4-9 Using Similar Figures

Lesson PresentationLesson Presentation

4-9 Using Similar Figures

MA.7.A.1.3 Solve problems involving similar figures.Also MA.7.A.1.1.

Sunshine State Standards

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

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 116 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 116 cm

5.8 cmx

5 cm

31°

59°

y

4-9 Using Similar Figures

Find the unknown measures in the similar figures.

Check It Out: Example 1

ABFE

= BCDE Write a proportion using corresponding sides.

147

= 9x

Substitute lengths of the sides.

14 · x = 9 · 7 Find the cross product.14x = 63 Multiply.

14x14

= 6314

x = 4.5

HG is 4.5 centimeters.

Divide each side by 12 to isolate the variable.

DB A

CEF

14 cm

9 cm 116 cm

5.8 cmx

7 cm

27°

63°

y

4-9 Using Similar Figures

Find the unknown measures in the similar figures.

Check It Out: Example 1 Continued

Step 2 Find y.

Corresponding angles of similar triangles have equal angle measures.

D corresponds to C

y = 63

DB A

CEF

10 cm

6 cm 116 cm

5.8 cmx

5 cm

27°

63°

y

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.

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

4-9 Using Similar Figures

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 cm12 cm

Let w = the width of the right rectangle.

612

= 3w

6 ·w = 12 · 3

6w = 36

6w6

= 366

w = 6

The right rectangle is 6 cm wide.

Write a proportion using correspondingside lengths.

Find the cross products.Multiply.

Divide each side by 6 to isolate the variable.

?

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

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

514.75

= h30.25

Write a proportion.

Use compatible numbers to estimate.

13

≈ h30

Simplify.

1 • 30 ≈ 3 • h

The outside triangle is about 10 feet tall.

14.75 ft

30.25 ft

h ft

515

≈ h30

30 ≈ 3h Divide each side by 3 to isolate the variable.

5 ft

Cross multiply.

10 ≈ h