Final answer:
To prove congruence using the HL (Hypotenuse-Leg) criterion, we need to know the lengths of the hypotenuse and one leg of each triangle.
Step-by-step explanation:
To prove that two triangles are congruent using the HL (Hypotenuse-Leg) criterion, we need to know the lengths of the hypotenuse and one leg of each triangle. So, additional information required would be the length of the hypotenuse of one triangle and the length of one of the legs of the same triangle, and the corresponding lengths for the other triangle. Without this information, we cannot determine if the triangles are congruent.