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¯¯¯¯¯¯¯

Answer 1

To use the Hypotenuse-Leg (HL) Congruence Theorem to show that triangles ΔABC and ΔXYZ are congruent, we need to confirm two conditions:

1. The hypotenuses of both triangles (AC and XZ) are congruent.
2. One pair of corresponding legs must also be congruent.

Given the information:

• Angle B is congruent to angle Y (∠B ≅ ∠Y).
• Hypotenuse AC ≅ XZ.

Since we need to identify a leg of the triangles that also corresponds to the congruence statement, we have the following pairs of legs to consider:

• AB and XY
• BC and XZ
• BC and YZ

Given that we need to show that a pair of legs is congruent, we can use the following response based on congruence:

• AB ≅ XY.

This confirms that triangle ΔABC is congruent to triangle ΔXYZ by the HL theorem since we have both hypotenuses and one corresponding leg congruent.

Therefore, the answer is: AB ≅ XY.