Two-dimensional geometric space defined by a system of axioms.

A system of axioms for a geometric plane may include the following:

- A1 : A geometric plane is a set of points with at least two elements.
- A2 : Every line is included in the plane.
- A3 : Every pair of points in the plane determines a line.
- A4 : Consider a line
*l*in the plane and a point*P*that does not belong to the line; there is one and only one line*l’*n the plane that contains*P*and does not have a point in common with*l*. Therefore, lines*l*and*l’*are said to be parallel.

- A plane is a flat surface that extends infinitely in all directions and contains every line that joins two of its points.
- The term “plane” generally is a synonym for “geometric plane.”
- The Greek capital letter ∏, which is read “pi,” is often used as a symbol to refer to a plane.
- A
**projection plane**is a plane that contains the images of three-dimensional objects transformed by a projection of three-dimensional space onto a two-dimensional space (plane).