Question

Prove that every line segment has one and only one midpoint.

Answer 1

Let AB be a line segment

and let D and E be its two midpoints

now, since D is the midpoints of AB

so, $AD=DB$

$AB=AD+DB=2AD$-(1)

Also E is a point of AB

So, $AE=EB$

$AB=AE+EB=2AE$-(2)

From eq 1 &2

$2AD=2AE$

D and E coincide to each other

AB has one and only one mid points

Hence every line segments has one and only one midpoint.