Section 7.3 – Similar Figures
Similar Polygons –
Two polygons are similar if their
vertices can be paired so that:
1. Corresponding angles are congruent.
2. Corresponding sides are in proportion.
(lengths have same ratio)
Symbol for Similar: ~
7.3 – Similar Figures
Example:
S
Y
Z
T
R
P
Therefore –
Q
X
V
W
Pent. TSRQP ~
Pent. ZYXWV
V
Z
Y
1. P @ T
@ S
@ 
X
W
R @ Q
@ 
2. PQ  QR  RS  ST  TP
YZ
ZV
VW WX XY
7.3 – Similar Figures
When two polygons are similar,
then the ratio of the lengths
of two corresponding sides is
called the Scale Factor.
7.3 – Similar Figures
Example 1: A
DABC ~ DJKL
J
7
21
18
K
21 3

7
1
18 3

6 1
6
4
L
12 3

4 1
C
12
To determine the scale factor – match up the lengths
of the corresponding sides. Reduce ratios.
B
Scale factor of DABC to DJKL is 3 to 1.
ORDER MATTERS!
7.3 – Similar Figures
Example 2:
D
C
20
10
8
A
x
B
H
G
30
y
z
E
Quad. ABCD
______ ~ Quad. EFGH
______
92
1. If mD = 92, then mH = ____.
60
2. If mC = 60, then mG = ____.
F
7.3 – Similar Figures
Example 2: Once you determine the scale factor, you
can calculate the lengths of all of the sides of the
G
similar figures.
30
C
20
D
10
8
A
x
B
H
y
z
E
21
F
Scale factor of ABCD to EFGH is 2 to 3.
7.3 – Similar Figures
Example 2 continued:
C
20
D
Use the scale factor of 2 to 3 to
set up proportions.
G
30
H
10
8
A
2 x

3 21
2 10

3 y
2 8

3 z
x
B
y
z
42 = 3x; x = 14
30 = 2y; y= 15
24 = 2z; z = 12
E
21
F
14
x = _____
15
y = _____
12
z = _____
Example 3 – Find the missing side lengths and angle measures.
A
35z
5
15
122
x
B
DABC ~ DFDE
C
23
D
y
F
122
z 35
9
Scale Factor: 15 to 9 = 5 to 3
5 x
x: 3  6
y: 5  5
3 y
30  3x
x = 10
5y  15
y=3
6
23
E
Example 4: Name all of the pairs of congruent angles.
J
JIK @ JHL; JKI @ JLH
a. DIKJ ~
6
DHLJ
I
b. Find x.
12 3
 ; x  32
x 8
c. Find y.
y
H
6 3 9
6
; y  10
12
3

8 y6
12
9
K
15
x
6+y
L
8
x
24