To show that triangles ΔABC and ΔXYZ are congruent by the Hypotenuse-Leg (HL) Congruence Theorem, we need to confirm that two corresponding parts of the triangles are congruent. Since we know that the hypotenuses AC and XZ are congruent, and that angles B and Y are congruent (which are the right angles in each triangle), we only need to show that one leg from each triangle is also congruent.
Given the options provided:
- BC ≅ XY
- BC ≅ XZ
- AB ≅ YZ
- AB ≅ XY
The correct choice to satisfy HL is:
BC¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯
This means the leg BC in triangle ΔABC is congruent to leg XY in triangle ΔXYZ, thus fulfilling the requirements of the HL Congruence Theorem to conclude that ΔABC≅ΔXYZ.