Instructor: Malcolm M.
Malcolm has a Master's Degree in education and holds four teaching certificates. He has been a public school teacher for 27 years, including 15 years as a mathematics teacher.

## Segment Bisector (Definition, Examples, & Video)

The human eye is amazingly fast and accurate at visually dividing things down the middle. Whether you are looking at a piece of paper, a wall awaiting a picture, or a humble line segment, your binocular (twin) vision helps you find that halfway point easily. On a line segment, that halfway spot is the segment bisector.

## What you'll learn:

After working your way through this lesson and video, you will be 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
• Recall that a single segment may be bisected by an infinite number of bisectors, only one of which could be a perpendicular bisector

## What is a Line Segment?

Reviewing your basic geometry, a line segment is a portion of a line, bounded at both ends by identified points, like this:

[insert line segment AZ]

Point $A$, on the left, is the farthest to the left the line segment can go. Point $Z$, on the right, is as far to the right as the line segment will extend. Unlike a line, a line segment is finite; it ends at, well, its two ends.

## Segment Bisector Definition

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

All of these figures can be segment bisectors:

1. Points
2. Line segments
3. Rays
4. Lines

## Segment Bisector Examples

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

[same line segment; introduce Point M midway]

Here are two line segments, each passing through the exact middle of line segment $AZ$, each acting as segment bisectors:

[same line segment AZ but put large X-shaped bisectors from line segments BY and CX]

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

[Same line segment, same Point M, with Point M as the origin of Ray MN]

## 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:

[insert line segment AZ with line DW intersecting it at Point M]

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:

[insert line segment AZ with line EV as a perpendicular bisector]

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.

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.

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