Segment Bisector
Overview
A segment bisector is anything — a point, line, ray, segment, or plane — that intersects a segment at its midpoint. Bisecting therefore creates two congruent halves, and that single fact drives the algebra of this lesson: the whole segment equals twice a half, and the two halves equal each other. A figure can contain more than one bisection at once, and each one contributes its own equation.
Vocabulary
- Midpoint
- The point that divides a segment into two congruent segments. The midpoint is equidistant from both endpoints.
- Segment Bisector
- A point, line, ray, line segment, or plane that intersects a segment at its midpoint.
- Bisect
- To divide into two congruent parts. A bisector of a segment divides it into two segments of equal measure.
- Congruent Segments
- Segments that have equal measures. The two halves created by a bisector are congruent, often shown with matching tick marks in a figure.
Main Ideas
- If a figure bisects a segment, the intersection point is the midpoint — label the two halves equal.
- Half + half = whole, so the whole segment measures twice one half: GH = 2 · GF when F is the midpoint.
- Nothing is known about the bisector itself — its length or direction — unless something else is stated. A bisector of one segment says nothing about parts of another segment.
- When two bisections share a figure, write one equation per bisection and solve each for its own variable.
- Substitute back: a question may ask for the whole segment after you have solved for x from a half.
Lesson Notes
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Lesson Video
Watch the lesson video.
Interactive Activity
Explore segment bisectors, name midpoints, and build bisections step by step.
Practice Problems
Want More Practice?
Download the practice worksheet for this lesson, work the problems, then check your work with the solutions.