# plane

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.

**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.

## Properties of the plane

A plane is uniquely determined by three points that do not lie in a straight line. If two points of a straight line lie in a plane, the whole line lies in the plane.

Two planes either intersect in a straight line (trace line or trace) or have no point in common. Planes that have no points in common are parallel. A plane and a straight line either intersect in a point (point of intersection, trace point, trace); or the whole line lies in the plane; or the plane and the line have no point in common, in which case the line is parallel to the plane. Two straight lines that lie in the same plane have either one or no points in common. A unique plane is determined either by a straight line and a point not lying on it, or by two different straight lines with a common point. A plane is unbounded on all sides and divides space into two parts. A plane is divided by every straight line within it into two parts.