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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.

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Exercise

Exercise

Compare by using >, <, or =.

912

1116

>


Exercise

Exercise

Compare by using >, <, or =.

1218

812

=


Exercise

Exercise

Compare by using >, <, or =.

1628

1321

<


Exercise

Exercise

Solve the proportion.

x15

1612

=

x = 20


Exercise

145

45

d = = 2 = 2.8

Exercise

Solve the proportion.

57

2d

=


Exercise

Congruent Polygons

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


Exercise

  • C

  • F

  • A

  • B

  • D

  • E


Exercise

  • same place in different figures

  • corresponding angles

  • corresponding sides


Exercise

Congruent Angles

  • Congruent angles are angles with the same measure.


Exercise

Congruent Segments

  • Congruent segments are segments with the same length.


Exercise

  • congruence symbol


Exercise

  • AD

  • BE

  • CF

  • Corresponding Angles

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


Exercise

  • C

  • F

  • A

  • B

  • D

  • E


Exercise

  • ACDF

  • ABDE

  • BCEF

  • Corresponding Sides

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


Exercise

X

Example 1

RSTXYZ. Complete each statement.

S

Y

R

T

Z

X

R


Exercise

Y

Example 1

RSTXYZ. Complete each statement.

S

Y

R

T

Z

X

S


Exercise

Z

Example 1

RSTXYZ. Complete each statement.

S

Y

R

T

Z

X

T


Exercise

XZ

Example 1

RSTXYZ. Complete each statement.

S

Y

R

T

Z

X

RT


Exercise

XY

Example 1

RSTXYZ. Complete each statement.

S

Y

R

T

Z

X

RS


Exercise

YZ

Example 1

RSTXYZ. Complete each statement.

S

Y

R

T

Z

X

ST


Exercise

Similar Polygons

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


Exercise

Theorem

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


Exercise

  • AD

  • BE

  • CF

B

  • Corresponding Angles

9

6

12

A

C

E

6

4

D

8

F


Exercise

  • ABDE

  • ACDF

  • BCEF

B

  • Corresponding Sides

9

6

12

A

C

E

6

4

D

8

F


Exercise

  • ABDE

  • 6 4

  • 3 2

=

=

  • ACDF

  • 12 8

  • 3 2

=

=

  • BCEF

  • 9 6

  • 3 2

=

=


Exercise

  • scale factor—ratio of corresponding dimensions in similar figures


Exercise

Example 2

RST ~ XYZ. Use a proportion to find XY.

Y

S

10

15

9

X

12

Z

18

R

T


Exercise

  • XZRT

  • XYRS

=

  • XY9

  • 2 3

=

  • 3

  • 3

  • 3(XY) = 18

XY = 6


Exercise

  • FD

  • ABFE

=

Example

ABC ~ FED. Complete the ratio.

D

C

8

6

A

F

B

E

AC


Exercise

Example

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

D

C

8

6

A

F

B

E

12


Exercise

Example

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


Exercise

D

C

8

6

A

F

B

E

40


Exercise

Example

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

D

C

8

6

A

F

B

E

65°


Exercise

Example

Are PQR and JKL similar?

L

Q

8

6

18

J

12

P

12

8

K

no

R


Exercise

Example

What length of PQ would make them similar?

L

Q

8

6

18

J

12

P

12

8

K

9

R


Exercise

Example

Assume the two parallelograms are similar.

12

B

C

F

G

9

6

A

D

E

FG =

8


Exercise

Example

Assume the two parallelograms are similar.

12

B

C

F

G

9

6

A

D

E

AE =

4


Exercise

Example

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

12

B

C

F

G

9

6

A

D

E

10


Exercise

Example

What is the perimeter of EFGD?

12

B

C

F

G

9

6

A

D

E

28


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