There are two possible cases. One where the hypotenuses and one pair of corresponding legs are congruent, and another where both corresponding legs are congruent.
See solution.
Practice makes perfect
To answer the question, we need to consider two cases.
Case 1: The hypotenuses and one pair of corresponding legs are congruent.
Case 2: Both corresponding legs are congruent.
Let's work on each case separately.
Case 1
Let's draw two right triangles such that the hypotenuses and one pair of corresponding legs are congruent.
Let's draw two right triangles such that both corresponding legs are congruent.
As we can see, two sides and the included angle of â–ł ABC are congruent to two sides and the included angle of â–ł PQR. Therefore, by the Side-Angle-Side (SSS) Congruence Postulate we conclude that both right triangles are congruent. Consequently, in any case the answer is Yes, the triangles are congruent.
