Question

if the point C is called a mid-point of a line segment AB,prove that Every line segment has one only midpoint.​

Answer 1

This is a contradiction unless C and D coincide. Therefore our assumption that a line segment AB has two midpoints is incorrect. Thus every line segment has one and only one midpoint.

Answer 2

Step-by-step explanation:

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.