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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

- AD

- 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.

- AD

- 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

28