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¯¯¯¯¯¯¯¯≅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 AB¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯ Modifying above upper A upper B with bar congruent to Modifying above upper X upper Y with bar BC¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯

Answer 1

To show that triangles ΔABC and ΔXYZ are congruent by the Hypotenuse-Leg (HL) Congruence Theorem, we need to verify that one leg of each triangle is congruent.

Given:

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

To apply the HL Congruence Theorem, we need a pair of corresponding legs from both triangles to be congruent. We need to identify the correct response from the options provided.

The correct choice would be the option that states that one of the legs (either AB or BC from ΔABC) is congruent to the corresponding leg (either YZ or XY from ΔXYZ).

Therefore, the correct answer is:

AB ≅ YZ

This satisfies the condition needed to apply the HL Congruence Theorem, where the hypotenuse and one leg are congruent in both triangles.