Geometry Basic Concepts

Basic geometric vocabulary and postulates covering points, lines, planes, segments, and rays based on the lecture notes.

Geometry

A branch of mathematics that studies shapes, measurements, lines, angles, and space.

Undefined terms

In geometry, the words point, line, and plane do not have a formal definition, but there is an agreement regarding what they mean.

Point

This entity has no measurements or extension and is primarily used to indicate or locate coordinates; they are named with a capital letter.

Line

This entity extends to infinity in both directions and lacks width; it is named with a lowercase letter or with two capital letters for two points on it.

Postulate: Two points

Through any two points there is exactly one line.

Plane

This entity extends to infinity in every direction and has no thickness; it can be named with a cursive or Greek letter ($\alpha$, $\beta$, $\gamma$) or with three coplanar points.

Postulate: Three points

Through three non-collinear points there is exactly one plane that contains them.

Postulate: Line in a plane

If two points are in a plane, then the line that contains those points is in the plane.

Segment

The part of a line that has an initial point and a final point, or simply has two endpoints.

Ray

A portion of a line that has an initial point (endpoint) but does not have a final point.

Collinear points

Points that are located on the same line.

Coplanar points

Points that are located within the same geometric plane.