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# Exercise PowerPoint PPT Presentation

Exercise. Compare by using >, <, or =. 9 12. 11 16. >. Exercise. Compare by using >, <, or =. 12 18. 8 12. =. Exercise. Compare by using >, <, or =. 1628. 13 21. <. Exercise. Solve the proportion. x 15. 16 12. =. x = 20. 14 5. 4 5. d = = 2 = 2.8. Exercise.

Exercise

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Exercise

Compare by using >, <, or =.

912

1116

>

Exercise

Compare by using >, <, or =.

1218

812

=

Exercise

Compare by using >, <, or =.

1628

1321

<

Exercise

Solve the proportion.

x15

1612

=

x = 20

145

45

d = = 2 = 2.8

Exercise

Solve the proportion.

57

2d

=

Congruent Polygons

• Congruent polygons are polygons with the same size and shape.

• C

• F

• A

• B

• D

• E

• same place in different figures

• corresponding angles

• corresponding sides

Congruent Angles

• Congruent angles are angles with the same measure.

Congruent Segments

• Congruent segments are segments with the same length.

• congruence symbol

• BE

• CF

• Corresponding Angles

• Corresponding angles are congruent (have the same measure).

• C

• F

• A

• B

• D

• E

• ACDF

• ABDE

• BCEF

• Corresponding Sides

• Corresponding sides are congruent (have the same length).

X

Example 1

RSTXYZ. Complete each statement.

S

Y

R

T

Z

X

R

Y

Example 1

RSTXYZ. Complete each statement.

S

Y

R

T

Z

X

S

Z

Example 1

RSTXYZ. Complete each statement.

S

Y

R

T

Z

X

T

XZ

Example 1

RSTXYZ. Complete each statement.

S

Y

R

T

Z

X

RT

XY

Example 1

RSTXYZ. Complete each statement.

S

Y

R

T

Z

X

RS

YZ

Example 1

RSTXYZ. Complete each statement.

S

Y

R

T

Z

X

ST

Similar Polygons

• Similar polygons are polygons that have the same shape but not necessarily the same size. The symbol ~ means “is similar to.”

Theorem

• If two polygons are similar, then the corresponding angles are congruent and the lengths of the corresponding sides are proportional.

• BE

• CF

B

• Corresponding Angles

9

6

12

A

C

E

6

4

D

8

F

• ABDE

• ACDF

• BCEF

B

• Corresponding Sides

9

6

12

A

C

E

6

4

D

8

F

• ABDE

• 6 4

• 3 2

=

=

• ACDF

• 12 8

• 3 2

=

=

• BCEF

• 9 6

• 3 2

=

=

• scale factor—ratio of corresponding dimensions in similar figures

Example 2

RST ~ XYZ. Use a proportion to find XY.

Y

S

10

15

9

X

12

Z

18

R

T

• XZRT

• XYRS

=

• XY9

• 2 3

=

• 3

• 3

• 3(XY) = 18

XY = 6

• FD

• ABFE

=

Example

ABC ~ FED. Complete the ratio.

D

C

8

6

A

F

B

E

AC

Example

ABC ~ FED. If BC = 9, what is ED?

D

C

8

6

A

F

B

E

12

Example

ABC ~ FED. If the perimeter of ABC is 30, what is the perimeter of FED?

D

C

8

6

A

F

B

E

40

Example

ABC ~ FED. If mA = 85° and m E = 30°, what is the mC?

D

C

8

6

A

F

B

E

65°

Example

Are PQR and JKL similar?

L

Q

8

6

18

J

12

P

12

8

K

no

R

Example

What length of PQ would make them similar?

L

Q

8

6

18

J

12

P

12

8

K

9

R

Example

Assume the two parallelograms are similar.

12

B

C

F

G

9

6

A

D

E

FG =

8

Example

Assume the two parallelograms are similar.

12

B

C

F

G

9

6

A

D

E

AE =

4

Example

If the diagonal AC = 15, what is the length of EG?

12

B

C

F

G

9

6

A

D

E

10

Example

What is the perimeter of EFGD?

12

B

C

F

G

9

6

A

D

E

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