Before we compare the given measures, let's recall the Hinge Theorem.
Hinge Theorem
If two sides of a triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle.
Now, let's copy the diagram and highlight the segments we are asked to compare.
We can make some observations about the sides of the two triangles by using the fact that segments of equal length are congruent. Notice that two sides of △ KLM are congruent to two sides of △ JKL.
KJ≅LM
KL≅KL
However, the included angle in △ KLM is larger than the included angle in △ JKL. Therefore, by the Hinge Theorem, the third side of △ KLM is longer than the third side of △ JKL.
m∠ KLM> m∠ JKL
⇓
KM> JL
