Given a line segment, a perpendicular bisector is a line (or segment) that intersects the given segment at right angles to the segment's midpoint.
Here's a pic....
AB is the given segment.....and CD is the perpendicular bisector
BTW.....Euclid presents this easy construction in his "Elements".... it is demonstrated here in a step-by-step fashion.....http://www.mathopenref.com/constbisectline.html