7.3B STUDENT ACTIVITY #1

Transcription

1 E MAT I CS 7.3B STUDENT ACTIVITY #1 PROBLEM: Right triangles MNP and DEF are similar. Find the length in inches of side EF. D M 6 in. P 9 in. N 24 in. F x E Since the triangles are similar, their corresponding sides are. MN corresponds to. MP corresponds to. NP corresponds to. If two figures are similar, then the ratios of corresponding sides form a. small large MP NP Substitute the lengths of the sides in the proportion. = To find the value of x, solve the proportion. x = Divide both sides of the equation by. x = The length of side EF is inches. TEKSING TOWARD TAKS Weeks 3 - Lesson 6 Page 1

2 7.3B STUDENT ACTIVITY #2 PROBLEM #1: On a scale drawing of a storage shed, the entrance is 3.5 inches high. The scale used was 1 inch equals 2 feet. What is the height of the actual entrance to the storage shed? Identify the quantities being compared. Let h equal the height of the actual storage shed. Write a proportion. height in scale drawing to actual height in. in. ft h ft height in scale drawing actual height h To find the value of h, solve the proportion. First use. = h h = The actual storage shed entrance is feet high. PROBLEM #2: An engineer drew a scale model of a ramp that will be used to move large boxes in a warehouse from the floor to the storage shelves. x 6 in. 15 in. 8 ft What will be the length, x, of the ramp? Identify the quantities being compared. Let x equal the length of the actual ramp. length in scale drawing to actual length in. ft in. x ft TEKSING TOWARD TAKS Weeks 3 - Lesson 6 Page 2

3 Write a proportion. length in scale drawing actual length x To find the value of x, solve the proportion. First use. = x Then both sides by. x = The actual ramp length is feet. TEKSING TOWARD TAKS Weeks 3 - Lesson 6 Page 3

4 7.3B STUDENT ACTIVITY #3 Materials: 1 geoboard and geobands per pair of students, rulers, geodot paper and isometric dot paper Procedure: Work with a partner. PART I Your teacher will make a triangle on the geoboard on the overhead projector. Use the geoboard and geobands and work with your partner to form as many triangles as you can that have the same shape as the one on the overhead geoboard. Record the triangle on the overhead geoboard and all the triangles you made on your geoboard onto the geodot paper. Number the triangle like the one on the overhead geoboard as triangle #1. Number the triangles you made beginning with #2. What does same shape mean for all the triangles that you have drawn? Explain why each of the triangles you have drawn is similar to triangle #1. Explain how you achieved the same shape in making your triangles. Draw 2 triangles on the geodot paper that do not have the same shape as triangle #1 and identify those triangles as triangle X and triangle Y. Explain why triangles X and Y are not similar to triangle #1. PART II Draw a geometric figure other than a triangle on isometric dot paper and exchange with your partner. Draw at least 4 figures that have the same shape, both larger and smaller than the figure drawn. Justify to each other why the figures you drew are similar to the original shape on the isometric dot paper. TEKSING TOWARD TAKS Weeks 3 - Lesson 6 Page 4

5 Geodot Paper TEKSING TOWARD TAKS Weeks 3 - Lesson 6 Page 5

6 Isometric Dot Paper TEKSING TOWARD TAKS Weeks 3 - Lesson 6 Page 6

7 7.3B OPEN ENDED #1 Larry wants to enlarge his drawing so that the longest side will be 20 inches. 8 inches 4 inches 6 inches Write two proportions that you can use to find the other sides of the larger triangle. Draw a sketch of the enlargement and label the lengths on all three sides. 1. What mathematical concepts and vocabulary do I need to know to be able to work this problem? 2. Will the Grade 7 Mathematics Formula Chart be helpful on this problem? Why or why not? 3. How can I determine the scale factor for this relationship? 4. What problem-solving strategy or strategies will I use to help solve this problem? 5. Extension (7.9A): Find the perimeter of both triangles. What is the ratio of the large perimeter to the small perimeter? TEKSING TOWARD TAKS Weeks 3 - Lesson 6 Page 7

8 7.3B OPEN ENDED #2 Write a proportion that can be used to solve each of the following problems. Then find the solution to each problem. Billy used a scale of 1 inch represents 100 yards to draw a map of his neighborhood for his friend. If the map has a distance of 3.5 inches from Billy s house to John s house, how many yards is it between the two houses? A blue print uses a scale of 1 centimeter represents 6 feet. If a room is 2.5 centimeters by 3.2 centimeters on the blueprint, what are the actual dimensions of the room? A map uses 1 inch to represent 20 miles. It is 45 miles from Fort Sumner to Melrose. What is the distance between the two cities on the map? 1. What mathematical concepts and vocabulary do I need to know to be able to work these problems? 2. Will the Grade 7 Mathematics Formula Chart be helpful on this problem? Why or why not? 3. Will a picture or graph help me on this problem? Why or why not? 4. What problem-solving strategy or strategies will I use to help solve this problem? 5. Extension (7.3B): Two triangles are similar. The smaller sides in the two triangles are 15 feet and 20 feet. What is the scale factor? TEKSING TOWARD TAKS Weeks 3 - Lesson 6 Page 8

9 NAME DATE SCORE /5 7.3B Homework #1 1. Leona is drawing a triangle that is similar to the one below. The longest side of the new triangle is 45 inches. What is the length of the shortest side of the new triangle? 15 inches 8 inches 10 inches Show your work and explain your answer. 2. A triangle has sides of 45 feet, 24 feet and 30 feet. A scale drawing of the triangle uses a scale of 1centimeter represents 2 feet. Determine the lengths of the sides of the scale drawing below. Show your work for determining the side lengths. 3. Two rectangles are similar. The larger rectangle has a width of 12 feet and a length of 18 feet. The ratio of the lengths of the two rectangles is 1:5. What are the dimensions of the smaller rectangle? Justify your answer. 4. ABC JKL and AB JK 5. If JK = 12, what is the length of AB? Show your work. 2 A J B C K L 5. Use the information in problem #4. If BC = 10, what is the length of KL? Show your work. TEKSING TOWARD TAKS Weeks 3 - Lesson 6 Page 9

10 NAME DATE SCORE /5 7.3B Homework #2 1. Laura is drawing a triangle that is similar to the one below. The longest side of the new triangle is 8 inches. What are the lengths of the other two sides of the new triangle? 20 inches 12 inches Show your work and explain your answer. 15 inches 2. A scale drawing of a triangular piece of land is shown below. The scale drawing has a scale of 1 centimeter represents 250 feet. Determine the lengths of the sides of the actual piece of land. Use your Mathematics chart rulers and find the lengths of the sides of the scale drawing to the nearest centimeter. Show your work. 3. Two rectangles are similar. The larger rectangle has a width of 8 feet and a length of 28 feet. The width of the smaller rectangle is 6 feet. What is the ratio of the length of the larger rectangle to the length of the smaller rectangle? 4. ABC MNO and AB MN 3. 2 If MO = 14, what is AC? Show your work. C N A B O M 5. A scale drawing uses a scale of 2 centimeters represents 8 yards. What measurement on the drawing would represent 48 yards? Show your work. TEKSING TOWARD TAKS Weeks 3 - Lesson 6 Page 10