Geometry

Question Analysis
The problem involves two non-overlapping triangles connected by a transversal. The given information suggests angle-side-angle (ASA) or angle-angle-side (AAS) congruence.

Key Concept Explanation
ASA (Angle-Side-Angle): Two angles and the included side must be congruent.
AAS (Angle-Angle-Side): Two angles and a non-included side must be congruent.
SAS (Side-Angle-Side): Requires two sides and the included angle, which is not given.
SSA (Side-Side-Angle): Not a valid triangle congruence postulate.

Option Analysis
ASA (Angle - Side - Angle): As explained, the side is not the included side for the equal angles, so this option is incorrect.
AAS (Angle - Angle - Side): Meets the requirements as there are two equal angles and a non - included equal side, so this option is correct.
SAS (Side - Angle - Side): Insufficient side - angle - side information as required by the postulate, so this option is incorrect.
SSA (Side - Side - Angle): Not a legitimate congruence postulate for proving triangle congruence in general, so this option is incorrec...