4.2.2 Triangle Congruence: ASA, AAS, and HL (continued)
In this example it is given that one pair of sides is congruent and that ∠ ACB is a right angle. Since ∠ ACB is a right angle, ∠ ACD is a right angle as well. Therefore, the pair of given congruent sides are the hypotenuses. If one pair of legs can be shown to be congruent, then the HL Theorem can be used to prove that these triangles are congruent. Since the triangles contain a common side, and that side is not the hypotenuse of either triangle, then by the Reflexive Property of Congruence, the triangles contain a pair of congruent legs. So, the triangles are congruent by HL.
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