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)

Question

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

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

AB¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯

GPT-4o mini · Answer

To show that $ \triangle ABC \cong \triangle XYZ $ by the Hypotenuse-Leg (HL) Congruence Theorem, we need to confirm that the legs of the triangles are congruent, given that the hypotenuses are already found to be congruent. Since angle B is congruent to angle Y and both triangles have congruent hypotenuses AC and XZ, we can conclude that it suffices to show that one corresponding leg is congruent. Since we are looking for a corresponding part that must be congruent under the HL theorem, the correct response would be: **$ AB \cong XY $** Thus, to satisfy the criteria for HL, you could select: **$ AB \cong XY $** Therefore, the correct option is: **$ AB \cong XY $**.