Transcript 8.3 – Similar Polygons

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
Angles are Congruent
<A
<P
<I
<L




<G
<S
<R
<U
Sides are Proportional
PI
IL
LA PA



SR RU UG SG
I
P
A
PILA~SRUG
R
L
U
S
G
Are the two triangles similar?
If so, write the similarity statement.
R
I
5
3
P
4
30º
10
S
G
SIP~RGU
60º
6
8
U
Scale Factor – the common ratio of the
corresponding sides of similar polygons
R
I
5
3
P
4
30º
S
Find the scale factor of
PSI to URG
½
10
G
60º
6
8
U
Are the two triangles similar?
If so, what is the scale factor?
8
4
40º
5
Not similar!
12
50º
6
8
Given that PILA~SRUG, determine the
values of a, b, x and y.
a= 60º
X=4
b = 20º
Y=3
3
I
bº
1
P
2
60º
A
x
L
R
9
y
20º
12
S
6
aº
G
U
ABC and ABD are both isosceles triangles
with AB = AC and AD = BD.
1) Are the corresponding angles congruent?
2) Write a similarity statement.
A
B
70°
C
D
Given that QP // ON, Prove that the
triangles are similar.
-Because QP // ON, there are 2 sets of
corresponding angles.
Q
-The triangles share the third angle at M, so
corresponding angles are congruent
6
12
O
3
3 2 4
 
9 6 12
- Since
are proportional!
4
M 70°
2
N
4
P
, corresponding sides
The figures are both squares. Are they similar?
4 to 7
What is the scale factor?
Find the perimeter of ABCD 8
What is the ratio of
their perimeters?
8/14 = 4/7
Find the perimeter of EFGH 14
E
A
D
2
F
B
C
H
7/2
G
So…
Theorem 8.1 – If two polygons are similar,
then the ratio of their perimeters is equal
to the ratio of their corresponding sides.