4 9 Using Similar Figures Indirect measurement is

4 -9 Using Similar Figures Indirect measurement is a method of using proportions to find an unknown length or distance of objects that are too difficult to measure directly.

4 -9 Using Similar Figures Example 1: Find the unknown measures in the similar H B figures. A 10 cm 31° 5. 8 cm 6 cm 11. 6 cm 59° C J 5 cm y x G

4 -9 Using Similar Figures Additional Example 1 Continued Find the unknown measures in the similar H B figures. A 10 cm 31° 5. 8 cm 6 cm 11. 6 cm 59° C J 5 cm y x G Step 2 Find y. Corresponding angles of similar H corresponds to C triangles have equal angle measures. y = 59

4 -9 Using Similar Figures Check It Out: Example 1 ΔQRS ~ ΔXYZ. Find the unknown measures. R Z 101° x Q 53° 18 in. 26° S y 12 in. 101° Y x 6 in

4 -9 Using Similar Figures Example 2: The inside triangle is similar in shape to the outside triangle. Find the length of the base of the inside triangle.

4 -9 Using Similar Figures Check It Out: Example 2 Van Gogh’s painting Starry Night is 73 cm high by 92 cm long. The museum gift shop sells a postcard of the painting. The image on the postcard is similar to the painting, and it is 10 cm high. What is the length of the postcard? Round to the nearest tenth.

4 -9 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 h ft 27. 25 ft 48. 75 ft 25 ≈ 50 15 h 5 ≈ 50 3 h 5 h ≈ 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.

4 -9 Using Similar Figures Check It Out: Example 3 Gus measures his shadow and the shadow of a lamp post, as shown at right. Estimate the height of the lamp post. 5 = x ; x 5 • 42 = 30; 30 ft = 7 42 7

4 -9 Using Similar Figures Lesson Quiz: Part I Find the unknown measures in each pair of similar figures. 1. 2. x = 120 cm y = 98 t = 150 cm s = 120

4 -9 Using Similar Figures Lesson Quiz: Part II 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

4 -9 Using Similar Figures 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

4 -9 Using Similar Figures 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

4 -9 Using Similar Figures 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.