4-9 using similar figures vocabulary indirect measurement

4-9 Using Similar Figures

Vocabulary

indirect measurement


Indirect measurement is 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

ABJG

= BCHG Write a proportion using corresponding sides.

105

= 6x

Substitute lengths of the sides.

10 · x = 5 · 6 Find the cross product.10x = 30 Multiply.

10x10

= 3010

x = 3

HG is 3 centimeters.

Divide each side by 12 to isolate the variable.

HB A

CGJ

10 cm

6 cm 11.6 cm

5.8 cmx

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

HB A

CGJ

10 cm

6 cm 11.6 cm

5.8 cmx

5 cm

31°

59°

y


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°

QRXY

= QSYZ

=X6

1812

6 . 18 12

; ; x= =9; mz=y=ms = 26°.


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.

82

=12x

8 · x = 2 · 128x = 24

8x8

= 248

x = 3The base of the inside triangle is 3 inches.

Write a proportion using corresponding sidelengths.

Find the cross products.Multiply.

Divide each side by 8 to isolate the variable.

Additional Example 2: Measurement Application



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.

1073

= x 92

=; x 10 92 73

≈ 12.6027; 12.6 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.

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.



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= =


Lesson Quiz: Part I

Find the unknown measures in each pair of similar figures.

1.

2.

x = 120 cmy = 98

t = 150 cms = 120


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 vocabulary indirect measurement

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