Download Similar Polygons

Similar
Polygons
Section 4-5

A simple, closed figure formed by
three or more line segments is called
a polygon.
A
I
H
B
C
J
L
K

Polygons that have the same shape
are called similar polygons.
B
A
C
D
X
W
Polygon ABCD ~ Polygon WXYZ
Y
Z

The parts of similar figures that “match”
are called corresponding parts.
B
A
C
D
Corresponding Angles
<A -- <W <B -- <X
<C -- <Y
<D -- <Z
X
W
Y
Z
Corresponding Sides
AB – WX
BC – XY
CD – YZ
DA -- ZW

If two polygons are similar, then:
• Their corresponding angles are
congruent, or have the same measure
• Their corresponding sides are
proportional.
A
L
ABC ~
C
B
LMN
N
M

How to identify if polygons are similar:
• Check to see if corresponding angles and
sides are congruent (Use a proportion).
A
L
7
C
AC
LN
7
=
14
7
14
B
5
AB
LM
=
14
N
7
BC
14
MN
10
=
5
10
M

The ratio of lengths of two
corresponding sides of two similar
polygons is called the scale factor.
A
B
E
6
D
C
The scale factor from square
ABCD to square EFGH is 6/3 or 2.
F
3
H
G
The scale factor from square
EFGH to square ABCD is 3/6 or
½.

How to find missing measures
ofA similar Bpolygons:
• Create a proportion andE cross F
10
multiply. 15
D
m
C
H
12
G
The scale factor from square ABCD to square EFGH is FG/BC 10/15 or 2/3.
12
M
=
2
3
12(3) = m(2)
36 = 2m
18 = m