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

Answer 1

In order to use the Hypotenuse-Leg (HL) Congruence Theorem to show that triangles ΔABC and ΔXYZ are congruent, we need to establish that one additional pair of corresponding legs (sides) of the triangles are congruent.

Given that:

1. Angle B (in ΔABC) is congruent to Angle Y (in ΔXYZ).
2. The hypotenuses AC and XZ are congruent.

The remaining corresponding legs to consider are BC (in ΔABC) and XY (in ΔXYZ), or AB and YZ.

To satisfy the HL Congruence Theorem, we have the following options:

• BC ≅ XY (the leg opposite the congruent angle).
• AB ≅ YZ (the other leg opposite the right angle).

Since we are specifically asked for an additional pair that must be congruent to show the triangles are congruent using HL, the appropriate choice here would be either:

BC ≅ XY or AB ≅ YZ.

Both of these options would complete the set needed for the HL theorem. Therefore, you can choose either of the above:

• BC ≅ XY
• AB ≅ YZ

Final answer: BC ≅ XY (or you could also choose AB ≅ YZ, but per the question’s context, BC ≅ XY is a clear choice).