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

Find the unknown measures in the similar figures.

Example 1:

HB A

CGJ

10 cm

6 cm 11.6 cm

5.8 cmx

5 cm

31°

59°

y

4-9 Using Similar Figures

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

HB A

CGJ

10 cm

6 cm 11.6 cm

5.8 cmx

5 cm

31°

59°

y

4-9 Using Similar Figures

ΔQRS ~ ΔXYZ. Find the unknown measures.

Check It Out: Example 1

Z

Y

y

18 in.

12 in. x

6 in

101°

53° 26° SQ

R

x

101°

4-9 Using Similar Figures

The inside triangle is similar in shape to the outside triangle. Find the length of the base of the inside triangle.

Example 2:

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.

27.2515

= 48.75h

Write a proportion.

Use compatible numbers to estimate.

53

≈ 50h

Simplify.

5h ≈ 150

The traffic light is about 30 feet tall.

27.25 ft

48.75 ft

h ft 2515

≈ 50h

Cross multiply.

h ≈ 30 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 • 427

= x57

; x 42

30; 30 ft= =

4-9 Using Similar Figures

Lesson Quiz: Part I

Find the unknown measures in each pair of similar figures.

1.

2.

x = 120 cmy = 98

t = 150 cms = 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

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

Lesson Quiz for Student Response Systems

4-9 Using Similar Figures

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

Lesson Quiz for Student Response Systems

4-9 Using Similar Figures

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.

Lesson Quiz for Student Response Systems