Holt CA Course 1 5-7 Using Similar Figures Warm Up Solve each proportion. 1. k4k4 = 75 25 2.2. 3. Triangles JNZ and KOA are similar. Identify the side.

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Holt CA Course Using Similar Figures Warm Up Solve each proportion. 1. k4k4 = Triangles JNZ and KOA are similar. Identify the side that corresponds to the given side of the similar triangles. JNKO k = 12 x = = 24 x

Holt CA Course Using Similar Figures NS1.3 Use proportions to solve problems (e.g., determine the value of N if T =, find the length of a side of a polygon similar to a known polygon). Use cross- multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. California Standards 4747 N 21

Holt CA Course Using Similar Figures Vocabulary indirect measurement

Holt CA Course Using Similar Figures Indirect measurement is a method of using proportions to find an unknown length or distance in similar figures.

Holt CA Course Using Similar Figures Find the unknown length in the similar figures. Additional Example 1: Finding Unknown Lengths in Similar Figures AC QS = AB QR Write a proportion using corresponding sides = 14 w Substitute lengths of the sides. 12 · w = 48 · 14Find the cross product. 12w = 672Multiply. 12w 12 = w = 56 QR is 56 centimeters. Divide each side by 12.

Holt CA Course Using Similar Figures Check It Out! Example 1 AC QS = AB QR Write a proportion using corresponding sides = 10 x Substitute lengths of the sides. 12 · x = 24 · 10 Find the cross product. 12x = 240Multiply. 12x 12 = x = 20 QR is 20 centimeters. Divide each side by 12. Find the unknown length in the similar figures. S A B C D 10 cm 12 cm Q R T 24 cm x

Holt CA Course Using Similar Figures 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 = 12 x 8 · x = 2 · 12 8x = 24 8x88x8 = 24 8 x = 3 The base of the inside triangle is 3 inches. Write a proportion using corresponding side lengths. Find the cross product. Multiply. Divide each side by 8. Additional Example 2: Measurement Application

Holt CA Course 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 the right rectangle. 3 cm 6 cm 12 cm Let w = the width of the right rectangle = 3w3w 6 · w = 12 · 3 6w = 36 6w66w6 = 36 6 w = 6 The right rectangle is 6 cm wide. Write a proportion using corresponding side lengths. Find the cross product. Multiply. Divide each side by 6. ?

Holt CA Course 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 = h Write a proportion. Use compatible numbers to estimate ≈ 50 h Simplify. 5h ≈ 150 The traffic light is about 30 feet high ≈ 50 h Cross multiply. h ≈ 30Divide each side by 5.

Holt CA Course 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. Write a proportion. Use compatible numbers to estimate ≈ h 30 Simplify ≈ 3 h The outside triangle is about 10 feet tall ft ft h ft 5 15 ≈ h ≈ 3h Multiply. 5 ft Cross multiply. 10 ≈ h = h Divide each side by 3.