Three of the most basic objects in geometry are the point, the line, and the plane. These are described in the table below.

Image

Object

Description

Point

A specific place in space. They are infinitely small (they have no size) and are denoted by a single capital letter; e.g. point $A$.

Line

A straight path that extends infinitely in both directions (denoted by the left and right arrows in the picture to the left. Lines are denoted by two points on the line under a left-right arrow symbol, such as ${\overleftrightarrow {AB}}$ or sometimes ${\overleftrightarrow {BA}}$. Also, lines are made up of an infinite number of points.

Plane

A flat surface that extends infinitely in all directions. Planes have no thickness whatsoever and can be made using a minimum of three points. Shown here is a plane being intersected by two lines. Planes are named by three points on the flat surface (i.e. "plane $ABC$"). Note that the letters cannot be on the same line, and the letters can be named in any order. When you can find a capital cursive letters in the plane you may do so. For example, if plane $ABC$ had a capital cursive letter ${\mathcal {Q}}$ on the plane, you may name it "plane ${\mathcal {Q}}$.