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 BC¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯ Modifying above upper B upper C with bar congruent to Modifying above upper X 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¯¯¯¯¯¯¯¯≅YZ¯¯¯¯¯¯¯

Answer 1

To show that triangles ΔABC and ΔXYZ are congruent by the HL (Hypotenuse-Leg) Congruence Theorem, we need to confirm two corresponding parts:

1. The hypotenuses AC and XZ are already stated to be congruent.
2. Since angles B and Y are congruent, we need to establish the congruence of one leg.

Thus, the other corresponding leg must be congruent. Since we have already established that the hypotenuses AC and XZ are congruent, we must have either of the legs AD or BC congruent.

The valid response would be:

AB ≅ XY

This is because we are establishing the required corresponding leg (AB and XY). Once we have both hypotenuses and one leg congruent, we can conclude with the HL congruence theorem that ΔABC ≅ ΔXYZ.