Question

could △jkl be congruent to △xyz? explain. no, because the leg of one triangle is equal in length to the leg of the other triangle. no, because the hypotenuse of one triangle is equal in length to the leg of the other triangle. yes, if xz = 10. yes, if \overline{jl} \cong \overline{xz}.

Explanation:

For two right - angled triangles to be congruent, we can use the Hypotenuse - Leg (HL) congruence criterion. In right - triangle \( \triangle JKL\), \(KL = 10\) is the hypotenuse. In right - triangle \( \triangle XYZ\), \(YZ = 10\) is a leg.
If \( \overline{JL}\cong\overline{XZ}\) (i.e., one leg of \( \triangle JKL\) is congruent to one leg of \( \triangle XYZ\)) and \(KL = YZ=10\) (hypotenuse of \( \triangle JKL\) is congruent to the hypotenuse of \( \triangle XYZ\) if we assume the right - angle positions are considered properly in terms of congruence mapping), by the Hypotenuse - Leg (HL) congruence theorem for right - angled triangles (\(HL\) states that if the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle, then the two right - triangles are congruent).

Answer:

Yes, if \( \overline{JL}\cong\overline{XZ}\)