Triangles J K L and X Y Z are shown. Angles K J L and Y X Z are right angles. The length of Y X is 10. The length of hypotenuse K L is 10.

To determine whether triangles JKL and XYZ are congruent, we must compare their properties, specifically the lengths of their sides and the relationships between them given the information provided.

1. Triangle JKL:

   • It is a right triangle, with \( \angle KJL \) as the right angle.
   • Hypotenuse KL = 10.

2. Triangle XYZ:

   • It is also a right triangle, with \( \angle YXZ \) as the right angle.
   • Side YX = 10.

To assess the congruence of these triangles, we can use the criteria for triangle congruence, notably using the Hypotenuse-Leg (HL) Theorem for right triangles. For two right triangles to be congruent under this theorem, they must have:

• One pair of congruent hypotenuses (which they do, since KL = YX = 10).
• One pair of congruent legs.

Now analyze the options:

1. Yes, if JL ≅ XZ.

   • This is a valid condition for congruence (specific case).

2. Yes, if XZ = 10.

   • This statement alone may not guarantee congruence, as we still need information about the other leg.

3. No, because the hypotenuse of one triangle is equal in length to the leg of the other triangle.

   • This statement does not apply here. Both hypotenuses are equal; this is not a reason to conclude they cannot be congruent.

4. No, because the leg of one triangle is equal in length to the leg of the other triangle.

   • Again, this is not sufficient to conclude non-congruence if we have not determined the specific lengths yet.

Thus, the most suitable answer based on the information given would be:

Yes, if JL ≅ XZ.

This takes into account that the hypotenuses are equal, and congruency could be achieved if the legs are appropriately congruent as well.