Short Answer 
The answer explains triangle congruence through three key postulates: SAS, ASA, and SSS. It describes how to apply these criteria to determine congruence among pairs of triangles, highlighting cases of congruence and non-congruence based on side and angle measures.
Step 1: Understanding Congruence Criteria
The concept of triangle congruence is based on specific postulates that determine when two triangles are identical in shape and size. The main postulates are:
- SAS (Side-Angle-Side): Two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
- ASA (Angle-Side-Angle): Two angles and the included side of one triangle are equal to two angles and the included side of another triangle.
- SSS (Side-Side-Side): All three sides of one triangle are equal to all three sides of another triangle.
Step 2: Applying SAS and ASA Postulates
The first pair of triangles are shown to be congruent using the SAS postulate since they have two sides and the included angle equal. In contrast, the second pair of triangles utilizes the ASA postulate, as they exhibit two equal angles and the included side, confirming their congruence.
Step 3: Identifying Non-Congruent and SSS Congruent Figures
The third pair of triangles does not meet any criteria for congruence since they lack the SSA (Side-Side-Angle) rule. In the final figure, the triangles are congruent by the SSS postulate, indicating that all three sides of both triangles are equal, thus establishing their congruence.