Question

prove that every line segment has one and only one mid point​

Answer 1

Prove that every line segment has one and only one midpoint.

Suppose C and C' are two mid points of segment AB.

Then AC = AB.

and AC' = AB.

AC = AC' [Things which are equal to the same thing are equal to one another.]

This is possible only when C and C' coincide.

Hence every line segment has one and only one midpoint.