determine the congruence information that is needed to show that the two triangles are congruent by the HL theorem in two different ways

HL = Hypotenuse & Leg of a right triangle are congruent to another right triangle.

Step-by-step explanation:

To prove a triangle is congruent to another using HL, you must prove that the triangles have a corresponding 90 degree angles, corresponding congruent hypotenuse side lengths, and corresponding congruent hypotenuse legs.