Angles ABK and KBM (KBC) have equal measure, because BK bisects angle ABC. Triangle BKM is isosceles because BM=MK, so angles KBM and BKM have equal measure. Therefore ABK and BKM have equal measure. So the transversal BK between lines AB and KM produces equal angles on each side of the transversal, which is a property of parallel lines, therefore AB and KM are parallel.