Similar Polygons

What are similar polygons?

Two polygons are similar if corresponding (matching) angles are congruent and the lengths of corresponding sides are proportional.

Angles and Sides in Similar Polygons

Angles

∠A ≅ ∠ E

∠B ≅ ∠ F

∠C ≅ ∠ G

ΔABC ~ ΔEFGA

B C

E

F G

Sides

AB ~ EF

AC ~ EG

BC ~ FG

You can find the missing length of a side in a pair of similar figures, by using

proportions

6 7

ΔRST ~ ΔUVW

R

ST

U

V W

x ft.

6 ft.

35 ft. 7 ft.

35=x x = 30 feet

Solve for x.

x 30

12 in.x in.

40 in. 30 in..

40=12 x = 9 inches

Solve for x. Round to the nearest tenth.

4 x

12 in.

4 in.

20 in.

x in..

20=12 x = 6.7 inches

Solve for x.

7 25

14 m.7 m.

x 25 m.

x=14 x = 50 meters

Solve for x. Round to the nearest tenth.

15 x

17 in.

x

35 in.

15 in.

17=3

5

x = 7.3 inches

15

12

9

6X

W

Z

Y

10

8

6

4Q

P

S

RWhat is the scale factor of the figure?

WX

PQ=

15

10=

3

2

XY

QR=

6

4=

3

2

YZ

RS=

9

6=

3

2

WX

PQ=

15

10=

3

2So, the two figures are similar and the scale factor is 3:2.

Patterns and Sequences

• Can you find the pattern?

• 1, 2, 4, 8, 16, ___

• 4, 8, 12, 16, 20, ____

• 4, 5, 7, 10, _____, _____

Dilations

A dilation is a transformation that

changes the size but not the shape of an

object or figure.

Every dilation has a fixed point that is called

the center of dilation.

DilationsTo dilate an object:

1) Graph object if necessary.

2) Multiply the coordinates of the object by the scale factor.

3) Graph new coordinates.

DilationsExample 1:

Dilations

Dilations

Dilations

DilationsYour turn:

DilationsYour turn:

Homework

• Page 582 14 - 18

• Page 588 14 – 16

• Page 597 12 – 15

Ex. 2: Comparing Similar Polygons

• If XYZW ~ QRSP by a scale factor of 2:1; what is a?

15

12

9

6X

W

Z

Y

10

8

6

4Q

P

S

R

a