Holt CA Course Using Similar Figures Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

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.

Holt CA Course Using Similar Figures Lesson Quiz Find the unknown length in each pair of similar figures x = 120 cmt = 150 cm 3. The rectangles below are similar. The width of the smaller rectangle is 5.75 in. The width of a larger rectangle is 9.25 in. Estimate the length of the larger rectangle. about 15 inches