onsider right triangles ABC and XYZB nd 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 thatABC ~= XYZ the HL Congruence Theroem? (1 point)

Answer 1

To apply the Hypotenuse-Leg (HL) Congruence Theorem to show that triangles ABC and XYZ are congruent, given the information that:

1. Angle Y in triangle XYZ is congruent to angle A in triangle ABC.
2. The hypotenuses AC and XZ are congruent.

We need one additional piece of information about the legs of the triangles. Since both triangles are right triangles, we can state that if one leg of triangle ABC is congruent to one leg of triangle XYZ, then we can conclude that the triangles are congruent.

So, to summarize, you need to show that one of the following pairs of legs are congruent:

• \( AB \cong XY \) (where leg AB corresponds to leg XY),

or

• \( BC \cong YZ \) (where leg BC corresponds to leg YZ).

Thus, to conclude that \( \triangle ABC \cong \triangle XYZ \) by the HL Congruence Theorem, you should state that the leg corresponding to the right angle in triangle ABC is congruent to the leg corresponding to the right angle in triangle XYZ.