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Basic Geometric Definitions

Introduction to terms such as point, line, and plane.

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Basic Geometric Definitions

Credit: CK-12 Foundation Source: CK-12 Foundation License: CC BY-NC 3.0 [Figure1]

Martin has been hiking with this father. He pulls out a map and draws a dot at their campsite then connects that dot to their next campsite. Martin says that he made a line, but his father tells him that the figure he has drawn is not technically a line. What is the figure that Martin has drawn below?

In this concept, you will learn about lines and line segments.

Basic Geometry Definitions

Geometry is a part of mathematics concerned with questions of size, shape and position of figures and with their location in space.

The first geometric figure to learn about is a point. A point is a definite place in space that doesn’t have a size or shape.

Here, point A\begin{align*}A\end{align*} is plotted on the graph. Although we generally use a dot to make it easy to see, a point is just a location without actually having a size or shape.

The point is named point A\begin{align*}A\end{align*}. Naming a geometric figure is a way to identify it in a mathematical sentence.

Next, let's look at a ray. A ray has an endpoint but extends in one direction indefinitely. Here is an example of a ray.

Notice that this ray has two points. It has point A\begin{align*}A\end{align*}, the endpoint, and point B\begin{align*}B\end{align*}, which is on the line.

To name the ray, use the letters of the two points and a symbol. The symbol looks like a small ray that is above the letters, AB\begin{align*}\overrightarrow{AB}\end{align*}.

The third geometric figure is a line.

A line has an arrow on each end. A line is a set of connected points that are infinitely close to each other and continue on forever in both directions, as indicated by the arrows. Two of the points have been named on the line. These are the two points that you will use to name the line. The symbol for a line is a small line with arrows on the end. The symbol goes above the named points on the line to name the line, CD.\begin{align*}\overleftrightarrow{CD}.\end{align*}

NOTE: Some people think of a line as looking like this:

However, in geometry, this would be a line segment. A line segment has two endpoints. This line segment does not have arrows on the ends, which means that the ends stop. Notice that the two ends of the segment have been named. They are points A\begin{align*}A\end{align*} and B\begin{align*}B\end{align*}.

Name this line segment by using a small line segment above the two endpoints. The symbol is the small line segment AB¯¯¯¯¯¯¯¯\begin{align*}\overline{AB}\end{align*}. When you see this symbol (a line without any arrows), you know that you are working with a line segment, and that it does not continue forever.

Examples

Example 1

Earlier, you were given a problem about Martin and his map.

He draws a dot at his campsite then connects that dot to the next campsite. What is the figure that Martin has drawn on the map?

First, note what is on the ends.

There are dots on the ends

Next, decide what the dots represent.

Endpoints

Then, determine if the figure is a line, a line segment or a ray.

Line segment

The answer is that the figure is a line segment.

Example 2

Which figure has an arrow on one end and an end point on the other end?

First, note what is on the ends.

An arrow on one end and an end point on the other

Then, determine if the figure is a line, a line segment or a ray.

A ray

The answer is that the figure is a ray.

Example 3

Which figure has two arrows on the ends?

First, note what is on the ends.

Arrows

Then, determine if the figure is a line, a line segment or a ray.

Line

The answer is that the figure is a line.

Example 4

is what kind of figure?

First, note what is at the ends.

Endpoints at both ends

Then, determine if the figure is a line, a line segment or a ray.

Line segment

The answer is that the figure is a line segment.

Example 5

is what kind of figure?

First, note what is at the ends.

Endpoint at one end and an arrow at the other end

Then, determine if the figure is a line, a line segment or a ray.

A ray

The answer is that the figure is a ray.

Review

Identify each of the following geometric figures.

Look at the following picture and then answer each question.

1. True or false. The vertical white lines of the structure can be considered line segments
2. Is this figure mostly made of lines or line segments?
4. Are there any rays in the picture?
6. Can a building ever be made of lines?
7. Why or why not?

Define the following terms.

1. Line
2. Line Segment
3. Ray
4. Point

To see the Review answers, open this PDF file and look for section 9.1.

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Color Highlighted Text Notes

1. [1]^ Credit: CK-12 Foundation; Source: CK-12 Foundation; License: CC BY-NC 3.0

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