Which of the following is an example of a segment bisector?

• A. A line that passes through the midpoint of a segment
• B. A line that passes through an endpoint of a segment
• C. A line perpendicular to a segment at its endpoint
• D. A line that divides a segment into three equal parts

Answer: (A)

A segment bisector is any line, ray, or other line that cuts a segment exactly at its midpoint, so the two resulting pieces are equal in length. If a line passes through the segment’s midpoint, it intersects the segment right at that halfway point, which guarantees AM = MB for the segment AB with midpoint M. That makes it an example of a segment bisector.

The other options don’t satisfy this condition: going through an endpoint doesn’t split the segment into two equal parts, since one piece would be zero length at the endpoint; a line perpendicular at an endpoint also meets the segment at the endpoint rather than at its midpoint; dividing a segment into three equal parts involves more than two pieces and isn’t a single bisection.