Question

What is a line segment

Answer 1

Solution:

In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints. A closed line segment includes both endpoints, while an open line segmentexcludes both endpoints; a half-open line segment includes exactly one of the endpoints.

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 otherwise a diagonal. When both the end points lie on a curve such as a circle, a line segment is called a chord (of that curve).

• A line segment is a connected, non-empty set.
• If V is a topological vector space, then a closed line segment is a closed set in V. However, an open line segment is an open set in V if and only if V is one-dimensional.
• More generally than above, the concept of a line segment can be defined in an ordered geometry.
• A pair of line segments can be any one of the following: intersecting, parallel, skew, or none of these. The last possibility is a way that line segments differ from lines: if two nonparallel lines are in the same Euclidean plane they must cross each other, but that need not be true of segments.