1. We are told that JM is perpendicular to GM and GK is perpendicular to KJ. 2. Thus, the triangle GMH and HKJ are right triangles. 3. It is given that GH and HJ are congruent. 4. By the vertical angle theorem, angle GHM is congruent to angle JHK. 5. By ASA, the two triangles are congruent. 6. Thus, by the definition of congruent triangles, opposite sides GM and JK are congruent.