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¯¯¯¯¯¯¯¯≅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¯¯¯¯¯¯¯¯
Modifying above upper B upper C with bar congruent to Modifying above upper X upper Y with bar
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GPT-4o mini · Answer

To show that triangles $ \Delta ABC $ and $ \Delta XYZ $ are congruent using the Hypotenuse-Leg (HL) Congruence Theorem, we need to establish that two of their corresponding sides are congruent besides the congruent hypotenuses (which are $ AC $ and $ XZ $) and the congruent angles (angle $ B $ and angle $ Y $) that are given. Since the hypotenuses $ AC $ and $ XZ $ are already stated to be congruent, and we know that angles $ B $ and $ Y $ are congruent, we can conclude two triangles are congruent if one other leg is proven congruent. The correct corresponding part that must be congruent is: **BC̅̅̅̅̅̅ ≅ XZ̅̅̅̅̅̅.** So the complete answer is that you must show that $ BC $ (one leg of triangle $ \Delta ABC $) is congruent to $ XY $ (the corresponding leg of triangle $ \Delta XYZ $). This satisfies the requirements of the HL theorem. Therefore, the answer is: **BC̅̅̅̅̅̅ ≅ XY̅̅̅̅̅̅**.