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Triangle Congruence
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Congruence in Right Triangles

The conditions for triangle congruence can be used to derive shorter proofs for congruence of right triangles, as stated in the next theorems.

Theorem. Leg-Leg (LL) Congruence Theorem
If the legs of one right triangle are congruent to the corresponding legs of another right triangle, then the two right triangles are congruent.

Given: Right triangles ABC and SRO with right angles B and R, respectively
AB __ SR __
BC ___ RO ___
Prove: ΔABCΔSRO

Proof: