{"id":6772,"date":"2022-03-28T21:57:25","date_gmt":"2022-03-28T16:27:25","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=6772"},"modified":"2022-04-07T12:45:18","modified_gmt":"2022-04-07T07:15:18","slug":"go-math-grade-8-answer-key-chapter-12-the-pythagorean-theorem","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/go-math-grade-8-answer-key-chapter-12-the-pythagorean-theorem\/","title":{"rendered":"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem"},"content":{"rendered":"<p>One has to learn the concepts if he\/she wants to become a master in maths. The fundamentals in Go Math Grade 8 Answer Key Chapter 12 The Pythagorean theorem will help you to learn the subject. You need to practice from the beginning itself. We will help you to achieve your dreams by providing simple methods to solve the problems in an easy manner. Download <a href=\"https:\/\/ccssmathanswers.com\/go-math-grade-8-answer-key\/\">Go Math Grade 8 Answer Key<\/a> Chapter 12 The Pythagorean Theorem free pdf to help you to gain a grip over the subject.<\/p>\n<h2><strong>Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem<\/strong><\/h2>\n<p>Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem will help you to complete your homework in time without any mistakes. The main aim of the ccssmathanswers.com site is to provide quick and simple methods to all the students of 8th grade. The solutions to all the questions in Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem are prepared by the math experts. Tap the links and practice the problems provided in the HMH Go Math 8th Grade Solution Key Chapter 12 The Pythagorean Theorem.<\/p>\n<p><strong>Chapter 12- Lesson 1:\u00a0<\/strong><\/p>\n<ul>\n<li><a href=\"#Guided Practice_The_Pythagorean_Theorem_Page_No_378\">Guided Practice &#8211; The Pythagorean Theorem &#8211; Page No. 378<\/a><\/li>\n<li><a href=\"#12.1_Independent_Practice_The_Pythagorean_Theorem_Page_No_379\">12.1 Independent Practice &#8211; The Pythagorean Theorem &#8211; Page No. 379<\/a><\/li>\n<li><a href=\"#FOCUS_ON_HIGHER_ORDER_THINKING_The_Pythagorean_Theorem_Page_No_380\">FOCUS ON HIGHER ORDER THINKING &#8211; The Pythagorean Theorem &#8211; Page No. 380<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 12- Lesson 2:\u00a0<\/strong><\/p>\n<ul>\n<li><a href=\"#Guided_Practice_Converse_of_the_Pythagorean_Theorem_Page_No_384\">Guided Practice &#8211; Converse of the Pythagorean Theorem &#8211; Page No. 384<\/a><\/li>\n<li><a href=\"#12.2_Independent_Practice_Converse_of_the_Pythagorean_Theorem_Page_No_385\">12.2 Independent Practice &#8211; Converse of the Pythagorean Theorem &#8211; Page No. 385<\/a><\/li>\n<li><a href=\"#Converse_of_the_Pythagorean_Theorem_Page_No_386\">Converse of the Pythagorean Theorem &#8211; Page No. 386<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 12- Lesson 3:\u00a0<\/strong><\/p>\n<ul>\n<li><a href=\"#Guided_Practice_Distance_Between_Two_Points_Page_No_390\">Guided Practice &#8211; Distance Between Two Points &#8211; Page No. 390<\/a><\/li>\n<li><a href=\"#12.3_Independent_Practice_Distance_Between_Two_Points_Page_No_391\">12.3 Independent Practice &#8211; Distance Between Two Points &#8211; Page No. 391<\/a><\/li>\n<li><a href=\"#Distance_Between_Two_Points_Page_No_392\">Distance Between Two Points &#8211; Page No. 392<\/a><\/li>\n<li><a href=\"#Ready_to_Go_On?_Model_Quiz_Page_No_393\">Ready to Go On? &#8211; Model Quiz &#8211; Page No. 393<\/a><\/li>\n<li><a href=\"#Selected_Response_Mixed_Review_Page_No_394\">Selected Response &#8211; Mixed Review &#8211; Page No. 394<\/a><\/li>\n<\/ul>\n<h3><\/h3>\n<h3><a id=\"Guided Practice_The_Pythagorean_Theorem_Page_No_378\"><\/a>Guided Practice &#8211; The Pythagorean Theorem &#8211; Page No. 378<\/h3>\n<p>Question 1.<br \/>\nFind the length of the missing side of the triangle<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-1.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 1: The Pythagorean Theorem img 1\" width=\"203\" height=\"89\" \/><br \/>\na<sup>2<\/sup> + b<sup>2<\/sup> = c<sup>2<\/sup> \u2192 24<sup>2<\/sup> + ? = c<sup>2<\/sup> \u2192 ? = c<sup>2<\/sup><br \/>\nThe length of the hypotenuse is _____ feet.<br \/>\n_____ feet<\/p>\n<p>Answer: The length of the hypotenuse is 26 feet.<\/p>\n<p>Explanation: According to Pythagorean Theorem, we shall consider values of a = 24ft, b = 10ft.<br \/>\nTherefore c = \u221a(a<sup>2<\/sup> +b<sup>2<\/sup>)<br \/>\nc = \u221a(24<sup>2 <\/sup>+ 10<sup>2<\/sup>)<br \/>\n= \u221a(576 + 100)<br \/>\n= \u221a676 = 26ft<\/p>\n<p>Question 2.<br \/>\nMr. Woo wants to ship a fishing rod that is 42 inches long to his son. He has a box with the dimensions shown.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-2.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 1: The Pythagorean Theorem img 2\" width=\"259\" height=\"102\" \/><br \/>\na. Find the square of the length of the diagonal across the bottom of the box.<br \/>\n________ inches<\/p>\n<p>Answer: 1700 inches.<\/p>\n<p>Explanation: Here we consider the length of the diagonal across the bottom of the box as d.<br \/>\n<span lang=\"EN-IN\">Therefore, according to Pythagorean Theorem<br \/>\n<\/span><span lang=\"EN-IN\">W<sup>2 <\/sup>+ l<sup>2 <\/sup>= d<sup>2<br \/>\n<\/sup>40<sup>2 <\/sup>+ 10<sup>2<\/sup> = d<sup>2<br \/>\n<\/sup>1600 + 100 = d<sup>2<\/sup><br \/>\n1700 = d<sup>2<\/sup><\/span><\/p>\n<p>Question 2.<br \/>\nb. Find the length from a bottom corner to the opposite top corner to the nearest tenth. Will the fishing rod fit?<br \/>\n________ inches<\/p>\n<p>Answer: 42.42 inches.<\/p>\n<p>Explanation: We denote by r, the length from the bottom corner to the opposite top corner. We use our Pythagorean formula to find r.<br \/>\nh<sup>2 <\/sup>+ s<sup>2 <\/sup>= r<sup>2<\/sup><br \/>\n10<sup>2 <\/sup>+ 1700 = r<sup>2<br \/>\n<\/sup>100 + 1700 = r<sup>2<br \/>\n<\/sup>1800 = r<sup>2<\/sup>,\u00a0\u00a0\u00a0 r = \u221a1800 =&gt; 42.42 inches<\/p>\n<p><strong>ESSENTIAL QUESTION CHECK-IN<\/strong><\/p>\n<p>Question 3.<br \/>\nState the Pythagorean Theorem and tell how you can use it to solve problems.<\/p>\n<p>Answer:<br \/>\nPythagorean Theorem: In a right triangle, the sum of squares of the legs a and b is equal to the square of the hypotenuse c.<br \/>\na<sup>2 <\/sup>+ b<sup>2 <\/sup>= c<sup>2<br \/>\n<\/sup>We can use it to find the length of a side of a right triangle when the lengths of the other two sides are known.<\/p>\n<h3><a id=\"12.1_Independent_Practice_The_Pythagorean_Theorem_Page_No_379\"><\/a>12.1 Independent Practice &#8211; The Pythagorean Theorem &#8211; Page No. 379<\/h3>\n<p><strong>Find the length of the missing side of each triangle. Round your answers to the nearest tenth.<\/strong><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-3.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 1: The Pythagorean Theorem img 3\" width=\"203\" height=\"129\" \/><br \/>\n________ cm<\/p>\n<p>Answer: 8.9 cm.<\/p>\n<p>Explanation: According to Pythagorean theorem we consider values of a = 4cm, b = 8cm.<br \/>\nc<sup>2 <\/sup>= a<sup>2<\/sup> + b<sup>2<\/sup><br \/>\n= 4<sup>2<\/sup> + 8<sup>2<br \/>\n<\/sup>= 16 + 64<br \/>\nc<sup>2<\/sup>= 80, c= \u221a80 =&gt; 8.944<br \/>\nAfter rounding to nearest tenth value c= 8.9cm<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-4.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 1: The Pythagorean Theorem img 4\" width=\"96\" height=\"165\" \/><br \/>\n________ in.<\/p>\n<p>Answer: 11.5 in.<\/p>\n<p>Explanation: According to Pythagorean theorem we consider values of b = 8in, c= 14in<br \/>\nc<sup>2 <\/sup>= a<sup>2<\/sup> + b<sup>2<br \/>\n<\/sup>14<sup>2 <\/sup>= a<sup>2<\/sup> + 8<sup>2<\/sup><br \/>\n196 = a<sup>2<\/sup> + 64<br \/>\na<sup>2<\/sup> = 196 \u2013 64<br \/>\na \u00a0= \u221a132 =&gt; 11.4891<br \/>\na = 11.5 in<\/p>\n<p>Question 6.<br \/>\nThe diagonal of a rectangular big-screen TV screen measures 152 cm. The length measures 132 cm. What is the height of the screen?<br \/>\n________ cm<\/p>\n<p>Answer: 75.4 cm<\/p>\n<p>Explanation: Let&#8217;s consider the diagonal of the TV screen as C = 152cm, length as A = 132 cm, and height of the screen as B.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-8152\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/09\/Screenshot-361.png\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem\" width=\"211\" height=\"146\" \/><br \/>\nAs C<sup>2 <\/sup>= A<sup>2<\/sup> + B<sup>2<br \/>\n<\/sup>\u00a0 \u00a0152<sup>2 <\/sup>= 132<sup>2 <\/sup>+ B<sup>2<\/sup><br \/>\n23,104 = 17,424 + B<sup>2<\/sup><br \/>\nB<sup>2<\/sup> = 23,104 \u2013 17,424<br \/>\nB = \u221a5680 =&gt; 75.365<br \/>\nSo the height of the screen B = 75.4cm<\/p>\n<p>Question 7.<br \/>\nDylan has a square piece of metal that measures 10 inches on each side. He cuts the metal along the diagonal, forming two right triangles. What is the length of the hypotenuse of each right triangle to the nearest tenth of an inch?<br \/>\n________ in.<\/p>\n<p>Answer: 14.1in.<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-8153\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/09\/Screenshot-363.png\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem\" width=\"198\" height=\"146\" \/><\/p>\n<p>Using the Pythagorean Theorem, we have:<br \/>\na<sup>2 <\/sup>+ b<sup>2<\/sup> = c<sup>2<\/sup><br \/>\n10<sup>2 <\/sup>+ 10<sup>2 <\/sup>= c<sup>2<\/sup><br \/>\n100 + 100 = c<sup>2<\/sup><br \/>\n200 = c<sup>2<br \/>\n<\/sup>We are told to round the length of the hypotenuse of each right triangle to the nearest tenth of an inch, therefore: c = 14.1in<\/p>\n<p>Question 8.<br \/>\nRepresent Real-World Problems A painter has a 24-foot ladder that he is using to paint a house. For safety reasons, the ladder must be placed at least 8 feet from the base of the side of the house. To the nearest tenth of a foot, how high can the ladder safely reach?<br \/>\n________ ft<\/p>\n<p>Answer: 22.6 ft.<\/p>\n<p>Explanation: Consider the below diagram. Length of the ladder C = 24ft, placed at a distance from the base B = 8ft, let the safest height be A.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-8154\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/09\/Screenshot-365.png\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem\" width=\"148\" height=\"120\" \/><\/p>\n<p>By using Pythagorean Theorem:<br \/>\nC<sup>2<\/sup> = A<sup>2 <\/sup>+ B<sup>2<\/sup><br \/>\n24<sup>2 <\/sup>= A<sup>2<\/sup> + 8<sup>2 <\/sup><br \/>\n576 = A<sup>2 <\/sup>+ 64<br \/>\nA<sup>2 <\/sup>= 576 \u2013 64 =&gt; 512<br \/>\nA = \u221a512 =&gt; 22.627<br \/>\nAfter rounding to nearest tenth, value of A = 22.6ft<\/p>\n<p>Question 9.<br \/>\nWhat is the longest flagpole (in whole feet) that could be shipped in a box that measures 2 ft by 2 ft by 12 ft?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-5.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 1: The Pythagorean Theorem img 5\" width=\"284\" height=\"106\" \/><br \/>\n________ ft<\/p>\n<p><span lang=\"EN-IN\">Answer: The longest flagpole (in whole feet) that could be shipped in this box is 12 feet.<\/span><\/p>\n<p><span lang=\"EN-IN\">Explanation: From the above diagram we have to find the value of r, which gives us the length longest flagpole that could be shipped in the box. Where width w = 2ft, height h = 2ft and length l = 12ft.<\/span><\/p>\n<p><span lang=\"EN-IN\">First find s, the length of the diagonal across the bottom of the box.<br \/>\nw<sup>2 <\/sup>+ l<sup>2 <\/sup>= s<sup>2<\/sup><br \/>\n2<sup>2 <\/sup>+ 12<sup>2 <\/sup>= s<sup>2<\/sup><br \/>\n4 + 144 = s<sup>2<br \/>\n<\/sup>148 = s<sup>2<br \/>\n<\/sup><\/span><span lang=\"EN-IN\">We use our expression for s to find r, since triangle with sides s, r, and h also form a right-angle triangle.<br \/>\nh<sup>2 <\/sup>+ s<sup>2 <\/sup>= r<sup>2<\/sup><br \/>\n2<sup>2 <\/sup>+ 148 = r<sup>2 <\/sup><br \/>\n4 + 148 = r<sup>2<br \/>\n<\/sup>152 = r<sup>2<br \/>\n<\/sup>r = 12.33ft.<\/span><\/p>\n<p>Question 10.<br \/>\nSports American football fields measure 100 yards long between the end zones, and are 53 \\(\\frac{1}{3}\\) yards wide. Is the length of the diagonal across this field more or less than 120 yards? Explain.<br \/>\n____________<\/p>\n<p><span lang=\"EN-IN\">Answer: The diagonal across this field is less than 120 yards.<\/span><\/p>\n<p><span lang=\"EN-IN\">Explanation: From the above details we will get a diagram as shown below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-8155\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/09\/Screenshot-367.png\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem\" width=\"300\" height=\"98\" \/><br \/>\n<\/span><\/p>\n<p>We are given l = 100 and w<em> = <\/em>53 \u00a0= \u00a0. If we denote with d the diagonal of the field, using the Pythagorean Theorem, we have:<br \/>\nl<sup>2 <\/sup>+ w<sup>2 <\/sup>= d<sup>2<\/sup><br \/>\n100<sup>2 <\/sup>+ (160\/3)<sup>2 <\/sup>= d<sup>2<br \/>\n<\/sup>10000 + (25600\/9) = d<sup>2 <\/sup><br \/>\n9*10000 + 9*(25600\/9) = 9* d<sup>2<\/sup><br \/>\n90000 + 25600 = 9 d<sup>2<\/sup><br \/>\n(115600\/9) = d<sup>2<\/sup><br \/>\n(340\/9) = d<sup>2<\/sup><br \/>\nd = 113.3<br \/>\nHence the diagonal across this field is less than 120 yards.<\/p>\n<p>Question 11.<br \/>\nJustify Reasoning A tree struck by lightning broke at a point 12 ft above the ground as shown. What was the height of the tree to the nearest tenth of a foot? Explain your reasoning.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-6.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 1: The Pythagorean Theorem img 6\" width=\"166\" height=\"88\" \/><br \/>\n________ ft<\/p>\n<p>Answer: The total height of the tree was 52.8ft<\/p>\n<p>Explanation:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-8156\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/09\/Screenshot-369.png\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem\" width=\"290\" height=\"156\" \/><br \/>\nBy using the Pythagorean Theorem<br \/>\na<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>12<sup>2 <\/sup>+ 39<sup>2 <\/sup>= c<sup>2<\/sup><br \/>\n144 + 1521 = c<sup>2<\/sup><br \/>\n1665 = c<sup>2<br \/>\n<\/sup>We are told to round the length of the hypotenuse to the nearest tenth of a foot, therefore: c = 40.8ft.<br \/>\nTherefore, the total height of the tree was:<br \/>\nheight = a+c<br \/>\nheight = 12 +40.8<br \/>\nheight = 52.8 feet<\/p>\n<h3><a id=\"FOCUS_ON_HIGHER_ORDER_THINKING_The_Pythagorean_Theorem_Page_No_380\"><\/a>FOCUS ON HIGHER ORDER THINKING &#8211; The Pythagorean Theorem &#8211; Page No. 380<\/h3>\n<p>Question 12.<br \/>\nMultistep Main Street and Washington Avenue meet at a right angle. A large park begins at this corner. Joe\u2019s school lies at the opposite corner of the park. Usually Joe walks 1.2 miles along Main Street and then 0.9 miles up Washington Avenue to get to school. Today he walked in a straight path across the park and returned home along the same path. What is the difference in distance between the two round trips? Explain.<br \/>\n________ mi<\/p>\n<p>Answer: Joe walks 1.2 miles less if he follows the straight path across the park.<\/p>\n<p>Explanation: Using the Pythagorean Theorem, we find the distance from his home to school following the straight path across the park:<br \/>\na<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>1.2<sup>2 <\/sup>+ 0.9<sup>2 <\/sup>= c<sup>2<\/sup><br \/>\n1.44 + 0.81 = c<sup>2<\/sup><br \/>\n2.25 = c<sup>2 <\/sup><br \/>\n1.5 = c<br \/>\nTherefore, the distance of Joe&#8217;s round trip following the path across the park is <strong>3 miles<\/strong> (<em>d<sub>home-school <\/sub>+ d<sub>school-home<\/sub> = <\/em>1.5 + 1.5). Usually, when he walks along Main Street and Washington Avenue, the distance of his round trip is <strong>4.2 miles <\/strong>(<em>d<sub>home-school <\/sub>+ d<sub>school-home<\/sub> = <\/em>(1.2 + 0.9) + (0.9+1.2)). As we can see, Joe walks 1.2 miles less if he follows the straight path across the park.<\/p>\n<p>Question 13.<br \/>\nAnalyze Relationships An isosceles right triangle is a right triangle with congruent legs. If the length of each leg is represented by x, what algebraic expression can be used to represent the length of the hypotenuse? Explain your reasoning.<\/p>\n<p>Answer: c = x\u221a 2<\/p>\n<p>Explanation: From the Pythagorean Theorem, we know that if a and b are legs and c is the hypotenuse, then a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<\/sup>. In our case, the length of each leg is represented by x, therefore we have:<br \/>\na<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>x<sup>2 <\/sup>+ x<sup>2<\/sup> = c<sup>2<br \/>\n<\/sup>2x<sup>2 <\/sup>= c<sup>2<br \/>\n<\/sup>c = x\u221a 2<\/p>\n<p>Question 14.<br \/>\nPersevere in Problem Solving A square hamburger is centered on a circular bun. Both the bun and the burger have an area of 16 square inches.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-7.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 1: The Pythagorean Theorem img 7\" width=\"113\" height=\"118\" \/><br \/>\na. How far, to the nearest hundredth of an inch, does each corner of the burger stick out from the bun? Explain.<br \/>\n________ in<\/p>\n<p><span lang=\"EN-IN\">Answer: Each corner of the burger sticks out 0.57 inches from the bun.<\/span><\/p>\n<p><span lang=\"EN-IN\">Explanation: Frist, we need to find the radius r of the circular bun. We know that its area A is 16 square inches, therefore:<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-8157\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/09\/Screenshot-371.png\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem\" width=\"191\" height=\"179\" \/><\/p>\n<p><span lang=\"EN-IN\">A = \u03c0r<sup>2<br \/>\n<\/sup>16 = 3.14*r<sup>2<br \/>\n<\/sup>r<sup>2 <\/sup>= (16\/3.14)<br \/>\nr = 2.26<\/span><\/p>\n<p><span lang=\"EN-IN\">Then, we need to find the side s of the square hamburger. We know that its area A is 16 square inches, therefore:<br \/>\nA = s<sup>2<\/sup><br \/>\n16 = s<sup>2<\/sup><br \/>\ns = 4<br \/>\n<\/span><span lang=\"EN-IN\">Using the Pythagorean Theorem, we have to find diagonal d of the square hamburger:<br \/>\ns<sup>2 <\/sup>+ s<sup>2<\/sup> = d<sup>2<\/sup><br \/>\n4<sup>2<\/sup> + 4<sup>2 <\/sup>= d<sup>2<\/sup><br \/>\n16 + 16 = d<sup>2<\/sup><br \/>\n32 = d<sup>2<br \/>\n<\/sup>d = 5.66<br \/>\n<\/span><span lang=\"EN-IN\">To find how far does each corner of the burger stick out from the bun, we denote this length by a and we get:<br \/>\na = (d\/2) \u2013 r =&gt; (5.66\/2) \u2013 2.26<br \/>\na = 0.57.<br \/>\n<\/span><span lang=\"EN-IN\">Therefore, Each corner of the burger sticks out 0.57 inches from the bun.<\/span><\/p>\n<p>Question 14.<br \/>\nb. How far does each bun stick out from the center of each side of the burger?<br \/>\n________ in<\/p>\n<p>Answer: Each bun sticks out 0.26 inches from the center of each side of the burger.<\/p>\n<p>Explanation:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-8158\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/09\/Screenshot-373.png\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem\" width=\"177\" height=\"190\" \/><\/p>\n<p><span lang=\"EN-IN\">We found that r = 2.26 and s = 4. To find how far does each bun stick out from the center of each side of the burger, we denote this length by b and we get:<br \/>\nb = r \u2013 (s\/2) = 2.26 \u2013 (4\/2)<br \/>\nb = 0.26 inches.<br \/>\n<\/span><\/p>\n<p>Question 14.<br \/>\nc. Are the distances in part a and part b equal? If not, which sticks out more, the burger or the bun? Explain.<\/p>\n<p>Answer: The distances a and b are <strong>not equal. <\/strong>From the calculations, we found that the burger sticks out more than the bun.<\/p>\n<h3><a id=\"Guided_Practice_Converse_of_the_Pythagorean_Theorem_Page_No_384\"><\/a>Guided Practice &#8211; Converse of the Pythagorean Theorem &#8211; Page No. 384<\/h3>\n<p>Question 1.<br \/>\nLashandra used grid paper to construct the triangle shown.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-8.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 2: Converse of the Pythagorean Theorem img 8\" width=\"259\" height=\"226\" \/><br \/>\na. What are the lengths of the sides of Lashandra\u2019s triangle?<br \/>\n_______ units, _______ units, _______ units,<\/p>\n<p>Answer: The length of Lashandra\u2019s triangle is 8 units, 6 units, 10 units.<\/p>\n<p>Question 1.<br \/>\nb. Use the converse of the Pythagorean Theorem to determine whether the triangle is a right triangle.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-9.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 2: Converse of the Pythagorean Theorem img 9\" width=\"252\" height=\"189\" \/><br \/>\nThe triangle that Lashandra constructed is \/ is not a right triangle.<br \/>\n_______ a right triangle<\/p>\n<p>Answer: Lashandra\u2019s triangle is right angled triangle as it satisfied Pythagorean theorem<\/p>\n<p>Explanation:<br \/>\nVerifying with Pythagorean formula a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>8<sup>2 + <\/sup>6<sup>2 <\/sup>= 10<sup>2<br \/>\n<\/sup>64 + 36 =100<br \/>\n100 = 100.<\/p>\n<p>Question 2.<br \/>\nA triangle has side lengths 9 cm, 12 cm, and 16 cm. Tell whether the triangle is a right triangle.<br \/>\nLet a = _____, b = _____, and c = ______.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-10.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 2: Converse of the Pythagorean Theorem img 10\" width=\"251\" height=\"184\" \/><br \/>\nBy the converse of the Pythagorean Theorem, the triangle is \/ is not a right triangle.<br \/>\n_______ a right triangle<\/p>\n<p>Answer: The given triangle is not a right-angled triangle<\/p>\n<p>Explanation: Verifying with Pythagorean formula a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2 <\/sup><br \/>\n9<sup>2 <\/sup>+ 12<sup>2 <\/sup>= 16<sup>2<br \/>\n<\/sup>81 + 144 = 256<br \/>\n225 \u2260 256.<br \/>\nHence given dimensions are not from the right angled triangle.<\/p>\n<p>Question 3.<br \/>\nThe marketing team at a new electronics company is designing a logo that contains a circle and a triangle. On one design, the triangle\u2019s side lengths are 2.5 in., 6 in., and 6.5 in. Is the triangle a right triangle? Explain.<br \/>\n_______<\/p>\n<p>Answer: It is a right-angled triangle.<\/p>\n<p>Explanation: Let a = 2.5, b = 6 and c= 6.5<br \/>\nVerifying with Pythagorean formula a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>2.5<sup>2 <\/sup>+ 6<sup>2 <\/sup>= 6.5<sup>2<br \/>\n<\/sup>6.25 + 36 = 42.25<br \/>\n42.25 = 42.25.<br \/>\nHence it is a right-angled triangle.<\/p>\n<p><strong>ESSENTIAL QUESTION CHECK-IN<\/strong><\/p>\n<p>Question 4.<br \/>\nHow can you use the converse of the Pythagorean Theorem to tell if a triangle is a right triangle?<\/p>\n<p>Answer:\u00a0Knowing the side lengths, we substitute them in the formula a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<\/sup>, where c contains the biggest value. If the equation holds true, then the given triangle is a right triangle. Otherwise, it is not a right triangle.<\/p>\n<h3><a id=\"12.2_Independent_Practice_Converse_of_the_Pythagorean_Theorem_Page_No_385\"><\/a>12.2 Independent Practice &#8211; Converse of the Pythagorean Theorem &#8211; Page No. 385<\/h3>\n<p><strong>Tell whether each triangle with the given side lengths is a right triangle.<\/strong><\/p>\n<p>Question 5.<br \/>\n11 cm, 60 cm, 61 cm<br \/>\n______________<\/p>\n<p>Answer: Since 11<sup>2 <\/sup>+ 60<sup>2 <\/sup>= 61<sup>2<\/sup>, the triangle is a right-angled triangle.<\/p>\n<p>Explanation: Let a = 11, b = 60 and c= 61<br \/>\nUsing the converse of the Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>11<sup>2 <\/sup>+ 60<sup>2 <\/sup>= 61<sup>2<br \/>\n<\/sup>121 + 3600 = 3721<br \/>\n3721 = 3721.<br \/>\nSince 11<sup>2 <\/sup>+ 60<sup>2 <\/sup>= 61<sup>2<\/sup>, the triangle is a right-angled triangle.<\/p>\n<p>Question 6.<br \/>\n5 ft, 12 ft, 15 ft<br \/>\n______________<\/p>\n<p>Answer: Since 5<sup>2 <\/sup>+ 12<sup>2 <\/sup>\u2260 15<sup>2<\/sup>, the triangle is not a right-angled triangle.<\/p>\n<p>Explanation: Let a = 5, b = 12 and c= 15<br \/>\nUsing the converse of the Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>\u00a05<sup>2 <\/sup>+ 12<sup>2 <\/sup>= 15<sup>2<br \/>\n<\/sup>25 + 144 = 225<br \/>\n169 \u2260 225.<br \/>\nSince 5<sup>2 <\/sup>+ 12<sup>2 <\/sup>\u2260 15<sup>2<\/sup>, the triangle is not a right-angled triangle.<\/p>\n<p>Question 7.<br \/>\n9 in., 15 in., 17 in.<br \/>\n______________<\/p>\n<p>Answer: Since 9<sup>2 <\/sup>+ 15<sup>2 <\/sup>\u2260 17<sup>2<\/sup>, the triangle is not a right-angled triangle.<\/p>\n<p>Explanation: Let a = 9, b = 15 and c= 17<br \/>\nUsing the converse of the Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>9<sup>2 <\/sup>+ 15<sup>2 <\/sup>= 17<sup>2<br \/>\n<\/sup>81 + 225 = 225<br \/>\n306 \u2260 225.<br \/>\nSince 9<sup>2 <\/sup>+ 15<sup>2 <\/sup>\u2260 17<sup>2<\/sup>, the triangle is not a right-angled triangle.<\/p>\n<p>Question 8.<br \/>\n15 m, 36 m, 39 m<br \/>\n______________<\/p>\n<p>Answer: Since 15<sup>2 <\/sup>+ 36<sup>2 <\/sup>= 39<sup>2<\/sup>, the triangle is a right-angled triangle.<\/p>\n<p>Explanation: Let a = 15, b = 36 and c= 39<br \/>\nUsing the converse of the Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>15<sup>2 <\/sup>+ 36<sup>2 <\/sup>= 39<sup>2<br \/>\n<\/sup>225 + 1296 = 1521<br \/>\n1521 = 1521.<br \/>\nSince 15<sup>2 <\/sup>+ 36<sup>2 <\/sup>= 39<sup>2<\/sup>, the triangle is a right-angled triangle.<\/p>\n<p>Question 9.<br \/>\n20 mm, 30 mm, 40 mm<br \/>\n______________<\/p>\n<p>Answer: Since 20<sup>2 <\/sup>+ 30<sup>2 <\/sup>\u2260 40<sup>2<\/sup>, the triangle is not a right-angled triangle.<\/p>\n<p>Explanation: Let a = 20, b = 30 and c= 40<br \/>\nUsing the converse of the Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>20<sup>2 <\/sup>+ 30<sup>2 <\/sup>= 40<sup>2<br \/>\n<\/sup>400 + 900 = 1600<br \/>\n1300 \u2260 1600.<br \/>\nSince 20<sup>2 <\/sup>+ 30<sup>2 <\/sup>\u2260 40<sup>2<\/sup>, the triangle is not a right-angled triangle.<\/p>\n<p>Question 10.<br \/>\n20 cm, 48 cm, 52 cm<br \/>\n______________<\/p>\n<p>Answer: Since 20<sup>2 <\/sup>+ 48<sup>2 <\/sup>= 52<sup>2<\/sup>, the triangle is a right-angled triangle.<\/p>\n<p>Explanation: Let a = 20, b = 48 and c= 52<br \/>\nUsing the converse of the Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>20<sup>2 <\/sup>+ 48<sup>2 <\/sup>= 52<sup>2<br \/>\n<\/sup>400 + 2304 = 2704<br \/>\n2704 = 2704.<br \/>\nSince 20<sup>2 <\/sup>+ 48<sup>2 <\/sup>= 52<sup>2<\/sup>, the triangle is a right-angled triangle.<\/p>\n<p>Question 11.<br \/>\n18.5 ft, 6 ft, 17.5 ft<br \/>\n______________<\/p>\n<p>Answer: Since 6<sup>2 <\/sup>+ 17.5<sup>2 <\/sup>= 18.5<sup>2<\/sup>, the triangle is a right-angled triangle.<\/p>\n<p>Explanation: Let a = 6, b = 17.5 and c= 18.5<br \/>\nUsing the converse of the Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>6<sup>2 <\/sup>+ 17.5<sup>2 <\/sup>= 18.5<sup>2<br \/>\n<\/sup>36 + 306.25 = 342.25<br \/>\n342.5 = 342.25.<br \/>\nSince 6<sup>2 <\/sup>+ 17.5<sup>2 <\/sup>= 18.5<sup>2<\/sup>, the triangle is a right-angled triangle.<\/p>\n<p>Question 12.<br \/>\n2 mi, 1.5 mi, 2.5 mi<br \/>\n______________<\/p>\n<p>Answer: Since 2<sup>2 <\/sup>+ 1.5<sup>2 <\/sup>= 2.5<sup>2<\/sup>, the triangle is a right-angled triangle.<\/p>\n<p>Explanation: Let a = 2, b = 1.5 and c= 2.5<br \/>\nUsing the converse of the Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>\u00a02<sup>2 <\/sup>+ 1.5<sup>2 <\/sup>= 2.5<sup>2<br \/>\n<\/sup>4 + 2.25 = 6.25<br \/>\n6.25 = 6.25.<br \/>\nSince\u00a0 2<sup>2 <\/sup>+ 1.5<sup>2 <\/sup>= 2.5<sup>2<\/sup>, the triangle is a right-angled triangle.<\/p>\n<p>Question 13.<br \/>\n35 in., 45 in., 55 in.<br \/>\n______________<\/p>\n<p>Answer: Since 35<sup>2 <\/sup>+ 45<sup>2 <\/sup>\u2260 55<sup>2<\/sup>, the triangle is not a right-angled triangle.<\/p>\n<p>Explanation: Let a = 35, b = 45 and c= 55<br \/>\nUsing the converse of the Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>35<sup>2 <\/sup>+ 45<sup>2 <\/sup>= 55<sup>2<br \/>\n<\/sup>1225 + 2025 = 3025<br \/>\n3250 \u2260 3025.<br \/>\nSince 35<sup>2 <\/sup>+ 45<sup>2 <\/sup>\u2260 55<sup>2<\/sup>, the triangle is not a right-angled triangle.<\/p>\n<p>Question 14.<br \/>\n25 cm, 14 cm, 23 cm<br \/>\n______________<\/p>\n<p>Answer: Since\u00a0 14<sup>2 <\/sup>+ 23<sup>2 <\/sup>\u2260 25<sup>2<\/sup>, the triangle is not a right-angled triangle.<\/p>\n<p>Explanation: Let a = 14, b = 23 and c= 25 (longest side)<br \/>\nUsing the converse of the Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>14<sup>2 <\/sup>+ 23<sup>2 <\/sup>= 25<sup>2<br \/>\n<\/sup>196 + 529 = 625<br \/>\n725 \u2260 625.<br \/>\nSince \u00a014<sup>2 <\/sup>+ 23<sup>2 <\/sup>\u226025<sup>2<\/sup>, the triangle is not a right-angled triangle.<\/p>\n<p>Question 15.<br \/>\nThe emblem on a college banner consists of the face of a tiger inside a triangle. The lengths of the sides of the triangle are 13 cm, 14 cm, and 15 cm. Is the triangle a right triangle? Explain.<br \/>\n________<\/p>\n<p>Answer: Since\u00a0 13<sup>2 <\/sup>+ 14<sup>2 <\/sup>\u2260 15<sup>2<\/sup>, the triangle is not a right-angled triangle.<\/p>\n<p>Explanation: Let a = 13, b = 14 and c= 15<br \/>\nUsing the converse of the Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>13<sup>2 <\/sup>+ 14<sup>2 <\/sup>= 15<sup>2<br \/>\n<\/sup>169 + 196 = 225<br \/>\n365 \u2260 225.<br \/>\nSince\u00a0 13<sup>2 <\/sup>+ 14<sup>2 <\/sup>\u2260 15<sup>2<\/sup>, the triangle is not a right-angled triangle.<\/p>\n<p>Question 16.<br \/>\nKerry has a large triangular piece of fabric that she wants to attach to the ceiling in her bedroom. The sides of the piece of fabric measure 4.8 ft, 6.4 ft, and 8 ft. Is the fabric in the shape of a right triangle? Explain.<br \/>\n________<\/p>\n<p>Answer: The triangular piece of fabric that Kerry has is in the shape of a right angle since it follows the Pythagorean theorem.<\/p>\n<p>Explanation: Let a = 4.8, b = 6.4 and c= 8<br \/>\nUsing the converse of the Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>4.8<sup>2 <\/sup>+ 6.4<sup>2 <\/sup>= 8<sup>2<br \/>\n<\/sup>23.04 + 40.96 = 64<br \/>\n64 = 64.<br \/>\nSince 4.8<sup>2 <\/sup>+ 6.4<sup>2 <\/sup>= 8<sup>2<\/sup>, the triangle is a right-angled triangle.<\/p>\n<p>Question 17.<br \/>\nA mosaic consists of triangular tiles. The smallest tiles have side lengths 6 cm, 10 cm, and 12 cm. Are these tiles in the shape of right triangles? Explain.<br \/>\n________<\/p>\n<p>Answer: Since 6<sup>2 <\/sup>+ 10<sup>2 <\/sup>\u2260 12<sup>2<\/sup>, by the converse of the Pythagorean Theorem, we say that the tiles are not in the shape of right-angled triangle.<\/p>\n<p>Explanation: Let a = 6, b = 10 and c= 12<br \/>\nUsing the converse of the Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>\u00a06<sup>2 <\/sup>+ 10<sup>2 <\/sup>= 12<sup>2<br \/>\n<\/sup>36 + 100 = 144<br \/>\n136 \u2260 144.<br \/>\nSince 6<sup>2 <\/sup>+ 10<sup>2 <\/sup>\u2260 12<sup>2<\/sup>, by the converse of the Pythagorean Theorem, we say that the tiles are not in the shape of right-angled triangle.<\/p>\n<p>Question 18.<br \/>\nHistory In ancient Egypt, surveyors made right angles by stretching a rope with evenly spaced knots as shown. Explain why the rope forms a right angle.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-11.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 2: Converse of the Pythagorean Theorem img 11\" width=\"265\" height=\"258\" \/><\/p>\n<p>Answer: The rope has formed a right-angled triangle because the length of its sides follows Pythagorean Theorem.<\/p>\n<p>Explanation: The knots are evenly placed at equal distances<br \/>\nThe lengths in terms of knots are a=4 knots, b = 3knots, c = 5 knots<br \/>\nTherefore a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>4<sup>2 <\/sup>+ 3<sup>2\u00a0 <\/sup>= 5<sup>2<br \/>\n<\/sup>16+9 = 25<br \/>\n25 = 25.<br \/>\nHence rope has formed a right-angled triangle because the length of its sides follows Pythagorean Theorem.<\/p>\n<h3><a id=\"Converse_of_the_Pythagorean_Theorem_Page_No_386\"><\/a>Converse of the Pythagorean Theorem &#8211; Page No. 386<\/h3>\n<p>Question 19.<br \/>\nJustify Reasoning Yoshi has two identical triangular boards as shown. Can he use these two boards to form a rectangle? Explain.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-12.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 2: Converse of the Pythagorean Theorem img 12\" width=\"271\" height=\"168\" \/><\/p>\n<p>Answer: Since it was proved that both can form a right-angled triangle, we can form a rectangle by joining them.<\/p>\n<p>Explanation: Given both triangles are identical, if both are right-angled triangles then we can surely join to form a rectangle.<br \/>\nLet\u2019s consider a = 0.75, b= 1 and c=1.25.<br \/>\nBy using converse Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>0.75<sup>2 <\/sup>+ 1<sup>2 <\/sup>= 1.25<sup>2<br \/>\n<\/sup>0.5625 + 1 = 1.5625<br \/>\n1.5625 = 1.5625.<br \/>\nSince it was proved that both can form right angled triangle, we can form a rectangle by joining them.<\/p>\n<p>Question 20.<br \/>\nCritique Reasoning Shoshanna says that a triangle with side lengths 17 m, 8 m, and 15 m is not a right triangle because 17<sup>2<\/sup> + 8<sup>2<\/sup> = 353, 15<sup>2<\/sup> = 225, and 353 \u2260 225. Is she correct? Explain<br \/>\n_______<\/p>\n<p>Answer: She is not right, A triangle with sides 15, 8, and 17 is a right-angled triangle.<\/p>\n<p>Explanation: Lets consider a =15, b= 8 and c = 17 (which is long side)<br \/>\nWe will verify by using converse Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>15<sup>2 <\/sup>+ 8<sup>2 <\/sup>= 17<sup>2<br \/>\n<\/sup>225 + 64 = 289<br \/>\n289 = 289.<br \/>\nSince the given dimensions satisfied Pythagorean Theorem, we can say it is a right-angled triangle. In the given above statement what Shoshanna did was c<sup>2 <\/sup>+ b<sup>2 <\/sup>= a<sup>2<\/sup>, which is not the correct definition of the Pythagorean Theorem.<\/p>\n<p><strong>FOCUS ON HIGHER ORDER THINKING<\/strong><\/p>\n<p>Question 21.<br \/>\nMake a Conjecture Diondre says that he can take any right triangle and make a new right triangle just by doubling the side lengths. Is Diondre\u2019s conjecture true? Test his conjecture using three different right triangles.<br \/>\n_______<\/p>\n<p>Answer: Yes, Diondre\u2019s conjecture is true. By doubling the sides of a right triangle would create a new right triangle.<\/p>\n<p>Explanation: Given a right triangle, the Pythagorean Theorem holds. Therefore,\u00a0a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>If we double the side lengths of that triangle, we get:<br \/>\n(2a)<sup>2 <\/sup>+ (2b)<sup>2\u00a0 <\/sup>= (2c)<sup>2<\/sup><br \/>\n4a<sup>2 <\/sup>+ 4b<sup>2 <\/sup>= 4c<sup>2<\/sup><br \/>\n4(a<sup>2 <\/sup>+ b<sup>2<\/sup>) = 4c<sup>2<\/sup><br \/>\na<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<\/sup> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<sup><br \/>\n<\/sup>As we can see doubling the sides of a right triangle would create a new right triangle.We can test that by using three different right triangles.<\/p>\n<p>The triangle with sides a = 6, b = 8 and c = 10 is a right triangle. We double its sides and check if the new triangle is a right triangle. After doubling value of a = 12, b = 16 and c = 20.<br \/>\n12<sup>2<\/sup> + 16<sup>2 <\/sup>= 20<sup>2<\/sup><br \/>\n144 + 256 = 400<br \/>\n400 = 400<br \/>\nHence proved!<br \/>\nSince 12<sup>2<\/sup> + 16<sup>2 <\/sup>= 20<sup>2<\/sup>, the new triangle is a right triangle by the converse of the Pythagorean Theorem.<\/p>\n<p>The triangle with sides a = 3, b = 4 and c = 5 is a right triangle. We double its sides and check if the new triangle is a right triangle. After doubling value of a = 6, b = 8 and c = 10.<br \/>\n6<sup>2<\/sup> + 8<sup>2 <\/sup>= 10<sup>2<\/sup><br \/>\n36 + 64 = 100<br \/>\n100 = 100<br \/>\nHence proved!<br \/>\nSince 6<sup>2<\/sup> + 8<sup>2 <\/sup>= 10<sup>2<\/sup>, the new triangle is a right triangle by the converse of the Pythagorean Theorem.<\/p>\n<p>The triangle with sides a = 12, b = 16 and c = 20 is a right triangle. We double its sides and check if the new triangle is a right triangle. After doubling value of a = 24, b = 32 and c = 40.<br \/>\n24<sup>2<\/sup> + 32<sup>2 <\/sup>= 40<sup>2<\/sup><br \/>\n576 + 1024 = 1600<br \/>\n1600 = 1600<br \/>\nHence proved!<br \/>\nSince 24<sup>2<\/sup> + 32<sup>2 <\/sup>= 40<sup>2<\/sup>, the new triangle is a right triangle by the converse of the Pythagorean Theorem.<\/p>\n<p>Question 22.<br \/>\nDraw Conclusions A diagonal of a parallelogram measures 37 inches. The sides measure 35 inches and 1 foot. Is the parallelogram a rectangle? Explain your reasoning.<br \/>\n_______<\/p>\n<p>Answer: Since 12<sup>2 <\/sup>+ 35<sup>2 <\/sup>= 37<sup>2<\/sup>, the triangle is right triangle. Therefore, the given parallelogram is a rectangle.<\/p>\n<p>Explanation: A rectangle is a parallelogram where the interior angles are right angles. To prove if the given parallelogram is a rectangle, we need to prove that the triangle formed by the diagonal of the parallelogram and two sides of it, is a right triangle. Converting all the values into inches, we have a = 12, b = 35 and c = 37. Using the converse of the Pythagorean Theorem, we have:<br \/>\na<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<\/sup><br \/>\n12<sup>2 <\/sup>+ 35<sup>2 <\/sup>= 37<sup>2<br \/>\n<\/sup>144 + 1225 = 1369<br \/>\n1369 = 1369.<br \/>\nSince 12<sup>2 <\/sup>+ 35<sup>2 <\/sup>= 37<sup>2<\/sup>, the triangle is right triangle. Therefore, the given parallelogram is a rectangle.<\/p>\n<p>Question 23.<br \/>\nRepresent Real-World Problems A soccer coach is marking the lines for a soccer field on a large recreation field. The dimensions of the field are to be 90 yards by 48 yards. Describe a procedure she could use to confirm that the sides of the field meet at right angles.<\/p>\n<p>Answer: To confirm that the sides of the field meet at right angles, she could measure the diagonal of the field and use the converse of the Pythagorean Theorem. If a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2 <\/sup>(where a = 90, b = 48 and c is the length of the diagonal), then the triangle is right triangle. This method can be used for every corner to decide if they form right angles or not.<\/p>\n<h3><a id=\"Guided_Practice_Distance_Between_Two_Points_Page_No_390\"><\/a>Guided Practice &#8211; Distance Between Two Points &#8211; Page No. 390<\/h3>\n<p>Question 1.<br \/>\nApproximate the length of the hypotenuse of the right triangle to the nearest tenth using a calculator.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-13.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 3: Distance Between Two Points img 13\" width=\"198\" height=\"173\" \/><br \/>\n_______ units<\/p>\n<p>Answer: The length of the hypotenuse of the right triangle to the nearest tenth is 5.8 units.<\/p>\n<p>Explanation: From the above figure let\u2019s take<br \/>\nLength of the vertical leg = 3 units<br \/>\nLength of the horizontal leg = 5 units<br \/>\nlet length of the hypotenuse = c<br \/>\nBy using Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>c<sup>2<\/sup> = 3<sup>2<\/sup> + 5<sup>2<br \/>\n<\/sup>c<sup>2 <\/sup>= 9 +25<br \/>\nc = \u221a34 =&gt; 5.830.<br \/>\nTherefore Length of the hypotenuse of the right triangle to the nearest tenth is 5.8 units.<\/p>\n<p>Question 2.<br \/>\nFind the distance between the points (3, 7) and (15, 12) on the coordinate plane.<br \/>\n_______ units<\/p>\n<p>Answer: Distance between points on the coordinate plane is 13<\/p>\n<p>Explanation: So (x<sub>1<\/sub>, y<sub>1<\/sub>) = (3,7) and\u00a0 (x<sub>2<\/sub>, y<sub>2<\/sub>) = (15, 12)<br \/>\ndistance formula d = \u221a( x<sub>2 <\/sub>\u2013 x<sub>1<\/sub>)<sup>2 <\/sup>+ \u221a( y<sub>2 <\/sub>\u2013 y<sub>1<\/sub>)<sup>2<\/sup><br \/>\nd = \u221a(15 -3)<sup>2 <\/sup>+ \u221a(12 \u2013 7)<sup>2<\/sup><br \/>\nd = \u221a12<sup>2 <\/sup>+ 5<sup>2<\/sup><br \/>\nd = \u221a144 + 25<br \/>\nd = \u221a169 =&gt; 13<br \/>\nTherefore distance between points on the coordinate plane is 13.<\/p>\n<p>Question 3.<br \/>\nA plane leaves an airport and flies due north. Two minutes later, a second plane leaves the same airport flying due east. The flight plan shows the coordinates of the two planes 10 minutes later. The distances in the graph are measured in miles. Use the Pythagorean Theorem to find the distance shown between the two planes.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-14.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 3: Distance Between Two Points img 14\" width=\"286\" height=\"199\" \/><br \/>\n_______ miles<\/p>\n<p>Answer: The distance between the two planes is 103.6 miles.<\/p>\n<p>Explanation:<br \/>\nLength of the vertical d<sub>v <\/sub>= \u221a(80 -1)<sup>2 <\/sup>+ \u221a(1-1)<sup>2<\/sup><br \/>\n= \u221a79<sup>2 <\/sup>=&gt; 79.<br \/>\nLength of the horizontal d<sub>h = <\/sub>\u221a(68 -1)<sup>2 <\/sup>+ \u221a(1-1)<sup>2<\/sup><br \/>\n= \u221a67<sup>2 <\/sup>=&gt; 67.<br \/>\nDistance between the two planes D = \u221a(79<sup>2<\/sup> + 67<sup>2<\/sup>)<br \/>\n= \u221a(6241+4489) =&gt; \u221a10730<br \/>\n= 103.5857 =&gt; 103.6 miles.<\/p>\n<p><strong>ESSENTIAL QUESTION CHECK-IN<\/strong><\/p>\n<p>Question 4.<br \/>\nDescribe two ways to find the distance between two points on a coordinate plane.<\/p>\n<p>Answer:<\/p>\n<p>Explanation: We can draw a right triangle whose hypotenuse is the segment connecting the two points and then use the Pythagorean Theorem to find the length of that segment. We can also the Distance formula to find the length of that segment.<\/p>\n<p>For example, plot three points; (1,2), (20,2) and (20,12)<\/p>\n<p>Using the Pythagorean Theorem:<\/p>\n<p>The length of the horizontal leg is the absolute value of the difference between the x-coordinates of the points (1,2) and (20,2).<br \/>\n|1 \u2013 20| = 19<br \/>\nThe length of the horizontal leg is 19.<\/p>\n<p>The length of the vertical leg is the absolute value of the difference between the y-coordinates of the points (20,2) and (20,12).<br \/>\n|2 \u2013 12| = 10<br \/>\nThe length of the vertical leg is 10.<\/p>\n<p>Let a = 19, b = 10 and let c represent the hypotenuse. Find c.<br \/>\na<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<\/sup><br \/>\n19<sup>2 <\/sup>+ 10<sup>2\u00a0 <\/sup>= c<sup>2<\/sup><br \/>\n361 + 100 = c<sup>2<\/sup><br \/>\n461 = c<sup>2<\/sup><br \/>\ndistance is 21.5 = c<\/p>\n<p>Using the Distance formula:<br \/>\nd= \u221a( x<sub>2 <\/sub>\u2013 x<sub>1<\/sub>)<sup>2 <\/sup>+ \u221a( y<sub>2 <\/sub>\u2013 y<sub>1<\/sub>)<sup>2<br \/>\n<\/sup>The length of the horizontal leg is between (1,2) and (20,2).<br \/>\nd= \u221a( x<sub>2 <\/sub>\u2013 x<sub>1<\/sub>)<sup>2 <\/sup>+ \u221a( y<sub>2 <\/sub>\u2013 y<sub>1<\/sub>)<sup>2<br \/>\n<\/sup>\u00a0 =\u00a0 \u221a(20 -1)<sup>2 <\/sup>+ \u221a(2-2)<sup>2<\/sup><br \/>\n= \u221a(19)<sup>2 <\/sup>+ \u221a(0)<sup>2<\/sup><br \/>\n= \u221a361 =&gt; 19<br \/>\nThe length of the vertical leg is between (20,2) and (20,12).<br \/>\nd= \u221a( x<sub>2 <\/sub>\u2013 x<sub>1<\/sub>)<sup>2 <\/sup>+ \u221a( y<sub>2 <\/sub>\u2013 y<sub>1<\/sub>)<sup>2<br \/>\n<\/sup>\u00a0 =\u00a0 \u221a(20 -20)<sup>2 <\/sup>+ \u221a(12-2)<sup>2<\/sup><br \/>\n= \u221a(0)<sup>2 <\/sup>+\u221a(10)<sup>2<\/sup><br \/>\n= \u221a100 =&gt; 10<br \/>\nThe length of the diagonal leg is between (1,2) and (20,12).<br \/>\nd= \u221a( x<sub>2 <\/sub>\u2013 x<sub>1<\/sub>)<sup>2 <\/sup>+ \u221a( y<sub>2 <\/sub>\u2013 y<sub>1<\/sub>)<sup>2<br \/>\n<\/sup>\u00a0 =\u00a0 \u221a(20 -1)<sup>2 <\/sup>+ \u221a(12-2)<sup>2<\/sup><br \/>\n= \u221a(19)<sup>2 <\/sup>+ \u221a(10)<sup>2<\/sup><br \/>\n= \u221a(361+100) =&gt; \u221a461 = 21.5<\/p>\n<h3><a id=\"12.3_Independent_Practice_Distance_Between_Two_Points_Page_No_391\"><\/a>12.3 Independent Practice &#8211; Distance Between Two Points &#8211; Page No. 391<\/h3>\n<p>Question 5.<br \/>\nA metal worker traced a triangular piece of sheet metal on a coordinate plane, as shown. The units represent inches. What is the length of the longest side of the metal triangle? Approximate the length to the nearest tenth of an inch using a calculator. Check that your answer is reasonable.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-15.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 3: Distance Between Two Points img 15\" width=\"268\" height=\"258\" \/><br \/>\n_______ in.<\/p>\n<p>Answer: The length of the longest side of the metal triangle to the nearest tenth is 7.8 units.<\/p>\n<p>Explanation: From the above figure let\u2019s take<br \/>\nLength of the vertical leg = 6 units<br \/>\nLength of the horizontal leg = 5 units<br \/>\nlet length of the hypotenuse = c<br \/>\nBy using Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>c<sup>2<\/sup> = 6<sup>2<\/sup> + 5<sup>2<br \/>\n<\/sup>c<sup>2 <\/sup>= 36 +25<br \/>\nc = \u221a61 =&gt; 7.8<br \/>\nTherefore Length of the longest side of the metal triangle to the nearest tenth is 7.8 units.<\/p>\n<p>Question 6.<br \/>\nWhen a coordinate grid is superimposed on a map of Harrisburg, the high school is located at (17, 21) and the town park is located at (28, 13). If each unit represents 1 mile, how many miles apart are the high school and the town park? Round your answer to the nearest tenth.<br \/>\n_______ miles<\/p>\n<p>Answer: The high school and the town park are 13.6 miles apart.<\/p>\n<p>Explanation: The coordinates of the high school are said to be (17,21), where as the coordinates of the park\u00a0 are (28,13). In a coordinate plane, the distance d between the points (17,21) and (28,13) is:<\/p>\n<p>d= \u221a( x<sub>2 <\/sub>\u2013 x<sub>1<\/sub>)<sup>2 <\/sup>+ \u221a( y<sub>2 <\/sub>\u2013 y<sub>1<\/sub>)<sup>2<br \/>\n<\/sup>\u00a0 =\u00a0 \u221a(28 -17)<sup>2 <\/sup>+ \u221a(13-21)<sup>2<\/sup><br \/>\n= \u221a(11)<sup>2 <\/sup>+ \u221a(-8)<sup>2<\/sup><br \/>\n= \u221a(121+64) =&gt; \u221a185 = 13.6014<\/p>\n<p>Rounding the answer to the nearest tenth:<br \/>\nd = 13.6.<br \/>\nTaking into consideration that each unit represents 1 mile, the high school and town park are 13.6 miles apart.<\/p>\n<p>Question 7.<br \/>\nThe coordinates of the vertices of a rectangle are given by R(- 3, &#8211; 4), E(- 3, 4), C (4, 4), and T (4, &#8211; 4). Plot these points on the coordinate plane at the right and connect them to draw the rectangle. Then connect points E and T to form diagonal \\(\\overline { ET } \\).<br \/>\na. Use the Pythagorean Theorem to find the exact length of \\(\\overline { ET } \\).<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-16.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 3: Distance Between Two Points img 16\" width=\"265\" height=\"273\" \/><\/p>\n<p><span lang=\"EN-IN\">Answer: The diagonal ET is about 10.63 units long.<\/span><\/p>\n<p>Explanation:<br \/>\nTaking into consideration the triangle TRE, the length of the vertical leg (ER) is 8 units. The length of the horizontal leg (RT) is 7 units. Let a = 8 and b =7. Let c represent the length of the hypotenuse, the diagonal ET. We use the Pythagorean Theorem to find c.<br \/>\na<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>c<sup>2<\/sup> = 8<sup>2<\/sup> + 7<sup>2<br \/>\n<\/sup>c<sup>2 <\/sup>= 64 +49<br \/>\nc = \u221a113 =&gt; 10,63.<br \/>\nThe diagonal ET is about 10.63 units long.<\/p>\n<p>Question 7.<br \/>\nb. How can you use the Distance Formula to find the length of \\(\\overline { ET } \\) ? Show that the Distance Formula gives the same answer.<\/p>\n<p>Answer: The diagonal ET is about 10.63 units long. As we can see the answer is the same as the one we found using the Pythagorean Theorem.<\/p>\n<p>Explanation: Using the distance formula, in a coordinate plane, the distance d between the points E(-3,4) and T(4, -4) is:<br \/>\nd= \u221a( x<sub>2 <\/sub>\u2013 x<sub>1<\/sub>)<sup>2 <\/sup>+ \u221a( y<sub>2 <\/sub>\u2013 y<sub>1<\/sub>)<sup>2<br \/>\n<\/sup>\u00a0 =\u00a0 \u221a(4 \u2013 (-3))<sup>2 <\/sup>+ \u221a(- 4 &#8211; 4)<sup>2<\/sup><br \/>\n= \u221a(7)<sup>2 <\/sup>+ \u221a(-8)<sup>2<\/sup><br \/>\n= \u221a(49+64) =&gt; \u221a113 = 10.63.<br \/>\nThe diagonal ET is about 10.63 units long. As we can see the answer is the same as the one we found using the Pythagorean Theorem.<\/p>\n<p>Question 8.<br \/>\nMultistep The locations of three ships are represented on a coordinate grid by the following points: P(- 2, 5), Q(- 7, &#8211; 5), and R(2, &#8211; 3). Which ships are farthest apart?<\/p>\n<p>Answer: Ships P and Q are farthest apart<\/p>\n<p>Explanation: Distance Formula: In a coordinate plane, the distance d between two points (x<sub>1<\/sub>,y<sub>1<\/sub>) and (x<sub>2<\/sub>,y<sub>2<\/sub>) is:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-8159\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/09\/Screenshot-375.png\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem\" width=\"222\" height=\"207\" \/><br \/>\nd= \u221a( x<sub>2 <\/sub>\u2013 x<sub>1<\/sub>)<sup>2 <\/sup>+ \u221a( y<sub>2 <\/sub>\u2013 y<sub>1<\/sub>)<sup>2<\/sup><br \/>\nThe distance d<sub>1 <\/sub>between the two points P(-2,5) and Q(-7,-5) is:<br \/>\nd<sub>1 =<\/sub> \u221a( x<sub>Q <\/sub>\u2013 x<sub>P<\/sub>)<sup>2 <\/sup>+ \u221a( y<sub>Q <\/sub>\u2013 y<sub>P<\/sub>)<sup>2<\/sup><br \/>\n= \u221a(-7 \u2013 (-2))<sup>2 <\/sup>+ \u221a(- 5 &#8211; 5)<sup>2<\/sup><br \/>\n= \u221a(-5)<sup>2 <\/sup>+ \u221a(-10)<sup>2<\/sup><br \/>\n= \u221a(25+100) =&gt; \u221a125 = 11.18<\/p>\n<p>The distance d<sub>2 <\/sub>between the two points Q(-7,-5) and R(2,-3) is:<br \/>\nd<sub>3 =<\/sub> \u221a( x<sub>R <\/sub>\u2013 x<sub>Q<\/sub>)<sup>2 <\/sup>+ \u221a( y<sub>R <\/sub>\u2013 y<sub>Q<\/sub>)<sup>2<\/sup><sup><br \/>\n<\/sup>\u00a0 = \u221a(2 \u2013 (-7))<sup>2 <\/sup>+ \u221a(- 3 &#8211; 5)<sup>2<\/sup><br \/>\n= \u221a(9)<sup>2 <\/sup>+ \u221a(2)<sup>2<\/sup><br \/>\n= \u221a(81+4) =&gt; \u221a85 = 9.22<\/p>\n<p>The distance d<sub>3 <\/sub>between the two points P(-2,5) and R(2,-3) is:<br \/>\nd<sub>3 =<\/sub> \u221a( x<sub>R <\/sub>\u2013 x<sub>P<\/sub>)<sup>2 <\/sup>+ \u221a( y<sub>R <\/sub>\u2013 y<sub>P<\/sub>)<sup>2<\/sup><br \/>\n= \u221a(2 \u2013 (-2))<sup>2 <\/sup>+ \u221a(- 3 &#8211; 5)<sup>2<\/sup><br \/>\n= \u221a(4)<sup>2 <\/sup>+ \u221a(-8)<sup>2<\/sup><br \/>\n= \u221a(16+64) =&gt; \u221a80 = 8.94.<br \/>\nAs we can see, the greatest distance is d<sub>1 <\/sub>11.8, which means that ships P and Q are farthest apart.<\/p>\n<h3><a id=\"Distance_Between_Two_Points_Page_No_392\"><\/a>Distance Between Two Points &#8211; Page No. 392<\/h3>\n<p>Question 9.<br \/>\nMake a Conjecture Find as many points as you can that are 5 units from the origin. Make a conjecture about the shape formed if all the points 5 units from the origin were connected.<\/p>\n<p>Answer: <span lang=\"EN-IN\"> (0,5), (3,4), (4,3),(5,0),(4,-3),(3,-4),(0,-5),(-3,-4),(-4,-3),(-5,0),(-4,3),(-3,4).<\/span><\/p>\n<p><span lang=\"EN-IN\">Explanation: Some of the points that are 5 units away from the origin are: (0,5), (3,4), (4,3),(5,0),(4,-3),(3,-4),(0,-5),(-3,-4),(-4,-3),(-5,0),(-4,3),(-3,4) etc, If all the points 5 units away from the origin are connected, a circle would be formed.<\/span><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-8160\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/09\/Screenshot-377.png\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem\" width=\"249\" height=\"225\" \/><\/p>\n<p>Question 10.<br \/>\nJustify Reasoning The graph shows the location of a motion detector that has a maximum range of 34 feet. A peacock at point P displays its tail feathers. Will the motion detector sense this motion? Explain.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-17.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 3: Distance Between Two Points img 17\" width=\"195\" height=\"191\" \/><\/p>\n<p>Answer: Considering each unit represents 1 foot, the motion detector, and peacock are 33.5 feet apart. Since the motion detector has a maximum range of 34 feet, it means that it will sense the motion of the peacock\u2019s feathers.<\/p>\n<p>Explanation: The coordinates of the motion detector are said to be (0,25), whereas the coordinates of the peacock are (30,10). In a coordinate plane, the distance d between the points (0,25) and (30,10) is:<br \/>\nd<sub> =<\/sub> \u221a( x<sub>2 <\/sub>\u2013 x<sub>1<\/sub>)<sup>2 <\/sup>+ \u221a( y<sub>2 <\/sub>\u2013 y<sub>1<\/sub>)<sup>2<\/sup><br \/>\n= \u221a(30 \u2013 0)<sup>2 <\/sup>+ \u221a(10 &#8211; 25)<sup>2<\/sup><br \/>\n= \u221a(30)<sup>2 <\/sup>+ \u221a(-15)<sup>2<\/sup><br \/>\n= \u221a(900+225) =&gt; \u221a1125.<br \/>\nRounding answer to the nearest tenth:<br \/>\nd = 33.5 feet.<br \/>\nConsidering each unit represents 1 foot, the motion detector and peacock are 33.5 feet apart. Since the motion detector has a maximum range of 34 feet, it means that it will sense the motion of the peacock\u2019s feathers.<\/p>\n<p><strong>FOCUS ON HIGHER ORDER THINKING<\/strong><\/p>\n<p>Question 11.<br \/>\nPersevere in Problem Solving One leg of an isosceles right triangle has endpoints (1, 1) and (6, 1). The other leg passes through the point (6, 2). Draw the triangle on the coordinate plane. Then show how you can use the Distance Formula to find the length of the hypotenuse. Round your answer to the nearest tenth.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-18.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 3: Distance Between Two Points img 18\" width=\"152\" height=\"161\" \/><\/p>\n<p>Answer: 7.1 units.<\/p>\n<p>Explanation:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-8165\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/09\/Screenshot-379.png\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem\" width=\"220\" height=\"216\" \/><\/p>\n<p>One leg of an isosceles right triangle has endpoints (1,1) and (6,1), which means that the leg is 5 units long. Since the triangle is isosceles, the other leg should be 5 units long too, therefore the endpoints of the second leg that passes through the point (6,2) are (6,1) and (6,6).<br \/>\nIn the coordinate plane, the length of the hypotenuse is the distance d between the points (1,1) and (6,6).<br \/>\nd<sub> =<\/sub> \u221a( x<sub>2 <\/sub>\u2013 x<sub>1<\/sub>)<sup>2 <\/sup>+ \u221a( y<sub>2 <\/sub>\u2013 y<sub>1<\/sub>)<sup>2<\/sup><br \/>\n= \u221a(6 \u2013 1)<sup>2 <\/sup>+ \u221a(6 &#8211; 1)<sup>2<\/sup><br \/>\n= \u221a(5)<sup>2 <\/sup>+ \u221a(5)<sup>2<\/sup><br \/>\n= \u221a(25+25) =&gt; \u221a50.<br \/>\nRounding answer to nearest tenth:<br \/>\nd = 7.1.<br \/>\nThe hypotenuse is around 7.1 units long.<\/p>\n<p>Question 12.<br \/>\nRepresent Real-World Problems The figure shows a representation of a football field. The units represent yards. A sports analyst marks the locations of the football from where it was thrown (point A) and where it was caught (point B). Explain how you can use the Pythagorean Theorem to find the distance the ball was thrown. Then find the distance.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-19.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 3: Distance Between Two Points img 19\" width=\"265\" height=\"141\" \/><br \/>\n_______ yards<\/p>\n<p>Answer: The distance between point A and B is 37 yards<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8166\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/09\/Screenshot-381-300x141.png\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem\" width=\"300\" height=\"141\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/09\/Screenshot-381-300x141.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/09\/Screenshot-381.png 369w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nTo find the distance between points A and B, we draw segment AB and label its length d. Then we draw vertical segment AC and Horizontal segment CB. We label the lengths of these segments a and b. triangle ACB is a right triangle with hypotenuse AB.<br \/>\nSince AC is vertical segment, its length, a, is the difference between its y-coordinates. Therefore, a = 26 &#8211; 14 = 12 units.<br \/>\nSince CB is horizontal segment, its length b is the difference between its x-coordinates. Therefore, b = 75 &#8211; 40 = 35units.<br \/>\nWe use the Pythagorean Theorem to find d, the length of segment AB.<br \/>\nd<sup>2 <\/sup>= a<sup>2 <\/sup>+ b<sup>2<br \/>\n<\/sup>d<sup>2 <\/sup>= 12<sup>2 <\/sup>+ 35<sup>2<\/sup><br \/>\nd<sup>2<\/sup> = 144 + 1225<br \/>\nd<sup>2 <\/sup>= 1369 =&gt; d = \u221a1369 =&gt; 37<br \/>\nThe distance between point A and B is 37 yards<\/p>\n<h3><a id=\"Ready_to_Go_On?_Model_Quiz_Page_No_393\"><\/a>Ready to Go On? &#8211; Model Quiz &#8211; Page No. 393<\/h3>\n<p><strong>12.1 The Pythagorean Theorem<\/strong><\/p>\n<p><strong>Find the length of the missing side.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-20.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Model Quiz img 20\" width=\"102\" height=\"144\" \/><br \/>\n________ meters<\/p>\n<p>Answer: Length of missing side is 28m<\/p>\n<p>Explanation: Lets consider value of a = 21 and c = 35.<br \/>\nUsing Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<\/sup><br \/>\n21<sup>2 <\/sup>+ b<sup>2 <\/sup>= 35<sup>2<\/sup> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<sup><br \/>\n<\/sup>441 + b<sup>2<\/sup> = 1225<br \/>\nb<sup>2<\/sup>= 784 =&gt; b = \u221a784 = 28.<br \/>\nTherefore length of missing side is 28m.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-21.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Model Quiz img 21\" width=\"185\" height=\"122\" \/><br \/>\n________ ft<\/p>\n<p>Answer: Length of missing side is 34ft<\/p>\n<p>Explanation: Let\u2019s consider value of a = 16 and b = 30.<br \/>\nUsing Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>16<sup>2 <\/sup>+ 30<sup>2 <\/sup>= c<sup>2<\/sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<sup><br \/>\n<\/sup>256 + 900 = c<sup>2<\/sup><br \/>\nc<sup>2<\/sup>= 1156 =&gt; c = \u221a1156 = 34.<br \/>\nTherefore length of missing side is 34ft.<\/p>\n<p><strong>12.2 Converse of the Pythagorean Theorem<\/strong><\/p>\n<p><strong>Tell whether each triangle with the given side lengths is a right triangle.<\/strong><\/p>\n<p>Question 3.<br \/>\n11, 60, 61<br \/>\n____________<\/p>\n<p>Answer: Since 11<sup>2 <\/sup>+ 60<sup>2 <\/sup>= 61<sup>2<\/sup>, by the converse of the Pythagorean Theorem, we say that the given sides are in the shape of right-angled triangle.<\/p>\n<p>Explanation: Let a = 11, b = 60 and c= 61<br \/>\nUsing the converse of the Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>11<sup>2 <\/sup>+ 60<sup>2 <\/sup>= 61<sup>2<\/sup><br \/>\n121 + 3600 = 3721<br \/>\n3721 = 3721<br \/>\nSince 11<sup>2 <\/sup>+ 60<sup>2 <\/sup>= 61<sup>2<\/sup>, by the converse of the Pythagorean Theorem, we say that the given sides are in the shape of right-angled triangle.\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<sup><br \/>\n<\/sup>Question 4.<br \/>\n9, 37, 40<br \/>\n____________<\/p>\n<p>Answer: Since\u00a0 9<sup>2 <\/sup>+ 37<sup>2 <\/sup>\u2260 40<sup>2<\/sup>, by the converse of the Pythagorean Theorem, we say that the given sides are not in the shape of right-angled triangle.<\/p>\n<p>Explanation: Let a = 9, b = 37 and c= 40<br \/>\nUsing the converse of the Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>9<sup>2 <\/sup>+ 37<sup>2 <\/sup>= 40<sup>2<br \/>\n<\/sup>81 + 1369 = 1600<br \/>\n1450 \u2260 3721.<br \/>\nSince\u00a0 9<sup>2 <\/sup>+ 37<sup>2 <\/sup>\u2260 40<sup>2<\/sup>, by the converse of the Pythagorean Theorem, we say that the given sides are not in the shape of right-angled triangle.<\/p>\n<p>Question 5.<br \/>\n15, 35, 38<br \/>\n____________<\/p>\n<p>Answer: Since 15<sup>2 <\/sup>+ 35<sup>2 <\/sup>\u2260 38<sup>2<\/sup>, by the converse of the Pythagorean Theorem, we say that the given sides are not in the shape of right-angled triangle.<\/p>\n<p>Explanation: Let a = 15, b = 35 and c= 38<br \/>\nUsing the converse of the Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>15<sup>2 <\/sup>+ 35<sup>2 <\/sup>= 38<sup>2<\/sup><br \/>\n225 + 1225 = 1444<br \/>\n1450 \u2260 1444<br \/>\nSince 15<sup>2 <\/sup>+ 35<sup>2 <\/sup>\u2260 38<sup>2<\/sup>, by the converse of the Pythagorean Theorem, we say that the given sides are not in the shape of right-angled triangle.\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/sup><\/p>\n<p>Question 6.<br \/>\n28, 45, 53<br \/>\n____________<\/p>\n<p>Answer: Since 28<sup>2 <\/sup>+ 45<sup>2 <\/sup>= 53<sup>2<\/sup>, by the converse of the Pythagorean Theorem, we say that the given sides are in the shape of right-angled triangle.<\/p>\n<p>Explanation: Let a = 28, b = 45 and c= 53<br \/>\nUsing the converse of the Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>28<sup>2 <\/sup>+ 45<sup>2 <\/sup>= 53<sup>2<br \/>\n<\/sup>784 + 2025 = 2809<br \/>\n2809 = 2809<br \/>\nSince 28<sup>2 <\/sup>+ 45<sup>2 <\/sup>= 53<sup>2<\/sup>, by the converse of the Pythagorean Theorem, we say that the given sides are in the shape of right-angled triangle. \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<sup><br \/>\n<\/sup>Question 7.<br \/>\nKeelie has a triangular-shaped card. The lengths of its sides are 4.5 cm, 6 cm, and 7.5 cm. Is the card a right triangle?<br \/>\n____________<\/p>\n<p>Answer: Since 4.5<sup>2 <\/sup>+ 6<sup>2 <\/sup>= 7.5<sup>2<\/sup>, by the converse of the Pythagorean Theorem, we say that the given sides are in the shape of right-angled triangle.<\/p>\n<p>Explanation: Let a = 4.5, b = 6 and c= 7.5<br \/>\nUsing the converse of the Pythagorean Theorem a<sup>2 <\/sup>+ b<sup>2\u00a0 <\/sup>= c<sup>2<br \/>\n<\/sup>4.5<sup>2 <\/sup>+ 6<sup>2 <\/sup>= 7.5<sup>2<br \/>\n<\/sup>20.25 + 36 = 56.25<br \/>\n56.25= 56.25<br \/>\nSince 4.5<sup>2 <\/sup>+ 6<sup>2 <\/sup>= 7.5<sup>2<\/sup>, by the converse of the Pythagorean Theorem, we say that the given sides are in the shape of right-angled triangle.\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/sup><\/p>\n<p><strong>12.3 Distance Between Two Points<\/strong><\/p>\n<p><strong>Find the distance between the given points. Round to the nearest tenth.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-22.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Model Quiz img 22\" width=\"259\" height=\"246\" \/><\/p>\n<p>Question 8.<br \/>\nA and B<br \/>\n________ units<\/p>\n<p>Answer: Distance between A and B is 6.7 units<\/p>\n<p>Explanation: A= (-2,3) and B= (4,6)<\/p>\n<p>Distance between A and B is d<sub> =<\/sub> \u221a( x<sub>2 <\/sub>\u2013 x<sub>1<\/sub>)<sup>2 <\/sup>+ \u221a( y<sub>2 <\/sub>\u2013 y<sub>1<\/sub>)<sup>2<\/sup><br \/>\n= \u221a(4 \u2013 (-2)<sup>2 <\/sup>+ \u221a(6 &#8211; 3)<sup>2<\/sup><br \/>\n= \u221a(6)<sup>2 <\/sup>+ \u221a(3)<sup>2<\/sup><br \/>\n= \u221a(36+9) =&gt; \u221a45 = 6.7 units<\/p>\n<p>Question 9.<br \/>\nB and C<br \/>\n________ units<\/p>\n<p>Answer: Distance between B and C is 7.07 units<\/p>\n<p>Explanation: B= (4,6) and C= (3,1)<\/p>\n<p>Distance between B and C is d<sub> =<\/sub> \u221a( x<sub>2 <\/sub>\u2013 x<sub>1<\/sub>)<sup>2 <\/sup>+ \u221a( y<sub>2 <\/sub>\u2013 y<sub>1<\/sub>)<sup>2<\/sup><br \/>\n= \u221a(4 \u2013 3)<sup>2 <\/sup>+ \u221a(6 \u2013 (-1))<sup>2<\/sup><br \/>\n= \u221a(1)<sup>2 <\/sup>+ \u221a(7)<sup>2<\/sup><br \/>\n= \u221a(1+49) =&gt; \u221a50 = 7.07 units<\/p>\n<p>Question 10.<br \/>\nA and C<br \/>\n________ units<\/p>\n<p>Answer: Distance between A and C is 6.403 units<\/p>\n<p>Explanation: A= (-2,3) and C= (3, -1)<\/p>\n<p>Distance between A and C is d<sub> =<\/sub> \u221a( x<sub>2 <\/sub>\u2013 x<sub>1<\/sub>)<sup>2 <\/sup>+ \u221a( y<sub>2 <\/sub>\u2013 y<sub>1<\/sub>)<sup>2<\/sup><br \/>\n= \u221a(3 \u2013 (-2)<sup>2 <\/sup>+ \u221a(-1 &#8211; 3)<sup>2<\/sup><br \/>\n= \u221a(5)<sup>2 <\/sup>+ \u221a(-4)<sup>2<\/sup><br \/>\n= \u221a(25+16) =&gt; \u221a41 = 6.403 units<\/p>\n<p><strong>ESSENTIAL QUESTION<\/strong><\/p>\n<p>Question 11.<br \/>\nHow can you use the Pythagorean Theorem to solve real-world problems?<\/p>\n<p><span lang=\"EN-IN\">Answer: We can use the Pythagorean Theorem to find the length of a side of a right triangle when we know the lengths of the other two sides. This application is usually used in architecture or other physical construction projects. For example, it can be used to find the length of a ladder, if we know the height of the wall and distance on the ground from the wall of the ladder.<\/span><\/p>\n<h3><a id=\"Selected_Response_Mixed_Review_Page_No_394\"><\/a>Selected Response &#8211; Mixed Review &#8211; Page No. 394<\/h3>\n<p>Question 1.<br \/>\nWhat is the missing length of the side?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-23.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Mixed Review img 23\" width=\"205\" height=\"114\" \/><br \/>\nA. 9 ft<br \/>\nB. 30 ft<br \/>\nC. 39 ft<br \/>\nD. 120 ft<\/p>\n<p>Answer: C<\/p>\n<p>Explanation:<br \/>\nGiven a= 80 ft<br \/>\nb= ?<br \/>\nc= 89 ft<br \/>\nAs a<sup>2<\/sup>+b<sup>2<\/sup>=c<sup> 2<br \/>\n<\/sup>80<sup>2<\/sup>+b<sup>2<\/sup>= 89<sup>2<br \/>\n<\/sup>6,400+b<sup>2<\/sup>= 7,921<br \/>\nb<sup>2<\/sup>= 7,921-6,400<br \/>\nb= \u221a1,521<br \/>\nb= 39 ft.<\/p>\n<p>Question 2.<br \/>\nWhich relation does not represent a function?<br \/>\nOptions:<br \/>\nA. (0, 8), (3, 8), (1, 6)<br \/>\nB. (4, 2), (6, 1), (8, 9)<br \/>\nC. (1, 20), (2, 23), (9, 26)<br \/>\nD. (0, 3), (2, 3), (2, 0)<\/p>\n<p>Answer: D<\/p>\n<p>Explanation: The value of X is the same for 2 points and 2 values of Y [(2, 3), (2, 0)]. The value of X is repeated for a function to exist, no two points can have the same X coordinates.<\/p>\n<p>Question 3.<br \/>\nTwo sides of a right triangle have lengths of 72 cm and 97 cm. The third side is not the hypotenuse. How long is the third side?<br \/>\nOptions:<br \/>\nA. 25 cm<br \/>\nB. 45 cm<br \/>\nC. 65 cm<br \/>\nD. 121 cm<\/p>\n<p>Answer: C<\/p>\n<p>Explanation:<br \/>\nGiven a= 72 cm<br \/>\nb= ?<br \/>\nc= 97 cm<br \/>\nAs a<sup>2<\/sup>+b<sup>2<\/sup>=c<sup> 2<br \/>\n<\/sup>72<sup>2<\/sup>+b<sup>2<\/sup>= 97<sup>2<br \/>\n<\/sup>5,184+b<sup>2<\/sup>= 9,409<br \/>\nb<sup>2<\/sup>= 9,409-5,184<br \/>\nb= \u221a4,225<br \/>\nb= 65 cm.<\/p>\n<p>Question 4.<br \/>\nTo the nearest tenth, what is the distance between point F and point G?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-24.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Mixed Review img 24\" width=\"275\" height=\"198\" \/><br \/>\nOptions:<br \/>\nA. 4.5 units<br \/>\nB. 5.0 units<br \/>\nC. 7.3 units<br \/>\nD. 20 units<\/p>\n<p>Answer: A.<\/p>\n<p>Explanation:<br \/>\nGiven F= (-1,6) =(x1,y1).<br \/>\nG= (3,4) = (x2,y2).<br \/>\nThe difference between F&amp;G points is<br \/>\nd= \u221a(x2-x1)<sup>2<\/sup> + (y2-y1)<sup>2<\/sup><br \/>\n=\u00a0 \u221a(3 &#8211; (-1))<sup>2<\/sup> + (4 &#8211; 6)<sup>2<br \/>\n<\/sup>\u00a0= \u221a(4)<sup>2<\/sup>\u00a0+ (-2)<sup>2<\/sup><br \/>\n= \u221a16+4<br \/>\n= \u221a20<br \/>\n= 4.471<br \/>\n= 4.5 units.<\/p>\n<p>Question 5.<br \/>\nA flagpole is 53 feet tall. A rope is tied to the top of the flagpole and secured to the ground 28 feet from the base of the flagpole. What is the length of the rope?<br \/>\nOptions:<br \/>\nA. 25 feet<br \/>\nB. 45 feet<br \/>\nC. 53 feet<br \/>\nD. 60 feet<\/p>\n<p>Answer: D<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-8149\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/09\/Screenshot-359.png\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem\" width=\"131\" height=\"151\" \/><br \/>\nBy Pythagorean theorem<br \/>\na<sup>2<\/sup>+b<sup>2<\/sup>=c<sup> 2<br \/>\n<\/sup>53<sup>2<\/sup>+28<sup>2<\/sup>= C<sup>2<br \/>\n<\/sup>2,809+784= C<sup>2<\/sup><br \/>\nC<sup>2 <\/sup>= 9,409-5,184<br \/>\nC<sup>2 <\/sup>= 3,593<br \/>\nC= \u221a3,593<br \/>\nC= 59.94 feet<br \/>\n=60 feet.<\/p>\n<p>Question 6.<br \/>\nWhich set of lengths are not the side lengths of a right triangle?<br \/>\nOptions:<br \/>\nA. 36, 77, 85<br \/>\nB. 20, 99, 101<br \/>\nC. 27, 120, 123<br \/>\nD. 24, 33, 42<\/p>\n<p>Answer: D.<\/p>\n<p>Explanation:<br \/>\nCheck if side lengths in option A form a right triangle.<br \/>\nLet a= 36, b= 77, c= 85<br \/>\nBy Pythagorean theorem<br \/>\na<sup>2<\/sup>+b<sup>2<\/sup>=c<sup> 2<br \/>\n<\/sup>36<sup>2<\/sup>+77<sup>2<\/sup>= 85<sup>2<\/sup><br \/>\n1,296+ 5,929= 7,225<br \/>\n7,225= 7,225<br \/>\nAs 36<sup>2<\/sup>+77<sup>2<\/sup>= 85<sup>2<\/sup> the triangle is a right triangle.<\/p>\n<p>Check if side lengths in option B form a right triangle.<br \/>\nLet a= 20, b= 99, c= 101<br \/>\nBy Pythagorean theorem<br \/>\na<sup>2<\/sup>+b<sup>2<\/sup>=c<sup> 2<br \/>\n<\/sup>20<sup>2<\/sup>+99<sup>2<\/sup>= 101<sup>2<\/sup><br \/>\n400+ 9,801= 10,201<br \/>\n10,201= 10,201<br \/>\nAs 20<sup>2<\/sup>+99<sup>2<\/sup>= 101<sup>2<\/sup>\u00a0the triangle is a right triangle.<\/p>\n<p>Check if side lengths in option B form a right triangle.<br \/>\nLet a= 27, b= 120, c= 123<br \/>\nBy Pythagorean theorem<br \/>\na<sup>2<\/sup>+b<sup>2<\/sup>=c<sup> 2<br \/>\n<\/sup>27<sup>2<\/sup>+120<sup>2<\/sup>= 123<sup>2<\/sup><br \/>\n729+ 14,400= 15,129<br \/>\n15,129= 15,129<br \/>\nAs 27<sup>2<\/sup>+120<sup>2<\/sup>= 123<sup>2 <\/sup>the triangle is a right triangle.<\/p>\n<p>Check if side lengths in option B form a right triangle.<br \/>\nLet a= 27, b= 120, c= 123<br \/>\nBy Pythagorean theorem<br \/>\na<sup>2<\/sup>+b<sup>2<\/sup>=c<sup> 2<br \/>\n<\/sup>24<sup>2<\/sup>+33<sup>2<\/sup>= 42<sup>2<\/sup><br \/>\n576+ 1,089= 1,764.<br \/>\n1,665= 1,764<br \/>\nAs 24<sup>2<\/sup>+33<sup>2 <\/sup>is not equal to 42<sup>2<\/sup><sup>\u00a0<\/sup>the triangle is a right triangle.<\/p>\n<p>Question 7.<br \/>\nA triangle has one right angle. What could the measures of the other two angles be?<br \/>\nOptions:<br \/>\nA. 25\u00b0 and 65\u00b0<br \/>\nB. 30\u00b0 and 15\u00b0<br \/>\nC 55\u00b0 and 125\u00b0<br \/>\nD 90\u00b0 and 100\u00b0<\/p>\n<p>Answer: A<\/p>\n<p>Explanation:<br \/>\nThe sum of all the angles of a triangle is 180<br \/>\n&lt;A+&lt;B+&lt;C= 180\u00b0<br \/>\n&lt;A+&lt;B+ 90\u00b0= 180\u00b0<br \/>\n&lt;A+&lt;B= 180\u00b0-90\u00b0<br \/>\n&lt;A+&lt;B= 90, here we will verify with the given options.<br \/>\n25\u00b0+65\u00b0= 90\u00b0<br \/>\nSo, the measure of the other two angles are 25\u00b0 and 65\u00b0<\/p>\n<p><strong>Mini-Task<\/strong><\/p>\n<p>Question 8.<br \/>\nA fallen tree is shown on the coordinate grid below. Each unit represents 1 meter.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-12-The-Pythagorean-Theorem-img-25.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Mixed Review img 25\" width=\"344\" height=\"232\" \/><br \/>\na. What is the distance from A to B?<br \/>\n_______ meters<\/p>\n<p>Answer: 13.34\u00a0 m.<\/p>\n<p>Explanation:<br \/>\nA= (-5,3)<br \/>\nB= (8,0)<br \/>\nDistance between A &amp; B is<br \/>\nD= \u221a{8-(-5)<sup>2<\/sup> + (0-3)<sup>2<br \/>\n<\/sup> = \u221a(13)<sup>2<\/sup> + (-3)<sup>2<\/sup><br \/>\n= \u221a169+9<br \/>\n= \u221a178<br \/>\n= 13.34\u00a0 m.<\/p>\n<p>Question 8.<br \/>\nb. What was the height of the tree before it fell?<br \/>\n_______ meters<\/p>\n<p>Answer: 16.3 m.<\/p>\n<p>Explanation:<br \/>\nLength of the broken part= 13.3 m<br \/>\nLength of vertical part= 3 m<br \/>\nTotal Length = 13.3 m + 3 m<br \/>\n= 16.3 m.<\/p>\n<h3>Final Words<\/h3>\n<p>In addition to the exercise problems, we have provided the solutions for the review questions. So all the students are requested to test your knowledge and solve the problems provided at the end of this chapter. Refer HMH Go Math Grade 8 Answer Keu and try to score the highest marks in the exams. Hope you liked the explanations provided in this chapter. Stay tuned to get the solutions according to the list of the chapters of all the grades.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>One has to learn the concepts if he\/she wants to become a master in maths. The fundamentals in Go Math Grade 8 Answer Key Chapter 12 The Pythagorean theorem will help you to learn the subject. You need to practice from the beginning itself. We will help you to achieve your dreams by providing simple &#8230; <a title=\"Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/go-math-grade-8-answer-key-chapter-12-the-pythagorean-theorem\/\" aria-label=\"More on Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem\">Read more<\/a><\/p>\n","protected":false},"author":6,"featured_media":8785,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[2],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/go-math-grade-8-chapter-12-the-pythagorean-theorem-answer-key.jpeg","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/6772"}],"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\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=6772"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/6772\/revisions"}],"predecessor-version":[{"id":92793,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/6772\/revisions\/92793"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/8785"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=6772"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=6772"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=6772"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}