Question

name the postulate, if possible, that makes the triangles congruent.

Explanation:

Step1: Recall triangle congruence postulates

AAS (Angle - Angle - Side) states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, the triangles are congruent. ASA (Angle - Side - Angle) requires two angles and the included side. SSS (Side - Side - Side) is for three sides.

Step2: Analyze the given angles

In the figure, we have two pairs of angles ($\angle H\cong\angle P$ and $\angle T\cong\angle M$) and the vertical angles at $A$ (which are congruent). The sides are not given as equal. But AAS can be applied as we have two angles and a non - included side (the side opposite one of the angles, which is determined by the angle - angle relationship and the vertical angles).

Answer:

A. AAS