Question

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

Explanation:

Step1: Recall the HL (Hypotenuse - Leg) theorem

The HL theorem states that if the hypotenuse and one leg of a right - triangle are congruent to the hypotenuse and one leg of another right - triangle, then the two right - triangles are congruent.
The first pair of triangles is a right - triangle pair. Let's assume the hypotenuse and one leg are marked as equal (from the given markings in the first triangle figure).

Step2: Check other congruence theorems for non - right triangles

• For AAS (Angle - Angle - Side): It requires two angles and a non - included side. But we don't have information about angles for a general check here.
• For SAS (Side - Angle - Side): It requires two sides and the included angle. There is no indication of an included angle in the non - right triangle pair.
• For SSA (Side - Side - Angle): SSA is not a valid congruence theorem in general (except for the HL case in right - triangles).

Answer:

HL