Point C is the midpoint of line segment AB, prove that every line segment has one and only one midpoint.

AC=BC.. (i)
If possible, let D be another mid-point of AB.
AD=DB.. (ii)
Subtracting (ii) from (i)
AC–AD=BC–DB
DC = −DC ( ∵ AC−AD=DC and CB−DB=−DC)
DC+DC=0
2DC=0
DC=0
So, C and D coincide.
Thus, every line segment has one and only one mid-point.