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

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

AB¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯

GPT-4o mini · Answer

To show that triangles ΔABC and ΔXYZ are congruent by the Hypotenuse-Leg (HL) Congruence Theorem, we need to confirm that two corresponding parts of the triangles are congruent. Since we know that the hypotenuses AC and XZ are congruent, and that angles B and Y are congruent (which are the right angles in each triangle), we only need to show that one leg from each triangle is also congruent.

Given the options provided:

BC ≅ XY
BC ≅ XZ
AB ≅ YZ
AB ≅ XY

The correct choice to satisfy HL is:

BC¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯

This means the leg BC in triangle ΔABC is congruent to leg XY in triangle ΔXYZ, thus fulfilling the requirements of the HL Congruence Theorem to conclude that ΔABC≅ΔXYZ.