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Question

Provethateverylinesegmenthasoneandonlyonemidpoint.

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Solution

Toprove:Everylinehasoneandonlyonemidpoint.Proof:SupposeCandCaretwomidpointsoflinesegmentABThen,AC=12ABandAC=12ABAC=AC(Thingswhichareequaltothesamethingareequaltooneanother)ThisispossibleonlywhenCandCcoincide.Henceeverylinesegmenthasoneandonlyonemidpoint.

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