Using Similar Figures 4-5

Vocabulary Indirect measurement- a method of using proportions to find an unknown length or distance in similar figures.

Find the unknown measures in the similar figures. Additional Example 1: Finding Unknown Lengths in Similar Figures AB JG = BC HG Write a proportion using corresponding sides = 6x6x Substitute lengths of the sides. 10 · x = 5 · 6 Find the cross product. 10x = 30 Multiply. 10x 10 = x = 3 HG is 3 centimeters. Divide each side by 12 to isolate the variable. H B A C GJ 10 cm 6 cm 116 cm 5.8 cm x 5 cm 31° 59° y

Find the unknown measures in the similar figures. Additional Example 1 Continued Step 2 Find y. Corresponding angles of similar triangles have equal angle measures. H corresponds to C y = 59 H B A C GJ 10 cm 6 cm 116 cm 5.8 cm x 5 cm 31° 59° y

Find the unknown measures in the similar figures. Check It Out: Example 1 D B A C EF 14 cm 9 cm 116 cm 5.8 cm x 7 cm 27° 63° y

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 products. Multiply. Divide each side by 8 to isolate the variable. Additional Example 2: Measurement Application

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 ?

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 tall ft ft h ft ≈ 50 h Cross multiply. h ≈ 30 Divide each side by 5 to isolate the variable.

Check It Out: Example 3 The inside triangle is similar in shape to the outside triangle. Find the height of the outside triangle ft ft h ft 5 ft