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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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Presentation Transcript
slide1
Exercise

Compare by using >, <, or =.

912

1116

>

slide2
Exercise

Compare by using >, <, or =.

1218

812

=

slide3
Exercise

Compare by using >, <, or =.

1628

1321

<

slide4
Exercise

Solve the proportion.

x15

1612

=

x = 20

slide5
145

45

d = = 2 = 2.8

Exercise

Solve the proportion.

57

2d

=

slide6
Congruent Polygons
  • Congruent polygons are polygons with the same size and shape.
slide7
C
  • F
  • A
  • B
  • D
  • E
slide8
same place in different figures
  • corresponding angles
  • corresponding sides
slide9
Congruent Angles
  • Congruent angles are angles with the same measure.
slide10
Congruent Segments
  • Congruent segments are segments with the same length.
slide12
AD
  • BE
  • CF
  • Corresponding Angles
  • Corresponding angles are congruent (have the same measure).
slide13
C
  • F
  • A
  • B
  • D
  • E
slide14
ACDF
  • ABDE
  • BCEF
  • Corresponding Sides
  • Corresponding sides are congruent (have the same length).
slide15
X

Example 1

RSTXYZ. Complete each statement.

S

Y

R

T

Z

X

R

slide16
Y

Example 1

RSTXYZ. Complete each statement.

S

Y

R

T

Z

X

S

slide17
Z

Example 1

RSTXYZ. Complete each statement.

S

Y

R

T

Z

X

T

slide18
XZ

Example 1

RSTXYZ. Complete each statement.

S

Y

R

T

Z

X

RT

slide19
XY

Example 1

RSTXYZ. Complete each statement.

S

Y

R

T

Z

X

RS

slide20
YZ

Example 1

RSTXYZ. Complete each statement.

S

Y

R

T

Z

X

ST

slide21
Similar Polygons
  • Similar polygons are polygons that have the same shape but not necessarily the same size. The symbol ~ means “is similar to.”
slide22
Theorem
  • If two polygons are similar, then the corresponding angles are congruent and the lengths of the corresponding sides are proportional.
slide23
AD
  • BE
  • CF

B

  • Corresponding Angles

9

6

12

A

C

E

6

4

D

8

F

slide24
ABDE
  • ACDF
  • BCEF

B

  • Corresponding Sides

9

6

12

A

C

E

6

4

D

8

F

slide25
ABDE
  • 6 4
  • 3 2

=

=

  • ACDF
  • 12 8
  • 3 2

=

=

  • BCEF
  • 9 6
  • 3 2

=

=

slide27
Example 2

RST ~ XYZ. Use a proportion to find XY.

Y

S

10

15

9

X

12

Z

18

R

T

slide28
XZRT
  • XYRS

=

  • XY9
  • 2 3

=

  • 3
  • 3
  • 3(XY) = 18

XY = 6

slide29
FD
  • ABFE

=

Example

ABC ~ FED. Complete the ratio.

D

C

8

6

A

F

B

E

AC

slide30
Example

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

D

C

8

6

A

F

B

E

12

slide31
Example

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

slide32
D

C

8

6

A

F

B

E

40

slide33
Example

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

D

C

8

6

A

F

B

E

65°

slide34
Example

Are PQR and JKL similar?

L

Q

8

6

18

J

12

P

12

8

K

no

R

slide35
Example

What length of PQ would make them similar?

L

Q

8

6

18

J

12

P

12

8

K

9

R

slide36
Example

Assume the two parallelograms are similar.

12

B

C

F

G

9

6

A

D

E

FG =

8

slide37
Example

Assume the two parallelograms are similar.

12

B

C

F

G

9

6

A

D

E

AE =

4

slide38
Example

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

12

B

C

F

G

9

6

A

D

E

10

slide39
Example

What is the perimeter of EFGD?

12

B

C

F

G

9

6

A

D

E

28

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