Every Point of Perpendicular Bisector is Equidistance from End Points of Line

Let AB is a line and PQ is perpendicular bisector of AB.

PQ has so many points on it.

Let, C, D are points on it. Now, PQ has four points two end points P and Q and two points C and D.

In figure above,

Point P is equidistant from the end points of the line AB.

PA = PB

Similarly, point C is equidistant from the end points of the line AB.

CA = CB

Similarly, point D is equidistant from the end points of the line AB.

DA = DB

Similarly, point Q is equidistant from the end points of the line AB.

QA = QB

Hence,proved.