Toprove:Everylinehasoneandonlyonemidpoint.Proof:SupposeCandC′aretwomidpointsoflinesegmentABThen,AC=12ABandAC′=12ABAC=AC′(Thingswhichareequaltothesamethingareequaltooneanother)ThisispossibleonlywhenCandC′coincide.Henceeverylinesegmenthasoneandonlyonemidpoint.