In
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
,
lines in a
plane or higher-dimensional
space
Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually con ...
are said to be concurrent if they
intersect
Intersection or intersect may refer to:
* Intersection in mathematics, including:
** Intersection (set theory), the set of elements common to some collection of sets
** Intersection (geometry)
** Intersection theory
* Intersection (road), a pl ...
at a single
point. They are in contrast to
parallel lines
In geometry, parallel lines are coplanar straight lines that do not intersect at any point. Parallel planes are planes in the same three-dimensional space that never meet. '' Parallel curves'' are curves that do not touch each other or inter ...
.
Examples
Triangles
In a
triangle
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC.
In Euclidean geometry, any three points, when non- colli ...
, four basic types of sets of concurrent lines are
altitudes,
angle bisectors,
medians, and
perpendicular bisectors:
* A triangle's altitudes run from each
vertex
Vertex, vertices or vertexes may refer to:
Science and technology Mathematics and computer science
*Vertex (geometry), a point where two or more curves, lines, or edges meet
*Vertex (computer graphics), a data structure that describes the position ...
and meet the opposite side at a
right angle. The point where the three altitudes meet is the