In geometry, a plane is a flat two-dimensional "surface" (similar to a sheet of paper, but with no thickness and no finite length or width). A plane is defined by three points, each of which forms a line with the other two points within the plane. In three dimensions, the simplest version of a plane would include all of the points with any x and y value that contain the same value for z.
A plane is a flat surface or a 2-dimensional object, stretching to infinity in all directions.
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Non-coplanar simply means not on the same plane (referring to points on a plane; geometry)
Two dimensional geometry is called "plane geometry" meaning that it occurs on a single surface or plane. The objects used in plane geometry are called plane figures.
Presumably it is simply geometry. However, plane geometry is geometry which is limited to objects with up to two dimensions, that is, objects that lie in a plane - or on a flat surface.
Point ; Line ; Plane - Remember the Point-Line-Plane Postulate
The geometry of similarity in the Euclidean plane or Euclidean space.