4-5 Using Similar Figures

Warm UpWarm Up

Lesson PresentationLesson PresentationProblem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

4-5 Using Similar FiguresWarm UpSolve each proportion.

1. k4

= 7525 2. 6

19= 24x

3.

Triangles JNZ and KOA are similar. Identify the side that corresponds to the given side of the similar triangles.

J

N Z K O

A

JN KO

k = 12 x = 76

4-5 Using Similar Figures

Problem of the DayHarvey starts to fill a 3-gallon tank from a hose that delivers 1 gallon per minute. However, the tanks leaks 1 quart per minute. In how many minutes will the tank begin to overflow?4

4-5 Using Similar Figures

Learn to use similar figures to find unknown lengths.

4-5 Using Similar Figures

Vocabularyindirect measurement

4-5 Using Similar Figures

Indirect measurement is a method of using proportions to find an unknown length or distance in similar figures.

4-5 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 = 6

x Substitute lengths of the sides.

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

10x10

= 3010

x = 3HG is 3 centimeters.

Divide each side by 12 to isolate the variable.

HB A

C GJ

10 cm

6 cm 116 cm5.8 cm x

5 cm

31°

59°

y

4-5 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

C GJ

10 cm

6 cm 116 cm5.8 cm x

5 cm

31°

59°

y

4-5 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 = 9

x Substitute lengths of the sides.

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

14x14

= 6314

x = 4.5HG is 4.5 centimeters.

Divide each side by 12 to isolate the variable.

DB A

C EF

14 cm

9 cm 116 cm5.8 cm x

7 cm

27°

63°

y

4-5 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

C EF

10 cm

6 cm 116 cm5.8 cm x

5 cm

27°

63°

y

4-5 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 =12

x8 · x = 2 · 12

8x = 248x8

= 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

4-5 Using Similar FiguresCheck 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 cm6 cm 12 cm

Let w = the width of the right rectangle.612

= 3w

6 ·w = 12 · 36w = 366w6

= 366

w = 6The 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.

?

4-5 Using Similar FiguresAdditional 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 = 48.75

hWrite a proportion.

Use compatible numbers to estimate.

53 ≈ 50

h Simplify.

5h ≈ 150

The traffic light is about 30 feet tall.

27.25 ft48.75 ft

h ft 2515 ≈50

h

Cross multiply.

h ≈ 30 Divide each side by 5 to isolate the variable.

4-5 Using Similar FiguresCheck It Out: Example 3

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

514.75 = h

30.25 Write a proportion.

Use compatible numbers to estimate.

13 ≈ h

30 Simplify.

1 • 30 ≈ 3 • h

The outside triangle is about 10 feet tall.

14.75 ft30.25 ft

h ft5

15 ≈ h30

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

5 ft

Cross multiply.

10 ≈ h

4-5 Using Similar Figures

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

4-5 Using Similar FiguresLesson Quiz: Part I

Find the unknown length in each pair of similar figures.

1.

2.

x = 120 cmy = 98◦

t = 150 cms = 120◦

33°49°

98° y

s

19°

120° 41°

4-5 Using Similar FiguresLesson Quiz: Part II

Find the unknown length in each pair of similar figures.

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

4-5 Using Similar Figures

1. Identify the unknown length in the given pair of similar figures.

A. x = 174 cmB. x = 182 cmC. x = 196 cmD. x = 204 cm

Lesson Quiz for Student Response Systems

4-5 Using Similar Figures

2. Identify the unknown length in the given pair of similar figures.

A. t = 166 cmB. t = 198 cmC. t = 206 cmD. t = 248 cm

Lesson Quiz for Student Response Systems

4-5 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