paraphrase this without any symbols: To show that triangles ΔABC and ΔXYZ are congruent by the HL (Hypotenuse-Leg) Congruence Theorem, we need to prove that one of the legs of each triangle is also congruent. Since we already know the hypotenuses AC and XZ are congruent, and angles B and Y are congruent, we can conclude that the legs AB and XY must be congruent as well. This means AB ≅ XY helps complete the requirements for the HL theorem, confirming the triangles are congruent.

Answer 1

To demonstrate that triangles ABC and XYZ are congruent using the Hypotenuse-Leg Congruence Theorem, we must establish that one leg from each triangle is also congruent. Given that the hypotenuses AC and XZ are known to be congruent, along with angles B and Y being congruent, we can deduce that the legs AB and XY are also congruent. This indicates that AB being congruent to XY meets the criteria for the HL theorem, thereby confirming that the triangles are congruent.