Question

which triangle congruence theorem can be used to prove the triangles are congruent?

Explanation:

Step1: Recall triangle congruence theorems

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.
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.
HL (Hypotenuse - Leg): For right - angled triangles, the hypotenuse and one leg of one right - angled triangle are equal to the hypotenuse and one leg of another right - angled triangle.
AAS (Angle - Angle - Side): Two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle.

Step2: Analyze the given triangles

Looking at the triangles, we have two angles and a non - included side. One triangle has two angles and a side, and the other triangle has the corresponding two angles and the corresponding non - included side.

Answer:

AAS.