Triangle Congruence Using ASA
Postulate and AAS Theorem
Angle-Side-Angle (ASA) Postulate
If two angles and the included side of
one triangle are congruent to two
angles and the included side of another
triangle, then the two triangles are
congruent.
Angle-Angle-Side (AAS) Theorem
If two angles and a nonincluded side of
one triangle are congruent to two
angles and a nonincluded side of
another triangle, then the two triangles
are congruent.
Angle-Angle-Side (AAS) Theorem
A
D
E
B
C
F
Steps
A  D; C  F
AB  DE
B  E
one triangles are
angles of
triangle, then
are also
ABC  DEF
Reasons
Given
Given
If two angles of
congruent to two
another
the third angles
congruent
ASA Post.
Given:
N  P, MO  QO
M
N
O
Prove:
MON  QOP
P
Q
Given: AE BD, AE  BD, E  D
E
A
D
B
Prove: AEB  BDC
C
Assignment:
Given: FG JH, F  H
F
J
Prove: FGJ  HJG
G
H
Given: 1  2 , DH bisects BDF
D
B
1 2
H
Prove: BDH  FDH
F