If we can show that △ JKM ≅ △ LKM, then we prove that JM ≅ LM. We notice a couple of things from our diagram. First, the two triangles share KM as a side. Second, since KM ⊥ JL, we know by the definition of perpendicular lines that ∠ JMK is a right angle as well. Let's mark this in our diagram.
Since two pairs of legs and the hypotenuses of our right triangles are congruent, we can by the HL Congruence Theorem prove that △ JKM ≅ △ LKM. Now we can also say that JM ≅ LM as these are corresponding sides.
