From Wikipedia:

RHS (Right-angle-Hypotenuse-Side), also known as HL (Hypotenuse-Leg): If two right-angled triangles have their hypotenuses equal in length, and a pair of shorter sides are equal in length, then the triangles are congruent.

I can’t picture why a right angle is needed. To me:

Given two triangles with congruent hypotenuses. If the angle opposite this hypotenuse is congruent then so are the triangles. The angle shouldn’t have to be a right angle.

What am I missing?