To apply the Hypotenuse-Leg (HL) Congruence Theorem, we need to establish that both triangles have a pair of congruent hypotenuses and a pair of congruent legs. In this case:
- The hypotenuses AC and XZ are congruent (as stated in the problem).
- Angle B and angle Y are congruent (as also stated).
Since we already have one pair of congruent hypotenuses, we now need to find a corresponding leg that must also be congruent.
The options presented are:
A. BC ≅ XZ
B. BC ≅ XY
C. AB ≅ XY
D. AB ≅ YZ
Since we want to find a pair of legs congruent to show that the triangles are congruent by the HL theorem, we need the leg opposite to angle B (which is BC) to be congruent to the leg opposite to angle Y (which is XY).
Thus, the correct answer would be:
B. BC ≅ XY
This ensures we have the two congruent properties needed (the hypotenuses and one pair of legs), which confirms ΔABC ≅ ΔXYZ by the HL Congruence Theorem.