Question

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

Answer 1

Given: C is the mid-point of AB such that AC = BC.

To prove: AB has one and only mid-point C.

Proof: Suppose C and C' be the two mid points of AB.

Therefore AC = AB/2 and AC' = AB/2 => AC = AC'

Which is possible only when C and C' coincide => points C and C' are identical.

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