Question

Make a conjecture about the diagram below. Do you think you can conclude that △JKL ≅ △XYZ? Explain your reasoning.

Triangles J K L and X Y Z are shown. Angles J K L and X Y Z are right angles. The lengths of J K and X Y are congruent and the lengths of J L and Z X are congruent.

Answer 1

Yes. Because ∠JKL and ∠XYZ are right, JL and XZ are the hypotenuses of the two right triangles and JK and XY are corresponding legs. In right triangles the Hypotenuse‑Leg (HL) congruence theorem applies: if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and the corresponding leg of another right triangle, the triangles are congruent. Therefore ΔJKL ≅ ΔXYZ (with correspondence J↔X, K↔Y, L↔Z).