Two sides and the non-included right angle of one right triangle are congruent to the corresponding parts of another right triangle. Which congruence theorem can be used to prove that the triangles are congruent?

The correct congruence theorem to use in this case is HL, which stands for Hypotenuse-Leg.

In this situation, you have two right triangles where two sides (the legs) and the non-included right angle (which is right angle in both triangles) are congruent. According to the HL theorem, if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

So, the answer is HL.