First, we will prove that KL ≅ QP. Note that according to the definition of a midpoint, M bisects KQ which means KM≅ MQ. Let's add this information to the diagram.
Examining the diagram, we also see a vertical angle pair at M. According to the Vertical Angles Theorem, these are congruent.
Now we can claim that △ KML≅ △ QMP by the AAS Congruence Theorem. Since KL and QP are corresponding sides, they must be congruent.
