
There are 3 ways to show two triangles
are similar to each other. Those 3 ways
are:
1. Angle-Angle Similarity Postulate. (AA~)
2. Side-Angle-Side Similarity Theorem. (SAS~)
3. Side-Side-Side Similarity Theorem. (SSS~)
Postulate
If two angles of
one triangle are
congruent to two
angles of another
triangle, then the
triangles are
similar.
If
S  M and R  L
R
L
M
S
T
Then
SRT ~ MLP
P
Theorem
If
If an angle of one
triangle is
congruent to an
angle of a second
triangle, and the
sides that include
the two angles are
proportional, then
the triangles are
similar.
RS RT

and R  L
LM LP
R
L
M
S
T
Then
SRT ~ MLP
P
Theorem
If
If corresponding
sides of two
triangles are
proportional, then
the triangles are
similar.
RS RT ST

=
LM LP MP
R
L
M
S
T
Then
SRT ~ MLP
P

Are the two triangles similar, how do you
know?
180  (90  59)  31
31°
59°
The two triangles
are similar by the
AA~ postulate.
Find the 3rd angle
in one of the
triangles to see if it
is congruent to the
other triangle.

Are the two triangles similar, how do you
know? H
10
K
6
I
8
GH 10 2


LJ 15 3
9
G
HI 6 2
 
JK 9 3
12
15
J
IG 8 2


KL 12 3
L
Find the
corresponding sides
and set up an
extended proportion.
The two triangles
are similar by the
SSS~ theorem.

Are the two triangles similar, how do you
know?
O
N
2
Both triangles share
angle M, so check the
ratios of the sides that
include angle M.
8
M
12
MN 8 4


MO 10 5
Q 3
P
MQ 12 4


MP 15 5
The two triangles
are Similar by the
SAS~ theorem.

P. 455 #’s 7-12, 15-20, 23-26, 37-44