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

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

AB¯¯¯¯¯¯¯¯≅YZ¯¯¯¯¯¯¯
Modifying above upper A upper B with bar congruent to Modifying above upper Y upper Z with bar

BC¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯

GPT-4o mini · Answer

To show that triangles ΔABC and ΔXYZ are congruent by the Hypotenuse-Leg (HL) Congruence Theorem, we already know that the hypotenuses AC and XZ are congruent, as well as that angles B and Y are congruent.

In addition to this information, we need to show that one pair of legs is also congruent. Therefore, the correct response would be to show that one of the sides (legs) of the triangles is congruent.

The appropriate choice to satisfy the HL theorem would be:

BC¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯

This indicates that the leg BC in triangle ABC is congruent to the leg XY in triangle XYZ, thereby allowing us to conclude that ΔABC ≅ ΔXYZ by the HL Congruence Theorem.