In triangle congruence, the HL criterion specifies congruence based on which parts of a right-angled triangle?

• A. Height and base
• B. A leg and the base
• C. Hypotenuse and a leg
• D. Hypotenuse and an angle

Answer: (C)

In the HL criterion for right triangles, two corresponding parts determine the triangles: the hypotenuse and one leg. Knowing the length of the hypotenuse and one leg fixes the entire shape of a right triangle, so if another right triangle has the same hypotenuse length and the same-length corresponding leg, all three sides and all three angles match, making the triangles congruent.

The other options don’t fit because they rely on a altitude or an angle rather than the two sides that uniquely determine a right triangle. A height and base isn’t about the triangle’s sides in this congruence context, pairing a leg with a base doesn’t ensure the hypotenuse matches, and a hypotenuse with an angle doesn’t fix the triangle’s size uniquely.