Segment Bisector — Definition & Examples

Written by

Malcolm McKinsey

January 11, 2023

Fact-checked by

Paul Mazzola

Segment bisector definition

A segment bisector is a geometric figure that divides the line segment exactly in half. Any geometric figure that can pass through (or sit on) the line segment can form a segment bisector.

All of these figures can be segment bisectors:

• Points

• Line segments

• Rays

• Lines

Segment bisector examples

Here is a point, Point M, that is exactly at the center of line segment AZ:

Here are two line segments, one passing through the exact middle of line segment AZ, acting as a segment bisector:

And here is our same beloved line segment AZ with Ray MN serving as the segment bisector:

Infinite segment bisectors

Rays are infinite in one direction. Lines are infinite in two directions. If either a ray or a line serves as a segment bisector, it will be infinite. We have seen Ray MN get the job done. Now let's see a line handle it:

The only infinite segment bisectors, then, are a ray and a line.

Perpendicular segment bisector

For every line segment, you can have an infinite number of rays, line segments, and lines passing through the midpoint of the line segment. You can only have one point on the line segment at the halfway mark.

You can also have only one segment bisector that is perpendicular to the segment, like this:

Notice that line EV bisects the line segment at an angle of exactly 90°. No other geometric figure can occupy that exact space, so every line segment has only one perpendicular segment bisector.

Facts about segment bisectors

Let's review and go over some facts about segment bisectors:

• A segment bisector always passes through the midpoint of the segment and divides a segment in two equal parts.

• A segment bisector may or may not be a perpendicular bisector.

• Points, lines, segments, and rays are all types of segment bisectors. If either a ray or a line serves as a segment bisector, it will be infinite.

• A segment may have many bisectors at the same time.

Lesson summary

Now that you have read and studied the lesson, you are able to recall and state the definition of a segment bisector, identify the various forms of segment bisectors, including line segments, lines, rays and points, and recall that a single segment may be bisected by an infinite number of bisectors, only one of which could be a perpendicular bisector.