Which method is used to prove right triangles congruent?

The Hypotenuse-Leg (HL) method is specifically designed to prove the congruence of right triangles. In a right triangle, the hypotenuse is the longest side opposite the right angle, and the leg refers to one of the two shorter sides. For two right triangles to be considered congruent using the HL criterion, one must demonstrate that the lengths of their hypotenuses are equal, as well as the lengths of one corresponding leg of each triangle. This method is unique to right triangles because the presence of the right angle guarantees that the angle measures have specific relationships, allowing for this streamlined approach to proving congruence.

The other methods listed, such as the Angle-Angle (AA) criterion, Side-Angle-Side (SAS) criterion, and Side-Side-Side (SSS) criterion, apply more broadly to various types of triangles but do not incorporate the specific properties unique to right triangles. The HL method takes advantage of the right angle's properties, thus making it the correct choice for proving the congruence of right triangles.