# Building Blocks of Geometry

Math
Summary

## Planes

Summary Planes

A plane is a boundless surface in space. It has length, like a line; it also has width, but not thickness. A plane is denoted by writing "plane P", or just writing "P". On paper, a plane looks something like this:

There are two ways to form a plane. First, a plane can be formed by three noncolinear points. Any number of colinear points form one line, but such a line can lie in an infinite number of distinct planes. See below how different planes can contain the same line. Figure %: Many different planes can contain the same line It takes a third, noncolinear point to form a specific plane. This point fixes the plane in position. The situation is something like a door being shut. Before the door is shut, it swings on hinges, which form a line. The door (a plane) can be opened to an infinite number of different positions, maybe just cracked a few inches, or maybe wide open (figures a, b in the diagram below). When the door is shut however, the wall on the other side of the hinges acts as the noncolinear third point and holds the door in place. At this point, the door represents one distinct plane (figure c).