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 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 using the HL (Hypotenuse-Leg) Congruence Theorem, you need to establish that the hypotenuses of both triangles are congruent (which is given as AC ≅ XZ) and that one of the legs (sides opposite the right angles) is also congruent.

Since we know that angle B ≅ angle Y (which are the right angles in their respective triangles), the only requirement left is that one pair of corresponding legs must also be congruent.

Given the options, if you want to show that ΔABC ≅ ΔXYZ using the HL Theorem, you could prove that either:

1. AB ≅ XY (the leg opposite angle A in triangle ABC is congruent to the leg opposite angle X in triangle XYZ), or
2. BC ≅ XZ (the leg opposite angle B in triangle ABC is congruent to the leg opposite angle Z in triangle XYZ), or
3. AB ≅ YZ (the leg opposite angle A in triangle ABC is congruent to the leg opposite angle Z in triangle XYZ), or
4. BC ≅ XY (the leg opposite angle B in triangle ABC is congruent to the leg opposite angle Y in triangle XYZ).

Based on the provided options, if we look at the two legs of the triangles, we could state the following:

• The correct corresponding parts to show that ΔABC ≅ ΔXYZ by the HL Congruence Theorem would be:

AB ≅ XY

This would mean that the leg AB of triangle ABC is congruent to the leg XY of triangle XYZ, thus satisfying the requirements of the HL theorem.