Download Similarity Postulates Notes File

Notes: More Similar Triangles
AA
Angle - Angle Similarity
If two angles of one triangle are congruent
to two angles of another triangle, then the triangles are
Similarity
similar.
M
1)
N
45
A
K
2)
3)
60+59=119
180-119=61
C
80
B
Q
60
59
E
J
W
T
51
45
V
YES
80
or
W
NO
YES
_NBM__VWQ_
or
NO
YES
____________
D
or
NO
_ECA__EBD_
and the sides including the angle are proportional, then the
triangles are similar.
Similarity
Q
4)
L
4 = 6
6
9
36 
5)
12 = 8
9
6
72 
N
12
120
N
P
6
9
120
R
L
YES
U
9
6
4
B
R
Side – Side - Side Similarity
In two triangles, if a pair of corresponding angles is congruent
SAS
M
60
S
or
NO
_MNL__ __PRQ___
8
M
T
YES
or
NO
6
_NLM_ _UTS_
S
Side – Side - Side Similarity
SSS
If all three pairs of corresponding sides of two triangles are
proportional, then the two triangles are similar.
Similarity
6)
S
7)
X
3
4 = 5
=
9
12
15

7
10
15
=
=
21
30
45
Q
7
9
4
3
T
U
5
12
W
YES
or
R
10
N
30
P
15
M
V
15
NO
YES
__TSU_ __WXV_

21
O
45
or
NO
_RQP_ __ONM_
EXAMPLES Are the two triangles similar? If so, state how and
write a similarity statement.
8)
9)
L
R
S
10)
5
3
10
6
D
E
6
6
F
G
M
K
3
5
10
6
N
J
T
YES
or
NO
HOW? SAS
JLN
KLM
_________________
Split the two triangles apart.
Since angle L is part of both triangles,
they the have one congruent angles.
Check so see if the sides are congruent
by cross multiplying. They are.
So, the triangles are similar: SAS
H
Q
YES
or
NO
YES
or
NO
HOW? SSS
HOW? SSS
TRS
SQT
_________________
EDG
FHE
_________________
Opposite sides are marked
parallel, so this is a
parallelogram. Therefore,
opposite sides are also
congruent. They share the
center side, so 3 sides are
proportional: SSS
All 3 sets of sides are
proportional, so the triangles
are similar: SSS