Points Lines and Planes
An Introduction to Geometry w/ 19+ Examples!

Today we’re going to cover the fundamentals terms in geometry.

We’re going to uncover the theories behind them and walk through several examples.

Let’s get started!

So what are the basic elements?

The ideas and definitions that help us to formulate and represent patterns and shapes, make predictions, and understand the properties of objects and space.

And the most basic terms necessary for success in geometry are:

• Points
• Lines
• Planes
• Segments
• Rays

Three Undefined Terms In Geometry

1. Points

Definition

A point denotes a specific location and has no dimension (i.e., width, length or depth). We describe a point using a small dot and a capital letter.

Example

2. Lines

Definition

A line is a straight path that extends indefinitely in two directions and has no thickness. And from Algebra, we know that we need two points to indicate a line, we represent a line with two arrowheads over two points on the same line or by using a cursive lowercase letter.

Example

3. Planes

Definition

To visualize a plane, I want you to think of a piece of paper or wall that extends in all directions without end. A plane extends in two dimensions with no thickness or boundary and is represented using three points or with a capital letter typically found in the corner of the plane.

Example

Collinear vs. Coplanar

It is important to note that for all points that lie on the same line are called collinear points, as Math Planet accurately states, and all points that lie on the same plane are called coplanar points. Moreover, while any three points are coplanar, we must select three noncollinear points when naming a plane.

Line Segments and Rays

A line segment, or segment, is a part of a line and contains two endpoints and all points between them. Whereas a ray consists of one endpoint, or initial point, and extends in only one direction. When writing lines, planes, or segments, the order of each point is not important but when naming rays we must always list the endpoint first.

Together we will look at the theory behind these terms and accurately identify and represent them all while working through countless examples.

Points, Lines, & Planes – Lesson & Examples (Video)

38 min

• Introduction to points, lines and planes
• 00:00:24 – Defining terms: Point, Line, Plane, Collinear, and Coplanar
• 00:08:40 – Identify each of the following points (Examples #1-4)
• Exclusive Content for Member’s Only

• 00:15:03 – True or false given the diagram of two planes (Examples #5-10)
• 00:18:57 – True or false about collinear and coplanar theory (Examples #11-16)
• 00:21:49 – Term Definitions: Line Segments and Rays
• 00:27:33 – Name the segments or rays given the illustration (Examples #17-20)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions