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7-4. Similar Figures. Course 1. Warm Up. Problem of the Day. Lesson Presentation. Warm Up Fill in the missing value. 1. c = 2 qt 2. 180 in. = yd 3. 3 tons = lb 4. min = 2,760 s. 8. 5. 6,000. 46. Problem of the Day

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7 4

7-4

Similar Figures

Course 1

Warm Up

Problem of the Day

Lesson Presentation


7 4

Warm Up

Fill in the missing value.

1. c = 2 qt

2. 180 in. = yd

3. 3 tons = lb

4. min = 2,760 s

8

5

6,000

46


7 4

Problem of the Day

How many 8 in. by 10 in. rectangular tiles would be needed to cover a 16 ft by 20 ft floor?

576


7 4

Learn to use proportions to find missing measures in similar figures.


7 4

Vocabulary

corresponding sides

corresponding angles

similar


7 4

Matching sides of two or more polygons are called corresponding sides, and matching angles are called corresponding angles.


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Similar figures have the same shape but not necessarily the same size.


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The two triangles are similar. Find the missing length y and the measure of D.

111

100

___

____

y

200

Additional Example 1: Finding Missing Measures in Similar Figures

Write a proportion using corresponding side lengths.

=

200 • 111= 100 •y

The cross products are equal.


7 4

The two triangles are similar. Find the missing length y and the measure of D.

22,200

100y

______

____

100

100

Additional Example 1 Continued

22,200= 100y

y is multiplied by 100.

Divide both sides by 100 to undo the multiplication.

=

222 mm= y

Angle D is congruent to angle C, and m C = 70°.

m D = 70°


7 4

52

50

___

____

y

100

Check It Out: Example 1

The two triangles are similar. Find the missing length y and the measure of B.

B

A

60 m

120 m

65°

50 m

100 m

52 m

45°

y

Write a proportion using corresponding side lengths.

=

100 • 52= 50 •y

The cross products are equal.


7 4

5,200

50y

_____

___

50

50

Check It Out: Example 1 Continued

The two triangles are similar. Find the missing length y and the measure of B.

5,200= 50y

y is multiplied by 50.

Divide both sides by 50 to undo the multiplication.

=

104 m= y

Angle B is congruent to angle A, and m A = 65°.

m B = 65°


7 4

1

Understand the Problem

Additional Example 2: Problem Solving Application

This reduction is similar to a picture that Katie painted. The height of the actual painting is 54 centimeters. What is the width of the actual painting?

  • The answer will be the width of the actual painting.

  • List the important information:

  • The actual painting and the reduction above are t similar.

  • The reduced painting is 2 cm tall and 3 cm wide.

  • The actual painting is 54 cm tall.


7 4

Make a Plan

2

Additional Example 2 Continued

Draw a diagram to represent the situation. Use the corresponding sides to write a proportion.

Actual

Reduced

2

54

3

w


7 4

3

Solve

3 cm

=

w cm

2 cm

162

2w

____

___

_____

2

54 cm

2

Additional Example 2 Continued

Write a proportion.

54 • 3= 2 •w

The cross products are equal.

w is multiplied by 2.

162= 2w

Divide both sides by 2 to undo the multiplication.

=

81= w

The width of the actual painting is 81 cm.


7 4

Look Back

4

Additional Example 2 Continued

Estimate to check your answer. The ratio of the heights is about 2:50 or 1:25. The ratio of the widths is about 3:90, or 1:30. Since these ratios are close to each other, 81 cm is a reasonable answer.


7 4

1

Understand the Problem

Check It Out: Example 2

4 in.

This reduction is similar to a picture that Marty designed. The height of the actual picture is 39 inches. What is the width of the actual picture?

3 in.

  • The answer will be the width of the actual painting.

  • List the important information:

  • The actual painting and the reduction above are t similar.

  • The reduced painting is 3 in. tall and 4 in. wide.

  • The actual painting is 39 in. tall.


7 4

Make a Plan

2

Check It Out: Example 2 Continued

Draw a diagram to represent the situation. Use the corresponding sides to write a proportion.

Actual

Reduced

3

39

4

w


7 4

3

Solve

156

4 in

3 in

3w

____

_____

___

____

3

3

w in

39 in

Check It Out: Example 2 Continued

=

Write a proportion.

39 • 4= 3 •w

The cross products are equal.

w is multiplied by 3.

156= 3w

Divide both sides by 3 to undo the multiplication.

=

52= w

The width of the actual painting is 52 inches.


7 4

Look Back

4

Check It Out: Example 2 Continued

Estimate to check your answer. The ratio of the heights is about 4:40, or 1:10. The ratio of the widths is about 5:50, or 1:10. Since these ratios are the same, 52 inches is a reasonable answer.


7 4

Lesson Quiz

These two triangles are similar.

1. Find the missing length x.

2. Find the measure of J.

3. Find the missing length y.

4. Find the measure of P.

5.Susan is making a wood deck from plans for an 8 ft by 10 ft deck. However, she is going to increase its size proportionally. If the length is to be 15 ft, what will the width be?

30 in.

36.9°

4 in.

90°

12 ft


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