What is the hypotenuse-leg theorem?
The Hypotenuse-Leg Theorem states that if the leg and hypotenuse of one triangle is equal to the leg and hypotenuse of another triangle, then they are congruent.
For example, if I had one triangle with a leg of 3 and a hypotenuse of 5, I'd need another triangle with a leg of 3 and a hypotenuse of 5 to be congruent.
This theorem is similar to the other theorems used to prove triangles congruent, like Side-Angle-Side, [SAS] Side-Side-Angle [SSA], Side-Side-Side [SSS], Angle-Side-Angle [ASA], Angle-Angle-Side [AAS], Angle-Angle-Angle [AAA].
Source and for more info:
My Geometry notes