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

BC¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯
AB¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯
AB¯¯¯¯¯¯¯¯≅YZ¯¯¯¯¯¯¯
BC¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯

Answer 1

To show that triangles \( \Delta ABC \) and \( \Delta XYZ \) are congruent by the Hypotenuse-Leg (HL) Congruence Theorem, we have:

• The hypotenuses \( AC \) and \( XZ \) are congruent.
• Angles \( \angle B \) and \( \angle Y \) are congruent.

According to the HL theorem, if the hypotenuses of two right triangles are congruent and one leg of one triangle is congruent to one leg of the other triangle, then the two triangles are congruent.

Since \( AC \) and \( XZ \) are both the hypotenuses and are congruent, and angle \( B \) is congruent with angle \( Y \), we only need one pair of legs to be congruent to apply the HL theorem.

Given the options provided, we need to determine which leg must correspond in congruence:

1. \( BC \cong XY \)
2. \( AB \cong XY \)
3. \( AB \cong YZ \)
4. \( BC \cong XZ \)

We already have the hypotenuse \( AC \cong XZ \), and we need one of the legs to match corresponding legs. The best choice would be:

• \( BC \cong XY \)

Thus, the proper corresponding part that must be congruent to show that \( \Delta ABC \cong \Delta XYZ \) by the HL Congruence Theorem is:

\( BC \cong XY \).