Let’s follow these steps
1.Given a line segment AB.
 Now with A as center, and radius more than half AB,
draw an arc on top and bottom of AB
 Now with B as center, and same radius ,
draw an arc on top and bottom of AB

Where the two arcs intersect above AB is point C
and where the two arcs intersect below AB is point D
Join CD
∴ CD is the perpendicular bisector of AB