What is a line or segment that is perpendicular to and cuts a segment in half called?

A line or segment that is perpendicular to another segment and divides it into two equal parts is specifically referred to as a perpendicular bisector. This term indicates both the perpendicularity and the bisection of the segment.

When a line is perpendicular to a segment, it forms right angles (90 degrees) with that segment. Additionally, to bisect means to cut into two equal parts, which is exactly what the perpendicular bisector does. Therefore, it not only intersects the original segment but ensures that both halves are congruent, fulfilling both conditions of perpendicularity and division into equal segments.

In contrast, an angle bisector divides an angle into two equal angles rather than a line segment. An altitude refers to a segment that drops perpendicularly from a vertex of a triangle to the opposite side, but it does not necessarily bisect that side. A median connects a vertex of a triangle to the midpoint of the opposite side but does not imply perpendicularity. Thus, the term that accurately describes the line segment meeting both criteria of being perpendicular and bisecting another segment is indeed the perpendicular bisector.