A plane is a flat (two-dimensional) surface such that a straight line joining any two points on it will also lie entirely on the surface. Its general equation in the three-dimensional Cartesian coordinate system is ax + by + cz = d, where a, b, c, and d are constants.


A plane may be determined by two intersecting parallel lines, by a line and a point that does not lie on the line, or by three points that do not lie in a straight line. The intersection of two planes is a straight line; the intersection of a plane and a line in a different plane is a point. An infinite number of planes may pass through a single point or line. A plane is parallel to another plane if all perpendiculars drawn between them are of equal length.


Plane geometry is a form of geometry in which all lines, angles, and figures are represented in two-dimensional (plane) form. In plane geometry, Euclid's postulates are valid.


A plane of symmetry is a plane cutting a geometrical figure such that the parts of it lying on either side are symmetrical.