Perpendicular bisector of a line segment
The perpendicular bisector of a line segment is a line that passes through the midpoint of the segment (it bisects it, or cuts it into two equal pieces) and it makes a angle with it (is perpendicular to it).
In the sketch below the red line pb is the perpendicular bisector of the line segment AB. A and B can be moved to change the segment and D is a point on the perpendicular bisector.
Draw the segments joining D to A and B.
How are the distance from a point on the perpendicular bisector to the endpoints of a segment (in our case DA and DB) related? What does that mean?