Consider right triangles A ABC and AXY Z. 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 ДАВС ~ AXY Z by the HL Congruence Theorem? (1 point)

Answer 1

To show that triangles \( \triangle ABC \) and \( \triangle XYZ \) are similar using the Hypotenuse-Leg (HL) Congruence Theorem, we already have the following information:

1. Angle \( B \) is congruent to angle \( Y \) (i.e., \( \angle B \cong \angle Y \)).
2. The hypotenuses \( AC \) and \( XZ \) are congruent (i.e., \( AC \cong XZ \)).

To apply the HL theorem, we need to establish that one of the legs of each triangle is also congruent. Therefore, we need to show that one of the following pairs of corresponding legs is congruent:

• Leg \( AB \) should be congruent to leg \( XY \) (i.e., \( AB \cong XY \)), or
• Leg \( BC \) should be congruent to leg \( YZ \) (i.e., \( BC \cong YZ \)).

If either of these conditions is met, we can conclude that \( \triangle ABC \sim \triangle XYZ \) by the HL Congruence Theorem.