Short Answer 
The ASA congruence postulate states that two triangles are congruent if two angles and the included side of one triangle match the corresponding parts of another triangle. Similarly, the AAS congruence postulate requires that two angles and a non-included side be congruent for triangle congruence. To verify congruence using these postulates, check for congruent angles and appropriate side lengths.
Step 1: Understand ASA Congruence Postulate
The ASA congruence postulate stands for Angle-Side-Angle. This means that if you have two triangles, and you find that two angles and the included side of one triangle are congruent to the corresponding angles and side of another triangle, then those triangles are deemed congruent. For example, if you have triangles where angles C and Q are congruent, and the sides BC and PQ are equal, then you can verify their congruence through this method.
Step 2: Comprehend AAS Congruence Postulate
The AAS congruence postulate stands for Angle-Angle-Side. This postulate indicates that if two angles and an associated non-included side of one triangle match the two angles and side of another triangle, then these triangles are also congruent. For instance, if angles A and T are congruent, and their sides AC and TQ are equal, then the triangles meet the criteria for congruence under this postulate.
Step 3: Apply the Congruence Postulates
To utilize the congruence postulates effectively, you need to check for congruency in angles and sides as stated in both ASA and AAS. Here’s a quick checklist for verification:
- Ensure two angles are congruent in both triangles.
- Confirm the included or non-included sides are of equal length.
- Conclude that if conditions are satisfied, the triangles are congruent.