Let us consider, a line segment AB .Assume that it has two mid points say C and D

Midpoint of a line segment divides it into two equal parts So, AC=BC and AD=DB Since, C is midpoint of AB, we have A, C and B are collinear Thus,

AC+ BC =AB................................................. (i)

Similarly, we get AD+DB=AB........................ (ii)

From eq (i) and (ii), we get AC + BC = AD + DB2 AC = 2ADAC = 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.

2021-10-10 09:56:03

## Prashant

Let us consider, a line segment AB .Assume that it has two mid points say C and D

Midpoint of a line segment divides it into two equal parts So, AC=BC and AD=DB Since, C is midpoint of AB, we have A, C and B are collinear Thus,

AC+ BC =AB................................................. (i)

Similarly, we get AD+DB=AB........................ (ii)

From eq (i) and (ii), we get AC + BC = AD + DB2 AC = 2ADAC = 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.