Noun

Singular line segment

Plural line segments

line segment (plural line segments)

1. (geometry) A part of a straight line bounded by two points.

In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points. Examples of line segments include the sides of a triangle or square. More generally, when the end points are both vertices of a polygon, the line segment is either an edge (of that polygon) if they are adjacent vertices, or otherwise a diagonal. When the end points both lie on a curve such as a circle, a line segment is called a chord (of that curve).

Definition

If is a vector space over or , and is a subset of then is a line segment if can be parameterized as

for some vectors , in which case the vectors and are called the end points of

Sometimes one needs to distinguish between "open" and "closed" line segments. Then one defines a closed line segment as above, and an open line segment as a subset that can be parametrized as

for some vectors .

An alternative, equivalent, definition is as follows: A (closed) line segment is a convex hull of two points.