Segment Bisector — Definition & Examples
Segment bisector definition
A segment bisector is a geometric figure that divides a line segment exactly in half. Any geometric figure that can pass through (or sit on) the line segment can form a segment bisector.
| Concept | Details |
|---|---|
| Definition | A geometric figure that divides a line segment into two equal parts at its midpoint |
| Types of Bisectors | Points, line segments, rays, lines |
| Key Requirement | Must pass through the exact midpoint of the segment |
All of these figures can be segment bisectors:
Points
Line segments
Rays
Lines
A line segment is a portion of a line, bounded at both ends by identified points. Unlike a line, a line segment is finite; it ends at its two endpoints.
Segment bisector examples
Here is a point, Point M, that is exactly at the center of line segment AZ:
| Example Type | Bisector Used | Description |
|---|---|---|
| Point bisector | Point M | A single point placed at the exact midpoint of segment AZ |
| Line segment bisector | A line segment through M | A finite segment crossing through the midpoint of AZ |
| Ray bisector | Ray MN | A ray originating at or passing through the midpoint of 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 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 accomplish this. Now let's see a line handle it:
| Bisector Type | Infinite? | Direction |
|---|---|---|
| Point | No | N/A |
| Line Segment | No | Finite in both directions |
| Ray | Yes | Infinite in one direction |
| Line | Yes | Infinite in both directions |
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.
| Property | Details |
|---|---|
| Angle of intersection | Exactly 90° |
| Uniqueness | Only one perpendicular bisector exists per line segment |
| Passes through | The midpoint of the segment |
| Key property | Every point on the perpendicular bisector is equidistant from the segment's two endpoints |
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. An important property to remember is that every point on a perpendicular bisector is equidistant from the two endpoints of the bisected segment.
Facts about segment bisectors
Let's review some key facts about segment bisectors:
| Fact | Explanation |
|---|---|
| Passes through midpoint | A segment bisector always passes through the midpoint and divides the segment into two equal parts |
| Perpendicular bisector | A segment bisector may or may not be a perpendicular bisector |
| Types | Points, lines, segments, and rays can all serve as segment bisectors |
| Infinite bisectors possible | A segment may have many bisectors at the same time |
| Unique perpendicular bisector | Only one perpendicular bisector exists for any given segment |
A segment bisector always passes through the midpoint of the segment and divides a segment into 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.
Every point on a perpendicular bisector is equidistant from the two endpoints of the segment.
Lesson summary
Now that you have read and studied the lesson, you can recall and state the definition of a segment bisector, identify the various forms of segment bisectors (including line segments, lines, rays, and points), and understand that a single segment may be bisected by an infinite number of bisectors, only one of which can be a perpendicular bisector. You also know that every point on a perpendicular bisector is equidistant from the endpoints of the bisected segment, a property with wide applications in geometry and construction.