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Basic Geometric Definitions

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

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Basic Geometric Definitions

Let's Think About It

License: CC BY-NC 3.0

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 a line. What is the figure that Martin has drawn below?

License: CC BY-NC 3.0

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

Guidance

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 is a point plotted on the graph. Notice that the point does name a location, but it does not have a size or shape.

The point is named point \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 \begin{align*}A\end{align*}, that is the endpoint and point \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, \begin{align*}\overrightarrow{AB}\end{align*}.

The third geometric figure is a line. 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. A line segment is a set of connected points, meaning that while you see a straight line segment here, it is really a whole bunch of connected points. Two of the points on the line have been named. They are points \begin{align*}A\end{align*} and \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 \begin{align*}\overline{AB}\end{align*}. When you see this symbol, you know that you are working with a line segment.

Let's look at an example of a line.

A line has an arrow on each end. A line is also a set of connected points, but the line does not end, as indicated by the arrows. A line goes on indefinitely. 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, \begin{align*}\overleftrightarrow{CD}\end{align*}.

Guided Practice

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.

Examples

Answer the following questions about geometric figures.

Example 1

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 2

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 3

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.

Follow Up

License: CC BY-NC 3.0

Remember 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.

Video Review

Explore More

Identify each of the following geometric figures.

1.

2.

3.

4.

Look at the following picture and then answer each question.

5. True or false. The vertical white lines of the structure can be considered line segments?

6. Is this figure mostly made of lines or line segments?

7. Explain your reason.

8. Are there any rays in the picture?

9. Explain your reason.

10. Can a building ever be made of lines?

11. Why or why not?

Define the following terms.

12. Line

13. Line Segment

14. Ray

15. Point

Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 9.1. 

Vocabulary

collinear

collinear

Three or more points are collinear when they lie on the same line.
coplanar

coplanar

Points and/or lines located on the same plane are coplanar.
endpoint

endpoint

An endpoint is a point at one end of a line segment or ray.
intersection

intersection

A point or set of points where lines, planes, segments, or rays cross.
line

line

Infinitely many points that extend forever in both directions.
line segment

line segment

A line segment is a part of a line that has two endpoints.
plane

plane

A plane is a flat, two-dimensional surface. It can be conceptualized as a sheet of paper of infinite area.
Point

Point

A point is a location in space that does not have size or shape.
postulate

postulate

A postulate is a statement that is accepted as true without proof.
ray

ray

A part of a line with one endpoint that extends forever in the direction opposite that point.
space

space

Space is the set of all points extending in three dimensions.
Dimensions

Dimensions

Dimensions are the measurements that define the shape and size of a figure.
Non-collinear

Non-collinear

A non-collinear point is located above or below a line.
Non-coplanar

Non-coplanar

A non-coplanar point is located above or below a plane.
theorem

theorem

A theorem is a statement that can be proven true using postulates, definitions, and other theorems that have already been proven.

Image Attributions

  1. [1]^ License: CC BY-NC 3.0
  2. [2]^ License: CC BY-NC 3.0
  3. [3]^ License: CC BY-NC 3.0

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