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¯¯¯¯¯¯¯¯

Answer 1

To show that triangles ΔABC and ΔXYZ are congruent using the HL (Hypotenuse-Leg) Congruence Theorem, we know that the following must hold:

1. The hypotenuses (AC and XZ) are congruent, which is given.
2. The angles opposite to the legs (angle B and angle Y) are congruent, which is also given.

To use the HL Congruence Theorem, we now need to establish that one pair of corresponding legs is also congruent.

Looking at the options provided:

• BC ≅ XY: This would mean that the leg BC and leg XY are congruent, which is needed for HL.
• AB ≅ XY: This is not sufficient since AB is not a leg of the triangle opposite to angle Y.
• AB ≅ YZ: This does not help us prove the congruence using the HL theorem since YZ is not the leg opposite the given angle.
• BC ≅ XZ: This is incorrect since XZ is the hypotenuse.

Therefore, the correct corresponding part that must be congruent to show that ΔABC ≅ ΔXYZ by the HL Congruence Theorem is:

BC ≅ XY