Plane
A plane is a flat surface that extends in all directions without ending. It is two-dimensional (2D), having length and width but no thickness.
Planes and geometry
Planes are probably one of the most widely used concepts in geometry. Some of the interesting characteristics of planes are listed below:
Any three non-collinear points determine a unique plane. A plane contains infinitely many points and can be named by any three of its non-collinear points. It can also be named by a letter.
A unique plane can be drawn through a line and a point not on the line.
A unique plane can also be drawn through two intersecting lines or two parallel lines.
Note: It is possible for two lines to neither intersect nor be parallel; these lines are called skew lines. Skew lines cannot be in a single plane and they cannot define a unique plane.
Skew lines a and b above do not intersect but are clearly not parallel. Thus, there is no single plane that can be drawn through lines a and b.
Infinitely many planes can be drawn through a single line or a single point. In the figure below, three of the infinitely many distinct planes contain line m and point A.
Points and lines lying in the same plane are called coplanar. In the figure below, Points A, B, C, D, F, G, and lines AC and BD all lie in plane p, so they are coplanar. Line EH and points E and H do not lie in plane p, so they are not coplanar with respect to plane p.
Plane figures
A plane figure is a geometric figure that has no thickness and lies entirely in one plane:
Angle
An angle consists of two rays that intersect at their endpoints. Since a ray is part of a line, the angle lies in a single plane, so it is a plane figure.
Polygon
A polygon is a plane figure. All of its sides as well as its interior lie in a single plane.
Other plane figures
Plane figures can also be curves, lines, line segments or a combination of them. The following are a few examples.
