Question

which postulate would prove these two triangles are congruent?asa aas neither

Explanation:

1. First, identify the given parts: Both triangles are right - angled (so one right angle is equal, $\angle = 90^{\circ}$). The vertical angles formed by the intersecting lines are equal (vertical angles theorem). Also, there is a pair of marked (congruent) sides.
2. For triangle congruence:

• AAS (Angle - Angle - Side) postulate states that if two angles and a non - included side of one triangle are congruent to the corresponding two angles and non - included side of another triangle, then the triangles are congruent.
• Here, we have two angles (the right angle and the vertical angle) and a non - included side (the marked side) that are congruent between the two triangles. So the AAS postulate can be used to prove the triangles are congruent.

Answer:

AAS