Question

name the postulate, if possible, that makes the triangles congruent.

Explanation:

Step1: Recall the HL (Hypotenuse - Leg) theorem

The HL theorem states that if the hypotenuse and one leg of a right - triangle are congruent to the hypotenuse and one leg of another right - triangle, then the two right - triangles are congruent.

Step2: Analyze the given triangles

In the first pair of triangles (top - right figure), we have right - triangles (marked with right - angle symbols). One pair of legs is marked as equal (the shorter sides), and the hypotenuses (the longer sides) are also marked as equal.
In the second pair of triangles (bottom - right figure), we have right - triangles (marked with right - angle symbols). One pair of legs is marked as equal, and the hypotenuses are also marked as equal.

Answer:

HL