using similar figures

5-8 Using Similar Figures

Course 2

Warm UpWarm Up

Problem of the DayProblem of the DayLesson PresentationLesson Presentation

Course 2

5-8 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

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

Course 2

5-8 Using Similar Figures

Learn to use similar figures to find unknown lengths.

Course 2

5-8 Using Similar Figures

Vocabularyindirect measurement

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Course 2

5-8 Using Similar Figures

Course 2

5-8 Using Similar Figures

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

Find the unknown length in similar figures.

Additional Example 1: Finding Unknown Lengths in Similar Figures

ACQS

= ABQR Write a proportion using corresponding sides.

1248 = 14

w Substitute lengths of the sides.

12 · w = 48 · 14 Find the cross product.12w = 672 Multiply.12w12

= 67212

w = 56QR is 56 centimeters.

Divide each side by 12 to isolate the variable.

Course 2

5-8 Using Similar Figures

Check It Out: Example 1

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Course 2

5-8 Using Similar Figures

A B

C D

10 cm

12 cm

Q R

S T

24 cm

ACQS

= ABQR Write a proportion using corresponding sides.

1224 = 10

xSubstitute lengths of the sides.

12 · x = 24 · 10 Find the cross product.12x = 240 Multiply.

12x12

= 24012

x = 20QR is 20 centimeters.

Divide each side by 12 to isolate the variable.

Find the unknown length in similar figures.x

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

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Course 2

5-8 Using Similar Figures

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

Check It Out: Example 2The rectangle on the left is similar in shape to the rectangle on the right. Find the width of the right rectangle.

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Course 2

5-8 Using Similar Figures

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.

?

Additional Example 3: Estimating with Indirect Measurement

Course 2

5-8 Using Similar Figures

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.

95 ≈ 49

h Simplify.

9h ≈ 245

The traffic light is about 30 feet tall.

27.25 ft48.75 ft

h ft 2715 ≈ 49

h

Cross multiply.

h ≈ 27 Multiply each side by 9 to isolate the variable.

Check It Out: Example 3

Course 2

5-8 Using Similar Figures

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 ft515 ≈ h

30

30 ≈ 3h Multiply each side by 5 to isolate the variable.

5 ft

Cross multiply.

10 ≈ h

Lesson Quiz: Part IFind the unknown length in each pair of similar figures.

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Course 2

5-8 Using Similar Figures

1.

2.

x = 120 cm

t = 150 cm

Lesson Quiz: Part IIFind the unknown length in each pair of similar figures.

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Course 2

5-8 Using 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.

x = 15 inches