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7-4 Similar Figures 7-4 Similar Figures

7-4 Similar Figures - PowerPoint Presentation

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7-4 Similar Figures - PPT Presentation

Course 1 Warm Up Lesson Presentation Problem of the Day Warm Up Fill in the missing value 1 c 2 qt 2 180 in yd 3 3 tons lb 4 min 2760 s 8 5 6000 ID: 142822

actual similar 100 painting similar actual painting 100 sides find missing continued check length width answer 200 additional write

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Slide1

7-4

Similar Figures

Course 1

Warm Up

Lesson Presentation

Problem of the DaySlide2

Warm Up

Fill in the missing value.

1.

c = 2 qt2. 180 in. = yd

3. 3 tons = lb4. min = 2,760 s

8

5

6,000

46Slide3

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?

576Slide4

Learn

to use proportions to find missing measures in similar figures.Slide5

Vocabulary

corresponding sides

corresponding angles

similarSlide6

Matching sides of two or more polygons are called

corresponding sides,

and matching angles are called corresponding angles.Slide7

Similar Figures

Two figures are similar if

• the measures of the corresponding angles are equal

• the ratios of the lengths of the corresponding sides

t

are proportional

Similar

figures have the same shape but not necessarily the same size.Slide8

Additional Example 1: Finding Missing Measures in Similar Figures

111

y

___

100

200

____

=

Write a proportion using corresponding side lengths.

The cross products are equal.

200 •

111

= 100

y

The two triangles are similar. Find the missing length

y

and the measure of

D

.Slide9

Additional Example 1 Continued

y is multiplied by 100.

22,200

= 100y

22,200

100

______

100

y

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°

The two triangles are similar. Find the missing length

y

and the measure of

D

.Slide10

Check It Out: Example 1

52

y

___

50

100

____

=

Write a proportion using corresponding side lengths.

The cross products are equal.

100 •

52

= 50

y

A

B

60 m

120 m

50 m

100 m

y

52 m

65

°

45

°

The two triangles are similar. Find the missing length

y

and the measure of

B

.Slide11

Check It Out: Example 1 Continued

y is multiplied by 50.

5,200

= 50y

5,200

50

_____

50

y

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°

The two triangles are similar. Find the missing length

y

and the measure of

B

.Slide12

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?

1

Understand the Problem

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.

Additional Example 2:

Problem Solving ApplicationSlide13

Additional Example 2 Continued

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

2

Make a Plan

Reduced

Actual

2

54

3

wSlide14

Additional Example 2 Continued

Solve

3

54 •

3

= 2 • w

162

= 2

w

162

2

____

2

w

2

___

=

81

=

w

The width of the actual painting is 81 cm.

Write a proportion.

The cross products are equal.

w is multiplied by 2.

Divide both sides by 2 to undo the multiplication.

3 cm

w

cm

2 cm

54 cm

_____

=Slide15

Additional Example 2 Continued

Look Back

4

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.Slide16

Check It Out: Example 2

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?

1

Understand the Problem

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.

4 in.

3 in.Slide17

Check It Out: Example 2 Continued

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

2

Make a Plan

Reduced

Actual

3

39

4

wSlide18

Check It Out: Example 2 Continued

Solve

3

4 in

w

in

____

3 in

39 in

_____

=

39 •

4

= 3

w

156

= 3

w

156

3

____

3

w

3

___

=

52

=

w

The width of the actual painting is 52 inches.

Write a proportion.

The cross products are equal.

w is multiplied by 3.

Divide both sides by 3 to undo the multiplication.Slide19

Check It Out: Example 2 Continued

Look Back

4

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.Slide20

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?

36.9°

30 in.

4 in.

90°

12 ft