8.3

1
8.3 Similar Polygons

• Two polygons are similar if
• -their corresponding angles are congruent
• -their corresponding sides are proportional
• similar to

R
U
I
L
P
S
A
G
2
Angles are Congruent Sides are Proportional

• ltA ltG
• ltP ltS
• ltI ltR
• ltL ltU

R
U
I
L
P
S
A
G
PILASRUG
3

• Are the two triangles similar?
• If so, write the similarity statement.

R
I
5
3
30º
10
8
S
P
4
60º
G
U
6
SIPRGU
4

• Scale Factor the common ratio of the
  corresponding sides of similar polygons

R
I
5
3
30º
10
8
S
P
4
60º
Find the scale factor of PSI to URG
G
U
6
½
5

• Are the two triangles similar?
• If so, what is the scale factor?

12
8
Not similar!
50º
6
6

• Given that PILASRUG, determine the values of a,
  b, x and y.

X 4 Y 3
a 60º b 20º
9
R
U
3
I
L
20º
bº
y
1
P
x
S
12
60º
2
6
A
aº
G
7

• ABC and ABD are both isosceles triangles with AB
  AC and AD BD.
• Are the corresponding angles congruent?
• Write a similarity statement.

A
70
B
D
C
8

• Given that QP // ON, Prove that the triangles are
  similar.

-Because QP // ON, there are 2 sets of
corresponding angles. -The triangles share the
third angle at M, so corresponding angles are
congruent - Since ,
corresponding sides are proportional!
Q
6
12
O
4
3
70
M
P
4
N
2
9

• The figures are both squares. Are they similar?

4 to 7
What is the scale factor?
What is the ratio of their perimeters?
Find the perimeter of ABCD
8
8/14 4/7
Find the perimeter of EFGH
14
E
F
2
B
A
D
C
H
G
7/2
10

• So
• Theorem 8.1 If two polygons are similar, then
  the ratio of their perimeters is equal to the
  ratio of their corresponding sides.

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