Question

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

Explanation:

Step1: Recall triangle congruence theorems

ASA (Angle - Side - Angle): If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
SAS (Side - Angle - Side): If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
SSS (Side - Side - Side): If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
AAS (Angle - Angle - Side): If two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle, the triangles are congruent.

Step2: Analyze the given triangles

From the image, we can see that there are two angles ($\angle A$ and $\angle D$) and a non - included side (the marked sides) that are equal.

Answer:

AAS (Angle - Angle - Side)