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