Question

Prove that every line segment has one and only one mid-point.​

Answer 1

Let $AB$ be a line segment and let $D$ and $E$ be its two midpoints of $AB$.
Now, since $D$ is the midpoint of $AB$
So,
$AD=DB$
$AB=AD+DB=2AD\dots .(eq.1)$
Also, $E$ is a point of $AB$
So, $AE=EB$
$AB=AE+EB=2AE\dots .(eq.2)$
But from $eq.1$ & $eq.2$, we can write,
$2AD=2AE$
Here, $D$ and $E$ coincide with each other.
So, $AB$ has one and only one midpoint.
Hence every line segment has one and only one midpoint.