**Theorem 6.12**: (HS) Two right triangles are
congruent if and only if their hypoteneuses and one other side are congruent.

**Proof**: If their hypoteneuses and one other side are congruent, then one could use the Pythagorean Theorem, Theorem 3.4 to conclude that the other sides are also congruent, so the triangles are congruent by SSS Theorem 6.7.

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