Consider right triangles ΔABC and ΔXYZ . Angle B and angle Y are congruent. The hypotenuse of each triangle is AC and XZ , and they are congruent. What other corresponding parts must be congruent to show that ΔABC≅ΔXYZ by the HL Congruence Theorem?(

A. BC ≅ XZ
B. BC ≅ XY
C. AB ≅ XY
D. AB ≅ YZ

1 answer

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:

  1. The hypotenuses AC and XZ are congruent (as stated in the problem).
  2. 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.