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Similar Polygons

J Pavlicek (2005) Edited J Stoops (2007)

Objectives

- Identify similar polygons
- Use similar polygons to solve real-life problems

Def Two polygons are similar if they have the

same shape.

If two polygons are similar, then their vertices

can be paired such that . . . 1.) corresponding

angles are congruent 2.) corresponding sides

are proportional

B

X

ABCD ? WXYZ

A

W

Y

Z

C

D

B

X

A

W

Similarity Statement

ABCD ? WXYZ

Y

Z

C

D

Proportionality Statement

- A ? ? W
- B ? ? X
- C ? ? Y
- D ? ? Z

Example Determine whether the following

polygons are similar.

G

S

14 cm

7 cm

4 cm

8 cm

H

F

10 cm

T

R

20 cm

1.) Are corresponding angles congruent?

2.) Are corresponding sides proportional?

Similarity Statement ?

Def The scale factor of similar polygons is the

ratio of any pair of corresponding sides.

Example What is the scale factor of the above

similar triangles?

Parallelogram ABCD ? Parallelogram GBEF

Example

B E C

60?

12

x?

y

G F

15

A D

24

1.) What is the scale factor of ABCD to GBEF?

2.) Find the values of x and y.

Theorem If two polygons are similar, then the

ratio of their perimeters is equal to

the scale factor.

Suppose the following are similar. Prove the

above theorem.

b

s

r

t

a

c

u

d

NOTE If two polygons are similar, then the

ratio of ANY corresponding lengths is equal to

the scale factor.

Example Quad ABCD ? JKLM. Complete each of the

following.

A

J

12t

28

K

1.) m?M ______ 2.) m?C ______

6

B

M

L

15

70?

C

D

20

3.) The scale factor of JKLM to ABCD is

_____ 4.) BC ______ 5.) JM ______ 6.)

JK ______ 7.) The ratio of the perimeter of

ABCD to the perimeter of JKLM ______

Tell whether the two polygons are sometimes,

always, or never similar.

1.) Two equilateral triangles. 2.) Two

isosceles triangles. 3.) Two squares 4.) Two

scalene triangles. 5.) Two rhombuses. 6.) A

right triangle and an acute triangle. 7.) Two

regular polygons. 8.) An isosceles triangle and

a scalene triangle. 9.) A right triangle and a

scalene triangle. 10.) Trapezoid and a rhombus.

Assignment pg 476 19 42 Quiz tomorrow over

Sections 8.1 and 8.2

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