(aa, sss, sas). aa similarity (angle-angle) if 2 angles of one triangle are congruent to 2 angles of...
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(AA, SSS, SAS)
AA Similarity (Angle-Angle)
A D
If 2 angles of one triangle are congruent to 2 angles of another triangle, then the triangles are similar.
E
DA
B
CF
B EABC ~ DEFConclusion:
andGiven:
SSS Similarity (Side-Side-Side)
If the measures of the corresponding sides of 2 triangles are proportional, then the triangles are similar.
E
DA
B
CF
Given:
Conclusion:
5
11 22
8 1610
BC
EF
AB
DEAC
DF
8
16
5
10
11
22
ABC ~ DEF
SAS Similarity (Side-Angle-Side)
ABC ~ DEF
If the measures of 2 sides of a triangle are proportional to the measures of 2 corresponding sides of another triangle and the angles
between them are congruent, then the triangles are similar.
Given:
Conclusion:
E
DA
B
CF
5
11 22
10
AB ACA D and
DE DF
CD
E
G
F
Example: Show that the two triangles are similar.
E
DF
G H44
44
1.
2.
Example: Which triangle is similar to triangle XYZ?
P
X
T
SU
R
Q
Y
Z
35
30
21
21
42
35
2015
30
Example:
Find the value of x that makes triangle XYZ similar to triangle PQR
20
Y
X
21
3(x - 2)
x+6
12
30
Z
R
Q
P