What Is a Line Segment?

The small rules behind a segment

Imagine stretching a ruler from one mark to another. The ruler covers a straight distance between two places. That is the basic idea of a segment. The endpoints belong to the segment, and every point between them belongs too. If the segment is labeled AB, both A and B are included, as well as all the locations between A and B.

A segment can be moved, turned, or drawn at an angle without changing what it is. Its direction on the page is not important. What matters is that it is straight and finite. A short segment and a long segment are still the same kind of figure; their lengths are simply different.

Segments appear in almost every larger geometry figure. The sides of a triangle are segments. The edges of a rectangle are segments. A diagonal connects two vertices with a segment, and a chord connects two points on a circle with a segment. Midpoints and segment bisectors also depend on the fact that a segment has a measurable halfway place.

When a problem gives a segment length, use the labels and the measurements instead of judging by the picture. A drawing may not be made to scale. The segment that looks longer may have a smaller written measurement. Geometry asks you to trust the information and the definition, not just your first visual impression.

• A line segment has two endpoints and a finite length.
• A segment has exactly two endpoints.
• A segment is straight and finite, so its length can be measured.
• Segment notation names the whole bounded part from one endpoint to the other.

Where a segment does useful work

• Use line segment when measuring distance between two points in a diagram.
• Use it when naming triangle sides, polygon sides, diagonals, and chords.
• Use it in midpoint, bisector, and segment-addition problems where finite length matters.

Three segment mix-ups to avoid

• Do not let the line continue past the endpoints if the figure is meant to be a segment.
• Do not forget that the endpoints belong to the segment itself.
• Do not confuse the visual length of the drawing with a labeled measurement unless the scale is known.