4 9 Using Similar Figures Vocabulary indirect measurement

4 -9 Using Similar Figures Vocabulary indirect measurement

4 -9 Using Similar Figures Indirect measurement is a method of using proportions to find an unknown length or distance in similar figures.

4 -9 Using Similar Figures Additional Example 1: Finding Unknown Lengths in Similar Figures Find the unknown measures in the similar H B figures. A 10 cm 31° 5. 8 cm 6 cm 11. 6 cm 59° AB = BC JG HG 10 = 6 x 5 10 · x = 5 · 6 10 x = 30 10 10 x=3 C y x J G 5 cm Write a proportion using corresponding sides. Substitute lengths of the sides. Find the cross product. Multiply. Divide each side by 12 to isolate the variable. HG is 3 centimeters.

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° x 6 in Y QR = QS ; X = 18 ; x = 6. 18 = 9; m z=y=m s = 26°. XY YZ 6 12 12

4 -9 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 8 x = 24 Write a proportion using corresponding side lengths. Find the cross products. Multiply. 8 x = 24 Divide each side by 8 to isolate the variable. 8 8 x=3 The base of the inside triangle is 3 inches.

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. 10 = x ; x = 10 92 ≈ 73 92 73 12. 6027; 12. 6 cm

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