Which postulate guarantees congruence of two right triangles when the hypotenuse and a corresponding leg are congruent?

• A. HL Congruence
• B. CPCTC
• C. AA Similarity
• D. SAS for Similarity

Answer: (A)

In right triangles, knowing the hypotenuse and one corresponding leg fixes the shape and size of the triangle. The Hypotenuse-Leg congruence postulate says that if two right triangles have their hypotenuses congruent and the leg that corresponds to that hypotenuse also congruent, then the two triangles are congruent. The right angle provides a fixed orientation, so those two sides determine the entire triangle, leaving no room for a different configuration of the remaining side. Once congruence is established this way, all other parts match as well (that last bit is the CPCTC consequence of having congruent triangles). The other options deal with similarity or with consequences of congruence, not with a criterion that guarantees congruence for right triangles in this specific setup.