Question

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

Explanation:

Step1: Recall congruence criteria

For right - triangles, we have HL (Hypotenuse - Leg) congruence criterion. In right - triangle $\triangle{JKL}$, $JL$ is the hypotenuse with length 10. In right - triangle $\triangle{XYZ}$, if $XZ$ is the hypotenuse and $XZ = 10$, and we can match the other corresponding parts, the triangles can be congruent.

Step2: Analyze options

The first option only says $\overline{JL}\cong\overline{XZ}$ but doesn't give the length. The third and fourth options are incorrect as the given information does not violate any congruence rules in that way. The second option is correct because if $XZ = 10$ (the length of the hypotenuse of $\triangle{JKL}$), and we can match the legs and right - angles, the two right - triangles $\triangle{JKL}$ and $\triangle{XYZ}$ can be congruent by the HL criterion.

Answer:

Yes, if XZ = 10.