Question

Prove that every line sigment has one and only one mid point​

Answer 1

Prove that every line segment has one and only one midpoint

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.