A perpendicular bisector is a line or line segment that both bisects a given line segment and is perpendicular to it.

Four possible cases of a line intersecting a line segment are shown below:

In both cases three and four the line bisects the segment. In both cases the line is a bisector of the segment.

In both cases two and four the line is perpendicular to the segment. In both cases the line is a perpendicular to the segment.

Only in case four is line a bisector of the segment AND perpendicular to the segment. In case four the line is a perpendicular bisector of the segment.