1. 4.5 – Prove Triangles Congruent by ASA and AAS
Geometry
Ms. Rinaldi

2. Angle-Side-Angle (ASA) Congruence PostulateB
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 Angle
Side
Angle
Then C A S T R

3. Decide whether the congruence statement is true.
EXAMPLE 1
Use ASA
Decide whether the congruence
statement is true.
Explain your reasoning.
SOLUTION
(A)
(S)
So, by ASA,

4. EXAMPLE 2
Use ASA
Decide whether the congruence
statement is true.
Explain your reasoning.

5. Angle-Angle-Side (AAS) Congruence PostulateB
If two angles and the non-included side of one triangle are congruent to two angles and the non-included side of a second triangle, then the two triangles are congruent.
If Angle
Angle
Side
Then C A S T R

6. Decide whether the congruence statement is true.
EXAMPLE 3
Use AAS
Decide whether the congruence
statement is true.
Explain your reasoning.
SOLUTION
(A)
(S)
So, by AAS,

7. EXAMPLE 4
Use AAS
Decide whether the congruence
statement is true.
Explain your reasoning.

8. State the third congruence that must be given to prove that
EXAMPLE 5
Use ASA or AAS
State the third congruence that must be given to prove that
using the indicated postulate. B E
Given:
Use the ASA Congruence Postulate. C A F D

9. State the third congruence that must be given to prove that
EXAMPLE 6
Use ASA or AAS
State the third congruence that must be given to prove that
using the indicated postulate. B E
Given:
Use the ASA Congruence Postulate. C A F D

10. State the third congruence that must be given to prove that
EXAMPLE 7
Use ASA or AAS
State the third congruence that must be given to prove that
using the indicated postulate. B E
Given:
Use the AAS Congruence Postulate. C A F D