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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 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).

- $L\; =\; \{\; mathbf\{u\}+tmathbf\{v\}\; mid\; tin[0,1]\}$

for some vectors $mathbf\{u\},\; mathbf\{v\}\; in\; V,!$ with $mathbf\{v\}\; neq\; mathbf\{0\},$ in which case the vectors $mathbf\{u\}$ and $mathbf\{u+v\}$ are called the end points of $L.,!$

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 $L,!$ that can be parametrized as

- $L\; =\; \{\; mathbf\{u\}+tmathbf\{v\}\; mid\; tin(0,1)\}$

for some vectors $mathbf\{u\},\; mathbf\{v\}\; in\; V,!$ with $mathbf\{v\}\; neq\; mathbf\{0\}.$

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

- 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.

- Definition of line segment With interactive animation
- Copying a line segment with compass and straightedge
- Dividing a line segment into N equal parts with compass and straightedge Animated demonstration

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Last updated on Saturday October 11, 2008 at 03:53:43 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Saturday October 11, 2008 at 03:53:43 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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