In geometry, a line segment is a part of a straight line that is bounded by two distinct endpoints (its extreme points), and contains every point on the line that is between its endpoints. It is a special case of an arc, with zero curvature. The length of a line segment is given by the Euclidean distance between its endpoints. A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints. In geometry, a line segment is often denoted using an overline (vinculum) above the symbols for the two endpoints, such as in AB.

Examples of line segments include the sides of a triangle or square. More generally, when both of the segment's end points are vertices of a polygon or polyhedron, the line segment is either an edge (of that polygon or polyhedron) if they are adjacent vertices, or 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).

If V is a vector space over ⁠${\displaystyle \mathbb {R} }$⁠ or ⁠${\displaystyle \mathbb {C} ,}$⁠ and L is a subset of V, then L is a line segment if L can be parameterized as

for some vectors ${\displaystyle \mathbf {u} ,\mathbf {v} \in V}$ where v is nonzero. The endpoints of L are then the vectors u and u + v.

Sometimes, one needs to distinguish between "open" and "closed" line segments. In this case, one would define a closed line segment as above, and an open line segment as a subset L that can be parametrized as

for some vectors ${\displaystyle \mathbf {u} ,\mathbf {v} \in V.}$

Equivalently, a line segment is the convex hull of two points. Thus, the line segment can be expressed as a convex combination of the segment's two end points.

In geometry, one might define point B to be between two other points A and C, if the distance |AB| added to the distance |BC| is equal to the distance |AC|. Thus in ⁠${\displaystyle \mathbb {R} ^{2},}$⁠ the line segment with endpoints ${\displaystyle A=(a_{x},a_{y})}$ and ${\displaystyle C=(c_{x},c_{y})}$ is the following collection of points: