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?(1 point)ResponsesAB¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯Modifying above upper A upper B with bar congruent to Modifying above upper X upper Y with barAB¯¯¯¯¯¯¯¯≅YZ¯¯¯¯¯¯¯Modifying above upper A upper B with bar congruent to Modifying above upper Y upper Z with barBC¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯Modifying above upper B upper C with bar congruent to Modifying above upper X upper Y with barBC¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯

Answer 1

To show that triangles ΔABC and ΔXYZ are congruent by the Hypotenuse-Leg (HL) Congruence Theorem, you need to confirm that you have a pair of congruent hypotenuses and a pair of congruent legs.

In this case, you've already established that:

1. The hypotenuses AC and XZ are congruent (AC ≅ XZ).
2. Angles B and Y are congruent (∠B ≅ ∠Y).

The HL theorem states that if the hypotenuse and one leg of a right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.

Since you need one leg to be congruent as well, you can choose:

AB ≅ XY or BC ≅ XZ

However, since XZ is the hypotenuse, the best option based on the choices is: AB ≅ XY

Thus, confirming AB ≅ XY will satisfy the HL congruence theorem, along with the previously established congruencies.