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5-7 Using Similar Figures Warm Up Solve each proportion. 1. k = 75 4 25 k = 12 2. 6 = 24 x = 76 19 x Triangles JNZ and KOA are similar. Identify the side that corresponds to the given side of the similar triangles. 3. JN Holt CA Course 1 KO 5-7 Using Similar Figures California Standards NS1.3 Use proportions to solve problems (e.g., determine the value of N if 4 T = N , find the length of a side of a polygon 7 21 similar to a known polygon). Use crossmultiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Holt CA Course 1 5-7 Using Similar Figures Vocabulary indirect measurement Holt CA Course 1 5-7 Using Similar Figures Indirect measurement is a method of using proportions to find an unknown length or distance in similar figures. Holt CA Course 1 5-7 Using Similar Figures Additional Example 1: Finding Unknown Lengths in Similar Figures Find the unknown length in the similar figures. AC = AB QS QR 12 = 14 w 48 12 · w = 48 · 14 12w = 672 Write a proportion using corresponding sides. Substitute lengths of the sides. Find the cross product. Multiply. 12w = 672 Divide each side by 12. 12 12 w = 56 QR is 56 centimeters. Holt CA Course 1 5-7 Using Similar Figures Check It Out! Example 1 Find the unknown length in the similar figures. A 10 cm B D C = AB QR = 10 x = 24 · 10 = 240 12x = 240 12 12 x = 20 R S T Write a proportion using corresponding sides. Substitute lengths of the sides. Find the cross product. Multiply. Divide each side by 12. QR is 20 centimeters. Holt CA Course 1 x 24 cm 12 cm AC QS 12 24 12 · x 12x Q 5-7 Using Similar Figures 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 = 12 2 x 8 · x = 2 · 12 8x = 24 Write a proportion using corresponding side lengths. Find the cross product. Multiply. 8x = 24 Divide each side by 8. 8 8 x=3 The base of the inside triangle is 3 inches. Holt CA Course 1 5-7 Using Similar Figures Check It Out! Example 2 The rectangle on the left is similar in shape to the rectangle on the right. Find the width of 12 cm the right rectangle. 6 cm 3 cm ? Let w = the width of the right rectangle. 6 = 3 12 w 6 · w = 12 · 3 6w = 36 6w = 36 6 6 w=6 Write a proportion using corresponding side lengths. Find the cross product. Multiply. Divide each side by 6. The right rectangle is 6 cm wide. Holt CA Course 1 5-7 Using Similar Figures 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. 27.25 = 48.75 Write a proportion. h 15 25 ≈ 50 15 h 5 ≈ 50 3 h Simplify. 5h ≈ 150 Cross multiply. h ≈ 30 The traffic light is about 30 feet high. Holt CA Course 1 Use compatible numbers to estimate. Divide each side by 5. 5-7 Using Similar Figures Check It Out! Example 3 The inside triangle is similar in shape to the outside triangle. Find the height of the outside triangle. 5 = h 14.75 30.25 5 ft h ft 5 ≈ h 15 30 1 ≈ h 3 30 14.75 ft 30.25 ft 1 • Write a proportion. Use compatible numbers to estimate. Simplify. 30 ≈ 3 • h Cross multiply. 30 ≈ 3h Multiply. 10 ≈ h Divide each side by 3. The outside triangle is about 10 feet tall. Holt CA Course 1