Consider right triangles ABC and XYZ. 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 ABC is congruent XYZ by the HL Congruence Theorem?

Question

BC is congruent XY
AB is congruent XY
BC is congruent XZ
AB is congruent YZ

Answer 1

To show that triangles ABC and XYZ are congruent by the Hypotenuse-Leg (HL) Congruence Theorem, we need to establish the following:

1. The hypotenuses: AC and XZ are congruent (as given).
2. One leg: One leg of triangle ABC must be congruent to the corresponding leg of triangle XYZ.

From your options, the correct statement would be:

BC is congruent to XY.

So, the full justification for using the HL Theorem is:

• AC is congruent to XZ (hypotenuses).
• BC is congruent to XY (one leg).

With both of these parts established, we can conclude that triangle ABC is congruent to triangle XYZ by the HL Congruence Theorem.