RHS Congruence

Theorem: 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.

Prerequisites:
Unique RHS triangle (proof)

Proof:

Let there be two right triangles $\triangle ABC$ and $\triangle DEF$ right angled at B and E respectively, such that the side BC $=$ EF, hypotenuse AC $=$ DF.

Since for the given lengths of hypotenuse and a side, a unique right triangle can be formed (see prerequisite), hence both the triangles are congruent.

Q.E.D.


Recommended:
Pythagoras Theorem
SSS congruence
SAS congruence