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
Let a line $AB$ have two mid-points, say, $C$ and $D.$ Then
$AB = AC + CB = 2AC . . . . (i) . . . [$As $C$ is the mid-point of $AB]$
and $AB = AD + DB = 2AD . . . . (ii) [$As $D$ is the mid-point of $AB]$
From equation $(i)$ and $(ii)$
$AC = AD$ and $CB = DB$
But this will possible only when $D$ lies on point $C$. So every line segment has one and only one mid-point.
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