Plane (geometry)

From Citizendium, the Citizens' Compendium

A plane is a surface such that any straight line linking any two points on the surface is part of the surface. A plane is made up of an infinite number of straight lines. At its simplest, a plane can be defined by a triangle whose vertices cannot be collinear.

In Euclidean geometry: A plane is a surface on which a line perpendicular to a line which lies on that surface also falls entirely on the surface. It can be described by three points which do not lie on the same line. A line is said to lie on a surface if its points fall on the surface. Surfaces can be parallel.

To distinguish between a plane and a surface think of a surface as a piece of paper (with no thickness) that could be twisted, or rolled, or crumpled up. A plane would be like that sheet of paper lying perfectly flat on a table.

A surface is usually designated by the names of the points which fall on it. Thus the surface has on it point A, point B, and point C is called surface ABC.

Plane figure

A plain figure is a combination of points and/or lines that fall on the same plane.

Rectilinear figure

A rectilinear figure is a plane figure consisting of straight lines only. Rectilinear figures include triangles and polygons.