A perpendicular bisector is a line segment which perpendicularly intersects another line, thereby dividing it into two equal parts. In fact, the Perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the segment’s endpoints.
The perpendicular bisector, AB, bisects CD at a point E, that is, the length CE is equal to ED. And the angle formed between the two lines is 90 degrees.
Therefore, the additional pertinent information that allows for the conclusion that AB is a perpendicular bisector of CD is that "CE congruent ED".
