Point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.

Here, C is the mid-point of line segment AB, such that

AC = BC

From Eqs. (i) and (ii),

which is only possible, when C and C’ coincide.

Therefore, points C and C’ are identical.

Hence, every line segment has one and only one mid-point.