Definition
Plane
A plane is a perfectly flat, two-dimensional surface that continues without end in every direction.
What it means
Think of the top of an endless, perfectly flat table. You can move left, right, forward, or backward, but there is no thickness and no edge. Paper and screens show only small pieces of a plane.
Remember it
An endless flat sheet: two directions to move, no thickness, no edge.
Example
Plot A(1, 2), B(4, 2), and C(4, 5) on a coordinate plane. The three points and the line segments joining them all lie in the same plane.
Watch for
A sheet of paper models only part of a plane: paper has edges and thickness, while a mathematical plane has neither.
Common mix-up
In geometry, plane does not mean an aircraft, a woodworking tool, or merely one flat shape.
Exact meaning
In Euclidean geometry, a plane is a flat, two-dimensional set of points that extends indefinitely in every direction.