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Geometry notes 5.3
Proving Triangles are Congruent: ASA and AAS
Angle-Side-Angle Congruence Postulate (ASA): If two angles and the included side of one
triangle are congruent to two angles and the included side of a second triangle, then the two
triangles are congruent.
If A  A' , and AC  A 'C ' ,
and C  C ' , then
ABC  A ' B 'C ' .
Angle-Angle-Side Congruence Theorem (AAS): If two angles and a non-included side of one
triangle are congruent to two angles and the corresponding non-included side of a second
triangle, then the two triangles are congruent.
If O  A , and W  N ,
and OB  AM , then BOW  MAN .
C
Examples of Using ASA and AAS Congruence:
What additional congruence is needed to show that
A
E
BAE  CDE by the AAS Congruence Theorem?
Decide whether the triangles are congruent:
D
B
Does the diagram give enough information to show that the triangles are congruent? If so
state the postulate or theorem you would use.
a.
b.
C
A
B
A
E
D
B
C
D
c.
B
A
D
C
A
C
Proof:
B
Prove that ABD  EBC .
D
E
Given: BD  BC , AD EC
Prove: ABD  EBC
Statement
Reason_________________________________
1. BD  BC
1. Given
2. AD EC
2. Given
3. D  C
3. Alternate Interior Angles Th.
4. ABD  EBC
4. Vertical Angles Th.
5.
ABD  EBC
5. ASA Congruence Postulate