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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 .
The word line may also refer, in everyday life, to a line segment, which is a part of a line delimited by two points (its endpoints). Euclid's Elements defines a straight line as a "breadthless length" that "lies evenly with respect to the points on itself", and introduced several postulates as basic unprovable properties on which the rest of ...
Given two points of interest, finding the midpoint of the line segment they determine can be accomplished by a compass and straightedge construction.The midpoint of a line segment, embedded in a plane, can be located by first constructing a lens using circular arcs of equal (and large enough) radii centered at the two endpoints, then connecting the cusps of the lens (the two points where the ...
Common lines and line segments on a circle, including a chord in blue. A chord (from the Latin chorda, meaning "bowstring") of a circle is a straight line segment whose endpoints both lie on a circular arc. If a chord were to be extended infinitely on both directions into a line, the object is a secant line.
The Encyclopedia of Mathematics [7] defines interval (without a qualifier) to exclude both endpoints (i.e., open interval) and segment to include both endpoints (i.e., closed interval), while Rudin's Principles of Mathematical Analysis [8] calls sets of the form [a, b] intervals and sets of the form (a, b) segments throughout.
a line segment whose endpoints are in is called a constructed segment, and a circle whose center is in S {\displaystyle S} and which passes through a point of S {\displaystyle S} (alternatively, whose radius is the distance between some pair of distinct points of S {\displaystyle S} ) is called a constructed circle .
Perpendicular bisector of a line segment. The perpendicular bisector of a line segment is a line which meets the segment at its midpoint perpendicularly.; The perpendicular bisector of a line segment also has the property that each of its points is equidistant from segment AB's endpoints:
No proper subset of the line segments has the same properties. [2] The qualifier simple is sometimes omitted, with the word polygon assumed to mean a simple polygon. [3] The line segments that form a polygon are called its edges or sides. An endpoint of a segment is called a vertex (plural: vertices) [2] or a corner.