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

Responses

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

Answer 1

To show that triangles ΔABC and ΔXYZ are congruent by the Hypotenuse-Leg (HL) Congruence Theorem, we need to confirm that the lengths of the legs of these right triangles are also congruent since it's given that the hypotenuses (AC and XZ) are congruent and angles B and Y are congruent.

Since angle B is congruent to angle Y, we need to establish one of the legs of each triangle as congruent. The congruence of one of the legs will allow us to apply the HL theorem.

The valid choices for showing this congruence can be summarized as follows:

1. If we show that leg BC of triangle ABC is congruent to leg XZ of triangle XYZ, it suffices, given that the hypotenuses are already known to be congruent and one angle between them (B & Y) is also congruent.

2. Similarly, if we show leg AB of triangle ABC is congruent to leg XY of triangle XYZ, that would work as well.

However, we can only pick one that leads to a direct conclusion:

Thus, we can conclude:

BC¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯

This statement asserts that the leg BC of triangle ΔABC is congruent to the leg XY of triangle ΔXYZ, fulfilling the requirements of the HL Congruence Theorem.