br \/>\nIn the second scale, the dimensions on the drawing are<br \/>\nl2 = 6 cm<br \/>\nw1 = 4 cm<br \/>\nWe determine the actual length using the original scale:<br \/>\n6 \u00d7 6 = 36<br \/>\nWe determine the actual width using the original scale:<br \/>\n4 \u00d7 6 = 24<br \/>\nThus the length is 36m<br \/>\nWidth is 24 m<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 5.<br \/>\nIf you have an accurate, complete scale drawing and the scale, which measurements of the object of the drawing can you find?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nIf we have an accurate, complete scale drawing and scale, we can determine all measurements of the object because they are all proportional with the dimensions on the drawing the ratio being the scale.<\/p>\n<h3><a id=\"Independent_Practice_Page_No_241\"><\/a>Independent Practice &#8211; Page No. 241<\/h3>\n<p>Question 6.<br \/>\nArt<br \/>\nMarie has a small copy of Rene Magritte\u2019s famous painting, The Schoolmaster. Her copy has dimensions 2 inches by 1.5 inches. The scale of the copy is 1 in.:40 cm.<br \/>\na. Find the dimensions of the original painting.<br \/>\nLength: _________ cm<br \/>\nWidth: _________ cm<\/p>\n<p>Answer:<br \/>\nLength: 80 cm<br \/>\nWidth: 60 cm<\/p>\n<p>Explanation:<br \/>\nWe are given the data<br \/>\nScale: 1 in:40 cm<br \/>\nCopy l1 = 2 in.<br \/>\nw1 = 1.5 inches<br \/>\nWe determine the length l of the original painting<br \/>\nl = 2 \u00d7 40 = 80cm<br \/>\nWe determine the width w of the original painting<br \/>\nw = 1.5 \u00d7 40 = 60 cm<\/p>\n<p>Question 6.<br \/>\nb. Find the area of the original painting.<br \/>\n_____________ sq cm<\/p>\n<p>Answer: 4800 square cm<\/p>\n<p>Explanation:<br \/>\nWe determine the width w of the original painting<br \/>\nA = l.w<br \/>\nA = 80 \u00d7 60 = 4,800 square cm<\/p>\n<p>Question 6.<br \/>\nc. Since 1 inch is 2.54 centimeters, find the dimensions of the original painting in inches.<br \/>\nLength: _________ inches<br \/>\nWidth: _________ inches<\/p>\n<p>Answer:<br \/>\nWe determine the length l of the original painting in inches:<br \/>\n1 in. = 2.54 cm<br \/>\nl = 80\/2.54 cm \u2248 31.5 inches<br \/>\nWe determine the width w of the original painting in inches:<br \/>\nw = 60\/2.54 \u2248 23.6 inches<\/p>\n<p>Question 6.<br \/>\nd. Find the area of the original painting in square inches<br \/>\n_____________ sq inches<\/p>\n<p>Answer: 743.4 square inches<\/p>\n<p>Explanation:<br \/>\nWe find the area of the original painting in the square inches:<br \/>\nl \u00d7 w = 31.5 \u00d7 23.6 = 743.4 square inches<br \/>\nThus the area of the original painting is 743.4 square inches.<\/p>\n<p>Question 7.<br \/>\nA game room has a floor that is 120 feet by 75 feet. A scale drawing of the floor on grid paper uses a scale of 1 unit:5 feet. What are the dimensions of the scale drawing?<br \/>\nLength: _________ units<br \/>\nWidth: _________ units<\/p>\n<p>Answer:<br \/>\nLength: 24 units<br \/>\nWidth: 15 units<\/p>\n<p>Explanation:<br \/>\nWe are given the data:<br \/>\nScale: 1 unit: 5 feet<br \/>\nActual dimensions: l = 120 feet, w = 75 feet<br \/>\nWe determine the number of units on the drawing corresponding to 1 foot from the actual dimensions.<br \/>\n1 unit\/ 5 feet<br \/>\n(1 unit \u00f7 5)\/(5 feet \u00f7 5) = 0.2 units\/1 feet<br \/>\nWe determine the length of the scale drawing:<br \/>\n120 \u00d7 0.2 = 24 units<br \/>\nWe determine the width of the scale drawing:<br \/>\n75 \u00d7 0.2 = 15 units<\/p>\n<p>Question 8.<br \/>\nMultiple Representations<br \/>\nThe length of a table is 6 feet. On a scale drawing, the length is 2 inches. Write three possible scales for the drawing.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nl = 6 feet<br \/>\nl1 = 2 inches<br \/>\nl = the actual length<br \/>\nl1 = the length on a scale drawing<br \/>\n2 inches:6 ft<br \/>\n1 in:3 ft<br \/>\n2\/6\u00d712 = 2\/72 = 1\/36<br \/>\n1 cm: 36 cm<\/p>\n<p>Question 9.<br \/>\nAnalyze Relationships<br \/>\nA scale for a scale drawing is 10 cm:1 mm. Which is larger, the actual object or the scale drawing? Explain.<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nWe are given the scale<br \/>\n10 cm: 1 mm<br \/>\n100 mm: 1 m<br \/>\nThis means that the correspondent in actual dimension for 100 mm of drawing is 1mm, so to a greater on the drawing there is a smaller actual distance, therefore the scale drawing is larger.<\/p>\n<p>Question 10.<br \/>\nArchitecture<br \/>\nThe scale model of a building is 5.4 feet tall.<br \/>\na. If the original building is 810 meters tall, what was the scale used to make the model?<br \/>\n______ ft. : ______ m<\/p>\n<p>Answer: 1 foot: 150 m<\/p>\n<p>Explanation:<br \/>\nLet&#8217;s note:<br \/>\nh1 = the height on the scale model<br \/>\nh = the actual height<br \/>\nWe are given the data<br \/>\nh1 = 5.4 feet<br \/>\nh = 810 meters<br \/>\nWe determine the scale for the model<br \/>\nh1\/h = 5.4 feet\/810 m = (5.4 feet \u00f7 5.4)\/(810 \u00f7 5.4)<br \/>\n1 foot\/150 m<br \/>\n1 foot: 150 m<\/p>\n<p>Question 10.<br \/>\nb. If the model is made out of tiny bricks each measuring 0.4 inch in height, how many bricks tall is the model?<br \/>\n___________ bricks<\/p>\n<p>Answer: 14 bricks<\/p>\n<p>Explanation:<br \/>\nWe determine the scale for the model:<br \/>\nh1\/0.4 = 5.4\/0.4 = 13.5<br \/>\nThe number of bricks: 14<\/p>\n<h3><a id=\"Page_No_242\"><\/a>Page No. 242<\/h3>\n<p>Question 11.<br \/>\nYou have been asked to build a scale model of your school out of toothpicks. Imagine your school is 30 feet tall. Your scale is 1 ft:1.26 cm.<br \/>\na. If a toothpick is 6.3 cm tall, how many toothpicks tall will your model be?<br \/>\n______ toothpicks<\/p>\n<p>Answer: 6<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nh = 30 feet<br \/>\n1 ft: 1.26 cm<br \/>\nh1 = the height on the scale model<br \/>\nh = the actual height<br \/>\nWe determine the height h1 of the model:<br \/>\nh1 = 30 \u00d7 1.26 = 37.8 cm<br \/>\nh1\/6.3 = 37.8\/6.3 = 6<br \/>\nThus the number of toothpicks = 6<\/p>\n<p>Question 11.<br \/>\nb. Your mother is out of toothpicks, and suggests you use cotton swabs instead. You measure them, and they are 7.6 cm tall. How many cotton swabs tall will your model be?<br \/>\n______ cotton swabs<\/p>\n<p>Answer: 5<\/p>\n<p>Explanation:<br \/>\nWe find the number of cotton wabs<br \/>\nh1\/7.6 = 37.8\/7.6 \u2248 5<br \/>\nThus the number of cotton wabs = 5<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 12.<br \/>\nDraw Conclusions<br \/>\nThe area of a square floor on a scale drawing is 100 square centimeters, and the scale of the drawing is 1 cm : 2 ft. What is the area of the actual floor? What is the ratio of the area in the drawing to the actual area?<br \/>\nArea = ______ sq. ft.<\/p>\n<p>Answer: 400 sq. ft<\/p>\n<p>Explanation:<br \/>\nA1 = the area of the drawing<br \/>\nA = the area of the actual floor<br \/>\nWe are given the data:<br \/>\nA1 = 100 cm\u00b2<br \/>\n1 cm: 2 ft<br \/>\n1 cm corresponds to 2 ft<br \/>\n1 cm \u00d7 1 cm corresponds to 2 ft \u00d7 2 ft<br \/>\n1 cm\u00b2 corresponds to 4 ft\u00b2<br \/>\nA = 100. 4 = 400 ft\u00b2<br \/>\nWe determine the ratio of the area in the drawing to the actual area:<br \/>\n1 ft = 0.3048 m = 30.48 cm<br \/>\nA1\/A = 100\/400 \u00d7 30.48\u00b2 \u2248 0.0003<\/p>\n<p>Question 13.<br \/>\nMultiple Representations<br \/>\nDescribe how to redraw a scale drawing with a new scale.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nIn order to redraw a scale drawing with a new scale we perform 2 steps:<br \/>\n1. We find how many times the new scale us bigger or smaller than the old one.<br \/>\n2. We multiply this scale factor by the dimensions of the old scale drawing to get a new drawing.<\/p>\n<p>Question 14.<br \/>\nRepresent Real-World Problems<br \/>\nDescribe how several jobs or professions might use scale drawings at work.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nScale drawings are extremely useful in jobs which need to represent bigger areas on smaller devices like<br \/>\n1. Architecture\/ constructions<br \/>\n2. medicine<br \/>\n3. agriculture<br \/>\n4. tourism<br \/>\n5. transportation<\/p>\n<h3><a id=\"Guided_Practice_Page_No_245\"><\/a>Guided Practice &#8211; Page No. 245<\/h3>\n<p><strong>Tell whether each figure creates the conditions to form a unique triangle, more than one triangle, or no triangle.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-6.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 6\" width=\"259\" height=\"137\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: A unique triangle<\/p>\n<p>Explanation:<br \/>\nWe are given two angles and the included side, thus there is a unique triangle as the sides leaving from B and A intersect in a unique point.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-7.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 7\" width=\"238\" height=\"96\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: No triangle<\/p>\n<p>Explanation:<br \/>\nWe are given the three sides of the triangle. We check if the sum of any two sides is greater than the other.<br \/>\n4 + 11 = 15 &gt; 3<br \/>\n11 + 3 = 14 &gt; 4<br \/>\n3 + 4 = 7 is not greater than 11.<br \/>\nBecause one inequality is not verified, the triangle doesn&#8217;t exist.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-8.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 8\" width=\"204\" height=\"95\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: A unique triangle<\/p>\n<p>Explanation:<br \/>\nWe are given two angles and the included side, thus there is a unique triangle as the sides leaving from B and A intersect in a unique point.<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-9.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 9\" width=\"129\" height=\"121\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: A unique triangle<\/p>\n<p>Explanation:<br \/>\nWe are given the three sides of the triangle. We check if the sum of any two sides is greater than the other.<br \/>\n6 + 12 = 18 &gt; 7<br \/>\n12 + 7 = 19 &gt; 6<br \/>\n6 + 7 = 13 &gt; 12<br \/>\nSince all inequalities are verified, there is a unique triangle.<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 5.<br \/>\nDescribe lengths of three segments that could not be used to form a triangle.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nFind the lengths of three segments not to be the sides of a triangle, at least one sum of two sides should be smaller than the other side.<br \/>\nLet a, b, c be the lengths of the three segments.<br \/>\na + b not &gt; a + b + k = c<\/p>\n<p><strong>Independent Practice<\/strong><\/p>\n<p>Question 6.<br \/>\nOn a separate piece of paper, try to draw a triangle with side lengths of 3 centimeters and 6 centimeters, and an included angle of 120\u00b0. Determine whether the given segments and angle produce a unique triangle, more than one triangle, or no triangle.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: A unique triangle<\/p>\n<p>Explanation:<br \/>\n\u2220A = 120\u00b0<br \/>\nAB = 6<br \/>\nAC = 3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-7839\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Chapter-8-Answer-Key-solution-img-2.jpg\" alt=\"Go Math Grade 7 Chapter 8 Answer Key solution img-2\" width=\"236\" height=\"236\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Chapter-8-Answer-Key-solution-img-2.jpg 236w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Chapter-8-Answer-Key-solution-img-2-150x150.jpg 150w\" sizes=\"(max-width: 236px) 100vw, 236px\" \/><br \/>\nWe draw the segment AB, the angle A and the segment AC, then we join B and C. The result is an unique triangle.<\/p>\n<p>Question 7.<br \/>\nA landscape architect submitted a design for a triangle-shaped flower garden with side lengths of 21 feet, 37 feet, and 15 feet to a customer. Explain why the architect was not hired to create the flower garden.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nWe are given the sides of a triangle<br \/>\n21 + 37 = 58 &gt; 15<br \/>\n37 + 15 = 52 &gt; 21<br \/>\n15 + 21 = 36 not &gt; 37<br \/>\nWe checked the three triangles inequalities<br \/>\nThus the triangle does not exist, that is the reason why the architect was not hired to create the flower garden.<\/p>\n<h3><a id=\"Independent_Practice_Page_No_246\"><\/a>Page No. 246<\/h3>\n<p>Question 8.<br \/>\nMake a Conjecture<br \/>\nThe angles in an actual triangle-shaped traffic sign all have measures of 60\u00b0. The angles in a scale drawing of the sign all have measures of 60\u00b0. Explain how you can use this information to decide whether three given angle measures can be used to form a unique triangle or more than one triangle.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-10.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 10\" width=\"195\" height=\"216\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: Three given angle measures whose sum is 180\u00b0 can be used to form an infinity of triangles, having the property that their corresponding sides are proportional.<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 9.<br \/>\nCommunicate Mathematical Ideas<br \/>\nThe figure on the left shows a line segment 2 inches long forming a 45\u00b0 angle with a dashed line whose length is not given. The figure on the right shows a compass set at a width of 1 \\(\\frac{1}{2}\\) inches with its point on the top end of the 2-inch segment. An arc is drawn intersecting the dashed line twice.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-11.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 11\" width=\"325\" height=\"130\" \/><br \/>\nExplain how you can use this figure to decide whether two sides and an angle not included between them can be used to form a unique triangle, more than one triangle, or no triangle.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nA trinagle does not exist because one side is shorter than the other two sides. The circle intersects the dashed line only once so that one angles is 45\u00b0, so there is only one solution. The circle with the center in B intersects the dashed line twice, thus there are two triangles formed.<\/p>\n<p>Question 10.<br \/>\nCritical Thinking<br \/>\nTwo sides of an isosceles triangle have lengths of 6 inches and 15 inches, respectively. Find the length of the third side. Explain your reasoning.<br \/>\n_______ inches<\/p>\n<p>Answer: 15 inches<\/p>\n<p>Explanation:<br \/>\nWe are given the two sides of an isosceles triangle<br \/>\na = 6<br \/>\nb = 15<br \/>\nThere are two possibilities the third side is equal to a or b. Lets study both of them<br \/>\nCase 1: a = c = 6, b = 15<br \/>\na + c = 6 + 6 = 12 not greater than 15 = b<br \/>\nWe check the three triangle&#8217;s inequalities<br \/>\na + b = 6 + 15 = 21 &gt; 15 = c<br \/>\na + c = 6 + 15 = 21 &gt; 15 = b<br \/>\nb + c = 15 + 15 = 30 &gt; 6 = a<br \/>\nCase 2: a = 6, b = c = 15<br \/>\nThus the third side of the triangle is 15.<\/p>\n<h3><a id=\"Guided_Practice_Page_No_249\"><\/a>Guided Practice &#8211; Page No. 249<\/h3>\n<p><strong>Describe each cross section.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-12.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 12\" width=\"217\" height=\"170\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: Triangle\/Quadrilateral triangle<br \/>\nThe given cross-section in a cube is a triangle\/equilateral triangle.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-13.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 13\" width=\"101\" height=\"167\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: Rectangle<br \/>\nThe given cross-section in a cylinder is a rectangle.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-14.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 14\" width=\"215\" height=\"134\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: Triangle<\/p>\n<p>Explanation:<br \/>\nThe given cross-section in the prism is the triangle.<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-15.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 15\" width=\"123\" height=\"178\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: Rainbow shaped curve<br \/>\nThe given cross-section in the cone is a rainbow-shaped curve.<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 5.<br \/>\nWhat is the first step in describing what figure results when a given plane intersects a given three-dimensional figure?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nThe first step in describing what figure results when a given plane intersects a given three-dimensional figure is to establish the number of sides the cross-section has.<\/p>\n<p><strong>Independent Practice<\/strong><\/p>\n<p>Question 6.<br \/>\nDescribe different ways in which a plane might intersect the cylinder and the cross section that results.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-16.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 16\" width=\"104\" height=\"138\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nThe cross-section can be:<br \/>\n1. a circle<br \/>\n2. an ellipse<br \/>\n3. a rectangle<\/p>\n<h3><a id=\"Page_No_250\"><\/a>Page No. 250<\/h3>\n<p>Question 7.<br \/>\nMake a Conjecture<br \/>\nWhat cross sections might you see when a plane intersects a cone that you would not see when a plane intersects a pyramid or a prism?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nThe cross-section can be:<br \/>\n1. a circle<br \/>\n2. an ellipse<br \/>\n3. a parabola<br \/>\n4. a hyperbola<br \/>\n5. a triangle<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 8.<br \/>\nCritical Thinking<br \/>\nThe two figures on the left below show that you can form a cross section of a cube that is a pentagon. Think of a plane cutting the cube at an angle in such a way as to slice through five of the cube\u2019s six faces. Draw dotted lines on the third cube to show how to form a cross section that is a hexagon.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-17.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 17\" width=\"429\" height=\"118\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nWe draw a plane cutting the cube so that the cross-section is a hexagon: for this, we take the middle of 6 adjacent sides:<\/p>\n<p>Question 9.<br \/>\nAnalyze Relationships<br \/>\nA sphere has a radius of 12 inches. A horizontal plane passes through the center of the sphere.<br \/>\na. Describe the cross section formed by the plane and the sphere<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: Circle<\/p>\n<p>Explanation:<br \/>\nWe are given a sphere and a cross-section passing through the center of the sphere:<br \/>\nThe cross section passing through the center of the sphere is a circle having the radius equal to the sphere&#8217;s radius.<\/p>\n<p>Question 9.<br \/>\nb. Describe the cross sections formed as the plane intersects the interior of the sphere but moves away from the center.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:\u00a0 The cross sections formed as a plane intersects the interior of the sphere outside the center are circles.<\/p>\n<p>Question 10.<br \/>\nCommunicate Mathematical Ideas<br \/>\nA right rectangular prism is intersected by a horizontal plane and a vertical plane. The cross section formed by the horizontal plane and the prism is a rectangle with dimensions 8 in. and 12 in. The cross section formed by the vertical plane and the prism is a rectangle with dimensions 5 in. and 8 in. Describe the faces of the prism, including their dimensions. Then find its volume.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: 480 cube inches<\/p>\n<p>Explanation:<br \/>\nThe horizontal cross section has the dimensions 8\u00d712, while the vertical 5\u00d78.<br \/>\nThe prism has the dimensions:<br \/>\n5 inches, 8 inches, 12 inches<br \/>\nWe find the volume of the prism:<br \/>\n5 \u00d7 8 \u00d7 12 = 480 cube inches<\/p>\n<p>Question 11.<br \/>\nRepresent Real-World Problems<br \/>\nDescribe a real-world situation that could be represented by planes slicing a three-dimensional figure to form cross sections.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nExamples of real-world situations that can be represented by planes slicing three-dimensional figures to form cross-sections:<br \/>\n&#8211; electrical wires<br \/>\n&#8211; water\/gas pipes<br \/>\n&#8211; house design<br \/>\n&#8211; geology<br \/>\n&#8211; seismology<\/p>\n<h3><a id=\"Guided_Practice_Page_No_256\"><\/a>Guided Practice &#8211; Page No. 256<\/h3>\n<p><strong>For 1\u20132, use the figure.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-18.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 18\" width=\"251\" height=\"198\" \/><\/p>\n<p>Question 1.<br \/>\nVocabulary<br \/>\nThe sum of the measures of \u2220UWV and \u2220UWZ is 90\u00b0, so \u2220UWV and \u2220UWZ are _____ angles.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: Complementary angles<\/p>\n<p>Explanation:<br \/>\nThe sum of \u2220UWV and \u2220UWZ is 90\u00b0, so \u2220UWV and \u2220UWZ are complementary angles.<\/p>\n<p>Question 2.<br \/>\nVocabulary<br \/>\n\u2220UWV and \u2220VWX share a vertex and one side. They do not overlap, so \u2220UWV and \u2220VWX are _____ angles.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: Adjacent angles<\/p>\n<p>Explanation:<br \/>\n\u2220UWV and \u2220VWX share a vertex and one side. They do not overlap, so \u2220UWV and \u2220VWX are adjacent angles.<\/p>\n<p><strong>For 3\u20134, use the figure.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-19.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 19\" width=\"169\" height=\"170\" \/><\/p>\n<p>Question 3.<br \/>\n\u2220AGB and \u2220DGE are _____ angles, so m\u2220DGE = _____.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: \u2220AGB and \u2220DGE are vertical angles, so m\u2220DGE = m\u2220AGB = 30\u00b0<\/p>\n<p>Question 4.<br \/>\nFind the measure of \u2220EGF.<br \/>\n_______ \u00b0<\/p>\n<p>Answer: 100\u00b0<\/p>\n<p>Explanation:<br \/>\nm\u2220CGD + m\u2220DGE + m\u2220EGF = 180\u00b0<br \/>\n50\u00b0 + m\u2220AGB + m\u2220EGF = 180\u00b0<br \/>\n50\u00b0 + 30\u00b0 + 2x = 180\u00b0<br \/>\n2x = 180\u00b0 &#8211; 80\u00b0<br \/>\n2x = 100\u00b0<br \/>\nmm\u2220EGF = 2x = 100\u00b0<\/p>\n<p>Question 5.<br \/>\nFind the value of x and the measure of \u2220MNQ.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-20.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 20\" width=\"167\" height=\"168\" \/><br \/>\nx = _______ \u00b0<br \/>\nmMNQ = _______ \u00b0<\/p>\n<p>Answer:<br \/>\n\u2220MNQ + \u2220QNP = 90\u00b0<br \/>\n3x &#8211; 13\u00b0 + 58\u00b0 = 90\u00b0<br \/>\n3x = 90\u00b0 + 13\u00b0 &#8211; 58\u00b0<br \/>\n3x = 45\u00b0<br \/>\nx = 15\u00b0<br \/>\nm\u2220MNQ = 3x &#8211; 13\u00b0<br \/>\n= 3\u00d715\u00b0 &#8211; 13\u00b0<br \/>\n= 45\u00b0 &#8211; 13\u00b0<br \/>\n= 32\u00b0<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 6.<br \/>\nSuppose that you know that \u2220T and \u2220S are supplementary and that m\u2220T = 3(m\u2220S). How can you find m\u2220T?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nm\u2220T + m\u2220S = 180\u00b0<br \/>\nm\u2220T = 3(m\u2220S)<br \/>\nm\u2220S = m\u2220T\/3<br \/>\nForm the second equation we write m\u2220S in terms of m\u2220T<br \/>\nm\u2220T + m\u2220T\/3 = 3 \u00d7 180\u00b0<br \/>\n3m\u2220T + m\u2220T = 3 \u00d7 180\u00b0<br \/>\n4m\u2220T = 540\u00b0<br \/>\nm\u2220T = 540\u00b0\/4<br \/>\nm\u2220T = 135\u00b0<\/p>\n<h3><a id=\"Independent_Practice_Page_No_257\"><\/a>Independent Practice &#8211; Page No. 257<\/h3>\n<p><strong>For 7\u201311, use the figure.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-21.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 21\" width=\"197\" height=\"175\" \/><\/p>\n<p>Question 7.<br \/>\nName a pair of adjacent angles. Explain why they are adjacent.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nThe pair of adjacent angles are:<br \/>\n\u2220SUR and \u2220RUN (common vertex U and one common side &#8211; UR &#8211; without overlapping)<br \/>\n\u2220NUQ and \u2220QUP (common vertex U and one common side &#8211; UQ &#8211; without overlapping)<br \/>\n\u2220PUT and \u2220TUS (common vertex U and one common side &#8211; UT &#8211; without overlapping)<\/p>\n<p>Question 8.<br \/>\nName a pair of acute vertical angles.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nBy seeing the above figure we can say that \u2220SUR and \u2220PUQ are the vertical angles.<\/p>\n<p>Question 9.<br \/>\nName a pair of supplementary angles.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nThe above figure shows that \u2220SUR and \u2220RUQ are supplementary angles.<\/p>\n<p>Question 10.<br \/>\nJustify Reasoning<br \/>\nFind m\u2220QUR. Justify your answer.<br \/>\n_______ \u00b0<\/p>\n<p>Answer:<br \/>\nWe have to find m\u2220QUR.<br \/>\n\u2220SUR and \u2220QURare supplementary angles.<br \/>\nm\u2220SUR + m\u2220QUR = 180\u00b0<br \/>\nm\u2220QUR + 41\u00b0 = 180\u00b0<br \/>\nm\u2220QUR = 180\u00b0 &#8211; 41\u00b0<br \/>\nm\u2220QUR = 139\u00b0<\/p>\n<p>Question 11.<br \/>\nDraw Conclusions<br \/>\nWhich is greater, m\u2220TUR or m\u2220RUQ? Explain.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nm\u2220QUR = 139\u00b0<br \/>\nm\u2220TUR = m\u2220TUS + m\u2220SUR<br \/>\n90\u00b0 + 41\u00b0 = 131\u00b0<br \/>\nWe find m\u2220TUR<br \/>\n139\u00b0 &gt; 131\u00b0<br \/>\nm\u2220QUR &gt; m\u2220TUR<\/p>\n<p><strong>For 12\u201313, use the figure. A bike path crosses a road as shown. Solve for each indicated angle measure or variable.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-22.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 22\" width=\"198\" height=\"192\" \/><\/p>\n<p>Question 12.<br \/>\nx = ?<br \/>\n_______ \u00b0<\/p>\n<p>Answer: x = 21\u00b0<\/p>\n<p>Explanation:<br \/>\n\u2220KMI and \u2220HMG are vertical, thus congruent.<br \/>\nWe determine x:<br \/>\n84\u00b0 = 4x<br \/>\n4x = 84\u00b0<br \/>\nx = 84\u00b0\/4<br \/>\nx = 21\u00b0<\/p>\n<p>Question 13.<br \/>\nm\u2220KMH = ?<br \/>\n_______ \u00b0<\/p>\n<p>Answer: 96\u00b0<\/p>\n<p>Explanation:<br \/>\n\u2220KMI and \u2220KMH are supplementary.<br \/>\nWe determine m\u2220KMH:<br \/>\nm\u2220KMH + m\u2220KMI = 180\u00b0<br \/>\nm\u2220KMH + 84\u00b0 = 180\u00b0<br \/>\nm\u2220KMH = 180\u00b0 &#8211; 84\u00b0<br \/>\nm\u2220KMH = 96\u00b0<\/p>\n<p><strong>For 14\u201316, use the figure. Solve for each indicated angle measure.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-23.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 23\" width=\"194\" height=\"167\" \/><\/p>\n<p>Question 14.<br \/>\nm\u2220CBE = ?<br \/>\n_______ \u00b0<\/p>\n<p>Answer: 118\u00b0<\/p>\n<p>Explanation:<br \/>\nWe determine m\u2220CBE:<br \/>\nm\u2220CBE + m\u2220EBF = 180\u00b0<br \/>\nm\u2220CBE + 62\u00b0= 180\u00b0<br \/>\nm\u2220CBE = 180\u00b0 &#8211; 62\u00b0<br \/>\nm\u2220CBE = 118\u00b0<\/p>\n<p>Question 15.<br \/>\nm\u2220ABF = ?<br \/>\n_______ \u00b0<\/p>\n<p>Answer: 28\u00b0<\/p>\n<p>Explanation:<br \/>\nWe determine m\u2220ABF<br \/>\nm\u2220ABF + m\u2220EBF = 90\u00b0<br \/>\nm\u2220ABF + 62\u00b0 = 90\u00b0<br \/>\nm\u2220ABF = 90\u00b0 &#8211; 62\u00b0<br \/>\nm\u2220ABF = 28\u00b0<\/p>\n<p>Question 16.<br \/>\nm\u2220CBA = ?<br \/>\n_______ \u00b0<\/p>\n<p>Answer: 152\u00b0<\/p>\n<p>Explanation:<br \/>\nWe determine m\u2220CBA<br \/>\nm\u2220CBA = m\u2220DBF = m\u2220DBE + m\u2220EBF<br \/>\n90\u00b0 + 62\u00b0 = 152\u00b0<br \/>\nm\u2220CBA = 152\u00b0<\/p>\n<p>Question 17.<br \/>\nThe measure of \u2220A is 4\u00b0 greater than the measure of \u2220B. The two angles are complementary. Find the measure of each angle.<br \/>\nmA = __________ \u00b0<br \/>\nmB = __________ \u00b0<\/p>\n<p>Answer:<br \/>\nmA = 47\u00b0<br \/>\nmB = 43\u00b0<\/p>\n<p>Explanation:<br \/>\nWe are given the data:<br \/>\nm\u2220A = m\u2220B + 4\u00b0<br \/>\nm\u2220A + m\u2220B = 90\u00b0<br \/>\nm\u2220B + 4\u00b0 + m\u2220B = 90\u00b0<br \/>\n2m\u2220B = 90\u00b0 &#8211; 4\u00b0<br \/>\n2m\u2220B = 86\u00b0<br \/>\nm\u2220B = 86\u00b0\/2<br \/>\nm\u2220B = 43\u00b0<br \/>\nm\u2220A = m\u2220B + 4\u00b0<br \/>\nm\u2220A = 43\u00b0\u00a0+ 4\u00b0<br \/>\nm\u2220A = 47\u00b0<\/p>\n<p>Question 18.<br \/>\nThe measure of \u2220D is 5 times the measure of \u2220E. The two angles are supplementary. Find the measure of each angle.<br \/>\nmD = __________ \u00b0<br \/>\nmE = __________ \u00b0<\/p>\n<p>Answer:<br \/>\nmD = 150\u00b0<br \/>\nmE = 30\u00b0<\/p>\n<p>Explanation:<br \/>\nWe are given the data<br \/>\nm\u2220D = 5(m\u2220E)<br \/>\nm\u2220D + m\u2220E = 180\u00b0<br \/>\n5(m\u2220E) + m\u2220E = 180\u00b0<br \/>\n6 m\u2220E = 180\u00b0<br \/>\nm\u2220E = 180\u00b0\/6<br \/>\nm\u2220E = 30\u00b0<br \/>\nm\u2220D = 5(m\u2220E)<br \/>\nm\u2220D = 5 \u00d7 30\u00b0<br \/>\nm\u2220D = 150\u00b0<\/p>\n<h3><a id=\"Page_No_258\"><\/a>Page No. 258<\/h3>\n<p>Question 19.<br \/>\nAstronomy<br \/>\nAstronomers sometimes use angle measures divided into degrees, minutes, and seconds. One degree is equal to 60 minutes, and one minute is equal to 60 seconds. Suppose that \u2220J and \u2220K are complementary, and that the measure of \u2220J is 48 degrees, 26 minutes, 8 seconds. What is the measure of \u2220K?<br \/>\n_______ \u00b0 _______ &#8216; _______ &#8221;<\/p>\n<p>Answer: 41\u00b0 33 &#8216; 52&#8243;<\/p>\n<p>Explanation:<br \/>\nWe are given the data<br \/>\nm\u2220J + m\u2220K = 90\u00b0<br \/>\nm\u2220J = 48\u00b0 26 &#8216; 8&#8243;<br \/>\n90\u00b0 &#8211; 48\u00b0 26 &#8216; 8&#8243;<br \/>\n89\u00b060&#8217; &#8211; 48\u00b0 26 &#8216; 8&#8243;<br \/>\n89\u00b059&#8217;60&#8221; &#8211; 48\u00b0 26 &#8216; 8&#8243; = 41\u00b0 33 &#8216; 52&#8243;<br \/>\nThus the measure of \u2220K is 41\u00b0 33 &#8216; 52&#8243;<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 20.<br \/>\nRepresent Real-World Problems<br \/>\nThe railroad tracks meet the road as shown. The town will allow a parking lot at angle K if the measure of angle K is greater than 38\u00b0. Can a parking lot be built at angle K ? Why or why not?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-24.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 24\" width=\"207\" height=\"206\" \/><br \/>\n_______<\/p>\n<p>Answer:<br \/>\nm\u2220K = 180\u00b0 &#8211; 50\u00b0 &#8211; 90\u00b0 = 40\u00b0<br \/>\nSince m\u2220K = 40\u00b0&gt; 38\u00b0, a parking lot can be built.<\/p>\n<p>Question 21.<br \/>\nJustify Reasoning<br \/>\nKendra says that she can draw \u2220A and \u2220B so that m\u2220A is 119\u00b0 and \u2220A and \u2220B are complementary angles. Do you agree or disagree? Explain your reasoning.<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nWe are given the data<br \/>\nm\u2220A = 119\u00b0<br \/>\nm\u2220A + m\u2220B = 90\u00b0<br \/>\nm\u2220B = 90\u00b0 &#8211; m\u2220A<br \/>\n= 90\u00b0 &#8211; 119\u00b0 = -29\u00b0<br \/>\nSince m\u2220B &lt; 0, Kendra is wrong, she cannnot draw the angles.<\/p>\n<p>Question 22.<br \/>\nDraw Conclusions<br \/>\nIf two angles are complementary, each angle is called a complement of the other. If two angles are supplementary, each angle is called a supplement of the other.<br \/>\na. Suppose m\u2220A = 77\u00b0. What is the measure of a complement of a complement of \u2220A? Explain.<br \/>\n_______ \u00b0<\/p>\n<p>Answer: 77\u00b0<\/p>\n<p>Explanation:<br \/>\n90\u00b0 &#8211; (90\u00b0 &#8211; m\u2220A) = 90\u00b0 &#8211; (90\u00b0 &#8211; 77\u00b0)<br \/>\n90\u00b0 &#8211; 77\u00b0 = 13\u00b0<br \/>\n77\u00b0<\/p>\n<p>Question 22.<br \/>\nb. What conclusion can you draw about a complement of a complement of an angle? Explain.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nThe complement of a complement of an angle is the angle itself:<br \/>\n90\u00b0 &#8211; (90\u00b0 &#8211; m\u2220A)<br \/>\n90\u00b0 &#8211; 90\u00b0 + m\u2220A<\/p>\n<h3><a id=\"8.1_Similar_Shapes_and_Scale_Drawings_Page_No_259\"><\/a>8.1 Similar Shapes and Scale Drawings &#8211; Page No. 259<\/h3>\n<p>Question 1.<br \/>\nA house blueprint has a scale of 1 in. : 4 ft. The length and width of each room in the actual house are shown in the table. Complete the table by finding the length and width of each room on the blueprint.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-25.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 25\" width=\"620\" height=\"132\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7873\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-25-1-300x64.jpg\" alt=\"Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-25\" width=\"300\" height=\"64\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-25-1-300x64.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-25-1.jpg 620w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThus for each 4 ft in actual dimension, there is 1 inch in the blueprint.<\/p>\n<p><strong>8.2 Geometric Drawings<\/strong><\/p>\n<p>Question 2.<br \/>\nCan a triangle be formed with the side lengths of 8 cm, 4 cm, and 12 cm?<br \/>\n______<\/p>\n<p>Answer:<br \/>\nWe are given the side lengths<br \/>\n8 + 12 = 20 &gt; 4<br \/>\n4 + 12 = 16 &gt; 8<br \/>\n8 + 4 not &gt; 12<br \/>\nSince one of the inequalities is not verified, the three given side lengths cannot form a triangle.<\/p>\n<p>Question 3.<br \/>\nA triangle has side lengths of 11 cm and 9 cm. Which could be the value of the third side, 20 cm or 15 cm?<br \/>\n______<\/p>\n<p>Answer: 15 cm<\/p>\n<p>Explanation:<br \/>\nWe are given the side lengths<br \/>\n11, 9<br \/>\n11 + 9 = 20 not &gt; 20<br \/>\nWe check the triangle&#8217;s inequalities if we add the third side of 20 cm<br \/>\nSince one of the inequalities is not verified, the three given side lengths cannot form a triangle.<br \/>\n11, 9, 15<br \/>\n11 + 9 = 20 &gt; 15<br \/>\n11 + 15 = 26 &gt; 9<br \/>\n15 + 9 = 24 &gt; 11<br \/>\nWe check the triangle&#8217;s inequalities are verified, 15 can be the value of the third side.<\/p>\n<p><strong>8.3 Cross Sections<\/strong><\/p>\n<p>Question 4.<br \/>\nName one possible cross section of a sphere.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: Circle<br \/>\nOne possible cross section of the sphere is a circle.<\/p>\n<p>Question 5.<br \/>\nName at least two shapes that are cross sections of a cylinder.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: Three possible cross-sections of a cylinder are a circle, an ellipse, and a rectangle.<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 5.<br \/>\nHow can you model geometry figures to solve real-world problems?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: You can model geometry for making buildings and sky scrapers, also stores.<\/p>\n<p><strong>8.4 Angle Relationships<\/strong><\/p>\n<p>Question 6.<br \/>\n\u2220BGC and \u2220FGE are _____ angles, so m\u2220FGE = _____<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-26.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 26\" width=\"124\" height=\"128\" \/><br \/>\n_____ \u00b0<\/p>\n<p>Answer: \u2220BGC and \u2220FGE are vertical angles, so m\u2220FGE = m\u2220BGC = 90\u00b0 &#8211; 40\u00b0 = 50\u00b0<\/p>\n<p>Question 7.<br \/>\nSuppose you know that \u2220S and \u2220Y are complementary, and that m\u2220S = 2(m\u2220Y) &#8211; 30\u00b0. Find m\u2220Y.<br \/>\nm?Y = _____ \u00b0<\/p>\n<p>Answer: 40\u00b0<\/p>\n<p>Explanation:<br \/>\nm\u2220S + m\u2220Y = 90\u00b0<br \/>\nm\u2220S = 2(m\u2220Y) &#8211; 30\u00b0<br \/>\nWe replace the expression of m\u2220S from the second equation into the first we can find m\u2220Y<br \/>\n2(m\u2220Y) &#8211; 30\u00b0 + m\u2220Y = 90\u00b0<br \/>\n3m\u2220Y = 90\u00b0 + 30\u00b0<br \/>\n3m\u2220Y = 120\u00b0<br \/>\nm\u2220Y = 120\u00b0\/3<br \/>\nm\u2220Y = 40\u00b0<\/p>\n<h3><a id=\"Selected_Response_Page_No_260\"><\/a>Selected Response &#8211; Page No. 260<\/h3>\n<p>Question 1.<br \/>\nWhich number can you add to 15 to get a sum of 0?<br \/>\nOptions:<br \/>\na. -10<br \/>\nb. -15<br \/>\nc. 0<br \/>\nd. 15<\/p>\n<p>Answer: -15<\/p>\n<p>Explanation:<br \/>\nThe number we add to a number in order to get a sum of zero is its opposite. In or case we should add -15 to 15.<br \/>\n15 + (-15) = 0<br \/>\nThus the correct answer is option B.<\/p>\n<p>Question 2.<br \/>\nStudents are painting the backdrop for the school play. The backdrop is 15 feet wide and 10 feet high. Every 16 inches on the scale drawing represents 5 feet on the backdrop. What is the area of the scale drawing?<br \/>\nOptions:<br \/>\na. 150 in<sup>2<\/sup><br \/>\nb. 6 in<sup>2<\/sup><br \/>\nc. 3096<br \/>\nd. 1536 in<sup>2<\/sup><\/p>\n<p>Answer: 1536 in<sup>2<\/sup><\/p>\n<p>Explanation:<br \/>\nWe are given the dimensions l and w of the backdrop and the drawing scale:<br \/>\nl = 15 ft<br \/>\nw = 10 ft<br \/>\n16 in: 5 ft<br \/>\n16 in.\/5 ft = (16 in. \u00f7 5)\/(5 ft \u00f7 5) = 3.2 in\/1 ft<br \/>\nl1 = 15 \u00d7 3.2 = 48 inches<br \/>\nw1 = 10 \u00d7 32 = 320 inches<br \/>\nl1 \u00d7 w1 = 48 \u00d7 32 = 1536 square inches<br \/>\nThus the correct answer is option D.<\/p>\n<p>Question 3.<br \/>\nTwo sides of a triangle measure 8 cm and 12 cm. Which of the following CANNOT be the measure of the third side?<br \/>\nOptions:<br \/>\na. 4<br \/>\nb. 12<br \/>\nc. 8<br \/>\nd. 16<\/p>\n<p>Answer: 4 cm<\/p>\n<p>Explanation:<br \/>\nWe are given two sides of a triangle<br \/>\na. 4<br \/>\n4 + 8 not &gt; 12<br \/>\nb. 12<br \/>\n12 + 8 &gt; 12<br \/>\n12 + 12 &gt; 8<br \/>\nc. 8<br \/>\n8 + 8 &gt; 12<br \/>\n8 + 12 &gt; 12<br \/>\nd. 16<br \/>\n8 + 12 &gt; 16<br \/>\n8 + 16 &gt; 12<br \/>\n12 + 16 &gt; 8<br \/>\nThus the only dimension which cannot be the measure of the third side f the triangle is 4 cm.<br \/>\nThus the correct answer is option A.<\/p>\n<p>Question 4.<br \/>\nA cross section is the intersection of a three-dimensional figure and a _____ .<br \/>\nOptions:<br \/>\na. point<br \/>\nb. plane<br \/>\nc. line<br \/>\nd. set<\/p>\n<p>Answer: Plane<\/p>\n<p>Explanation:<br \/>\nA cross section is the interaction of a three-dimensional figure and a plane.<br \/>\nThus the correct answer is option B.<\/p>\n<p><strong>For 5\u20136, use the diagram.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-27.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 27\" width=\"145\" height=\"141\" \/><\/p>\n<p>Question 5.<br \/>\nWhat is the measure of \u2220BFC?<br \/>\nOptions:<br \/>\na. 18<br \/>\nb. 108<br \/>\nc. 72<br \/>\nd. 144<\/p>\n<p>Answer: 108\u00b0<\/p>\n<p>Explanation:<br \/>\n\u2220BFC + \u2220BFA = 180\u00b0<br \/>\n\u2220BFC + 72\u00b0 = 180\u00b0<br \/>\n\u2220BFC = 180\u00b0 &#8211; 72\u00b0<br \/>\n\u2220BFC = 108\u00b0<br \/>\nThe angles \u2220BFC and \u2220BFA are supplementary. We determine \u2220BFC.<br \/>\nThus the correct answer is option B.<\/p>\n<p>Question 6.<br \/>\nWhich describes the relationship between \u2220BFA and \u2220CFD?<br \/>\nOptions:<br \/>\na. adjacent angles<br \/>\nb. complementary angles<br \/>\nc. supplementary angles<br \/>\nd. vertical angles<\/p>\n<p>Answer: vertical angles<\/p>\n<p>Explanation:<br \/>\nThe angles \u2220BFA and \u2220CFD are vertical angles because they are opposite angles formed at the intersection of two lines.<br \/>\nThus the correct answer is option D.<\/p>\n<p>Question 7.<br \/>\nAll clothing is being marked down 15%. Which expression represents the new retail price?<br \/>\nOptions:<br \/>\na. 0.85x<br \/>\nb. 1.15x<br \/>\nc. 1.85x<br \/>\nd. 0.15x<\/p>\n<p>Answer: 0.85x<\/p>\n<p>Explanation:<br \/>\nx = initial price<br \/>\nSince the price went down by 15%, the new price will be diminished by 15\/100 x<br \/>\nx &#8211; 0.15x = 0.85x<br \/>\nThus the correct answer is option A.<\/p>\n<p><strong>Mini-Tasks<\/strong><\/p>\n<p>Question 8.<br \/>\nIra built a model of the Great Pyramid in Egypt for a school project. The Great Pyramid has a square base with sides of length 756 feet. The height of the Great Pyramid is 481 feet. Ira made his model pyramid using a scale of 1 inch : 20 feet.<br \/>\na. What is the length of each side of the base of Ira\u2019s pyramid?<br \/>\n_____ in<\/p>\n<p>Answer: 37.8 inches<br \/>\nWe compute the number of inches corresponding to 1 feet from the actual dimensions:<br \/>\n1 in.\/20 ft = (1 in. \u00f7 20)\/(20 ft \u00f7 20) = 0.05 in\/1 ft.<br \/>\nThere are 0.05 inches for 1 feet.<br \/>\nWe determine the length of Ira&#8217;s\u00a0 pyramid base:<br \/>\n756 \u00d7 0.05 = 37.8 inches<\/p>\n<p>Question 8.<br \/>\nb. What is the area of the base of Ira\u2019s pyramid?<br \/>\n_____ square inches<\/p>\n<p>Answer: 1428.84 square inches<\/p>\n<p>Explanation:<br \/>\nWe determine the area of Ira&#8217;s pyramid base:<br \/>\n37.8 \u00d7 37.8 = 1,428.84 square inches.<\/p>\n<p>Question 8.<br \/>\nc. What is the height of Ira\u2019s pyramid?<br \/>\n_____ in<\/p>\n<p>Answer:<br \/>\nWe determine the height of Ira&#8217;s pyramid:<br \/>\n481 \u00d7 0.05 = 24.05 inches<\/p>\n<p>Question 8.<br \/>\nd. Ira built his model using cross sections that were cut parallel to the base. What shape was each cross section?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer: The cross sections parallel to the base have the shape of a square.<\/p>\n<p><em>Final Words:<\/em><\/p>\n<p>Hope the solutions provided in Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures is helpful for all the students. Get the answers for all the questions with the simple techniques for all chapters on Go Math Answer 7th grade Key Chapter 8 Modeling Geometric Figures. Stick to our Go Math Answer Key Page to get the latest information about the chapters.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Students of 7th grade can get a detailed explanation for all the problems in Go Math Answer Key Chapter 8 Modeling Geometric Figures. Redefine yourself by practicing problems from Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures. 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