Question

prove a line segament 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.

Answer 2

Answer:

let us consider a line segment AB.

Assume that it has two midpoints C and D.

so AC=BC and AD=BD

since C is the midpoint,A,C and B are collinear

AC+BC=AB...(1)

AD+BD=AB..(2)

from (1) and(2) we get..

AC+BC=AD+BD

2AC=2AD

i.e AC=AD

This means C and D coincide.

Therefore every line segment has only and only one midpoint.