Final answer:
To apply the HL congruence theorem to two right triangles, we need information that indicates XWE = XWY, which are angles, confirming the presence of right angles in each triangle.
Step-by-step explanation:
To determine that two triangles are congruent by the Hypotenuse-Leg (HL) congruence theorem, which is applicable only in right triangles, we need to establish that the hypotenuse and one leg of one triangle are respectively equal to the hypotenuse and one leg of another right triangle. In relation to the triangles mentioned, the additional information required would be B) XWE = XWY, assuming that XWE and XWY are angles that indicate the triangles contain right angles, which are essential for applying the HL congruence theorem, and that the legs WX and XY are understood to be congruent based on the figure or given information. None of the other options provided offer relevant information that would directly help us establish congruence by HL.