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) Responses AB¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯ Modifying above upper A upper B with bar congruent to Modifying above upper X upper Y with bar AB¯¯¯¯¯¯¯¯≅YZ¯¯¯¯¯¯¯ Modifying above upper A upper B with bar congruent to Modifying above upper Y upper Z with bar BC¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯ Modifying above upper B upper C with bar congruent to Modifying above upper X upper Y with bar BC¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯

Answer 1

To show that ΔABC ≅ ΔXYZ using the Hypotenuse-Leg (HL) Congruence Theorem, you already have the following information:

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

In order to apply the HL theorem, you also need to establish that one pair of corresponding legs is congruent.

The appropriate corresponding part to be shown congruent in this case would be one of the legs of the right triangles. Since you have the hypotenuses paired with congruent angles, you only need one leg to be congruent.

Thus, the correct response to use would be:

AB ≅ XY

So, the correct answer is:

• AB¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯