4-9 Using Similar Figures. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes
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1 Warm Up Problem of the Day Lesson Presentation Lesson Quizzes
2 Warm Up Solve each proportion. 1. k 4 = k = = 24 x = 76 x Triangles JNZ and KOA are similar. Identify the side that corresponds to the given side of the similar triangles. J A N Z K O JN KO
3 I can use similar figures to find unknown lengths.
4 Vocabulary indirect measurement
5 Indirect measurement is a method of using proportions to find an unknown length or distance in similar figures.
6 Additional Example 1: Finding Unknown Lengths in Similar Figures Find the unknown measures in the similar figures. B H 10 cm 31 A y 5.8 cm x 6 cm 116 cm 59 AB JG = BC J G C 5 cm HG Write a proportion using corresponding sides = 6 Substitute lengths of the sides. x 10 x = 5 6 Find the cross product. 10x = 30 Multiply. 10x = x = 3 HG is 3 centimeters. Divide each side by 12 to isolate the variable.
7 Additional Example 1 Continued Find the unknown measures in the similar figures. B H 10 cm 31 A 5.8 cm 6 cm 116 cm 59 J C 5 cm y x G Step 2 Find y. H corresponds to C y = 59 Corresponding angles of similar triangles have equal angle measures.
8 Check It Out: Example 1 Find the unknown measures in the similar figures. B D 14 cm 27 A y 5.8 cm x 9 cm 116 cm 63 AB FE = BC F E C 7 cm DE Write a proportion using corresponding sides = 9 Substitute lengths of the sides. x 14 x = 9 7 Find the cross product. 14x = 63 Multiply. 14x = x = 4.5 HG is 4.5 centimeters. Divide each side by 12 to isolate the variable.
9 Check It Out: Example 1 Continued Find the unknown measures in the similar figures. B D 10 cm 27 A 5.8 cm 6 cm 116 cm 63 F C 5 cm y x E Step 2 Find y. D corresponds to C y = 63 Corresponding angles of similar triangles have equal angle measures.
10 Additional Example 2: Measurement Application The inside triangle is similar in shape to the outside triangle. Find the length of the base of the inside triangle. Let x = the base of the inside triangle. 8 2 = 12 x 8 x = x = 24 Write a proportion using corresponding side lengths. Find the cross products. Multiply. 8x 8 = 24 Divide each side by 8 to isolate the variable. 8 x = 3 The base of the inside triangle is 3 inches.
11 Check It Out: Example 2 The rectangle on the left is similar in shape to the rectangle on the right. Find the width of the right rectangle. 12 cm 3 cm 6 cm Let w = the width of the right rectangle = 3 w 6 w = w = 36 6w = w = 6 Write a proportion using corresponding side lengths. Find the cross products. Multiply. Divide each side by 6 to isolate the variable. The right rectangle is 6 cm wide.?
12 Additional Example 3: Estimating with Indirect Measurement City officials want to know the height of a traffic light. Estimate the height of the traffic light = h Write a proportion ft ft h ft h h 5h 150 h 30 The traffic light is about 30 feet tall. Use compatible numbers to estimate. Simplify. Cross multiply. Divide each side by 5 to isolate the variable.
13 Check It Out: Example 3 The inside triangle is similar in shape to the outside triangle. Find the height of the outside triangle = h Write a proportion. 5 ft h ft 5 15 h h 30 Use compatible numbers to estimate. Simplify ft ft h Cross multiply. 30 3h Divide each side by 3 to 10 h isolate the variable. The outside triangle is about 10 feet tall.
14 Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems
15 Lesson Quiz: Part I Find the unknown length in each pair of similar figures y x = 120 cm y = s t = 150 cm s = 120
16 Lesson Quiz: Part II Find the unknown length in each pair of similar figures. 3. The width of the smaller rectangular cake is 5.75 in. The width of a larger rectangular cake is 9.25 in. Estimate the length of the larger rectangular cake. about 15 inches
17 Lesson Quiz for Student Response Systems 1. Identify the unknown length in the given pair of similar figures. A. x = 174 cm B. x = 182 cm C. x = 196 cm D. x = 204 cm
18 Lesson Quiz for Student Response Systems 2. Identify the unknown length in the given pair of similar figures. A. t = 166 cm B. t = 198 cm C. t = 206 cm D. t = 248 cm
19 Lesson Quiz for Student Response Systems 3. The width of the smaller rectangular box is 6.25 inches. The width of a similar larger rectangular box is 8.75 inches. Estimate the length of the larger rectangular box. A. about 16 in. B. about 17 in. C. about 18 in. D. about 19 in.
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