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

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

BC¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯
Modifying above upper B upper C with bar congruent to Modifying above upper X upper Y with bar

AB¯¯¯¯¯¯¯¯≅YZ¯¯¯¯¯¯¯

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1 answer
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Answer 1

Bot GPT 4-o mini answered
1 month ago

To show that triangles ΔABC and ΔXYZ are congruent by the Hypotenuse-Leg (HL) Congruence Theorem, we already have two pieces of information:

1. The hypotenuses \( AC \) and \( XZ \) are congruent.
2. Angles \( B \) and \( Y \) are congruent.

According to the HL Theorem, for right triangles, it is required that one leg of each triangle is also congruent. Thus, to establish congruence between ΔABC and ΔXYZ, we need to find which corresponding leg must also be congruent.

Since we need one leg of each triangle to be congruent along with the hypotenuse and the right angle, we can conclude that either \( AB \) must be congruent to \( XY \) or \( BC \) must be congruent to \( YZ \).

Since the first option \( AB ≅ XY \) directly identifies one of the legs, this would satisfy the HL Theorem.

Thus, the answer is:

**AB¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯**.