1.5: Points, Lines, and Planes
Learning Objectives
- Identify the undefined terms point, line, and plane.
- Name points, lines, and planes
- State important characteristics of points, lines, and planes
Undefined Terms: Points, Lines, and Planes
The three basic building blocks of geometry are points, lines and planes. These are undefined terms. While we cannot define these terms precisely, we can get an idea of what they are by looking at examples and models.
A point is a location that has no size. We use dots to represent points. Points are named and labeled with a single capital letter, as shown in the image below:
- A point is named and ____________________________ with a single capital letter.
A line is an infinite series of points in a row. It is a one-dimensional object. A line has direction and location, but still does not take up space. Lines are sometimes referred to by one italicized letter, but they can also be identified by two points that are on the line.
In the image below, the same line has several names. It can be called “line \begin{align*}g\end{align*}”.\begin{align*}\overleftrightarrow{PQ}\end{align*}, or \begin{align*}\overleftrightarrow{QP}\end{align*}:
- A line is a _____________-dimensional object that extends infinitely.
What does infinite mean? Let’s break it down.
The prefix "in-" means "not". So something that is infinite is "not" finite.
Finite means having an end. It is related to the word "final."
So something that is infinite does "not" "have an end." Something that is infinite goes on and on forever and ever.
- The word “infinite” means “does not have an ____________________.”
A plane is a surface which has infinite width and length. It is a two-dimensional object. Planes are named using a single capital letter or by naming three points contained in the plane. You already know one plane from your algebra class—the \begin{align*}xy\end{align*} coordinate plane.
The plane below can be called plane \begin{align*}M\end{align*} or “the plane defined by points \begin{align*}A, B,\end{align*} and \begin{align*}C\end{align*}.”
- A plane is a two-__________________________________ object that has infinite length and width.
Dimension
An object's dimensions refer to how the object extends into space. In geometry, we are going to focus on four types of objects:
Zero dimensions: | One dimension: | Two dimensions: | Three dimensions: |
---|---|---|---|
Does not extend into space. In other words, it extends in zero dimensions | Extends into space in only one way. For example, it has a length. | Extends into space in two ways. For example, it has a length and a width. | Extends into space in three ways. For example, it has a length, a width, and a height. |
Reading Check:
1. What are the three undefined terms in Geometry?
_____________________________
_____________________________
_____________________________
2. Draw a line that could be named "line \begin{align*}GJ\end{align*}."
\begin{align*}{\;}\end{align*}
\begin{align*}{\;}\end{align*}
\begin{align*}{\;}\end{align*}
3. Which undefined term in Geometry has two dimensions?
_____________________________
4. What does the word “infinite” mean in your own words?
\begin{align*}{\;}\end{align*}
\begin{align*}{\;}\end{align*}
\begin{align*}{\;}\end{align*}
5. Fill in the blanks:
A point has ________ dimensions, a line has ________ dimension, and a plane has ________ dimensions.
Graphic Organizer for Lesson 2
What is it? | How many dimensions? | Draw a picture. | How can you name it? | Give a real-life example. | |
---|---|---|---|---|---|
Point | |||||
Line | |||||
Plane |
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