Question

prove that every line segment has one and only one midpoint​

Answer 1

Step-by-step explanation:

Let us consider, a line segment AB. Assume that it has two midpoints say C and D Recall that the midpoint of a line segment divides it into two equal parts. That is AC = BC and AD = DB Since C is midpoint of AB, we have A, C and B are collinear ∴ AC + BC = AB → (1) Similarly, we get AD + DB = AB → (2) From (1) and (2), we get AC + BC = AD + DB 2 AC = 2AD ∴ AC = AD This is a contradiction unless C and D coincide. Therefore our assumption that a line segment AB has two midpoints is incorrect. Thus every line segment has one and only one midpoint.