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# Basic Geometric Definitions

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

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Basic Geometric Definitions

Have you ever been to a skateboard park?

The sixth grade class is working on designing a skateboard park. In the lobby of the school, the following drawing appeared. Cassie and James looked at the design on the way to gym class.

"This is going to be the best," Cassie commented.

"Yes, it will be great to just come to school to skateboard," James agreed.

"The lines for the soccer field have been drawn in," Cassie said.

"You mean "line segments", don't you?" James corrected.

"What do you mean by that?" Cassie responded.

What does James mean? Do you know the difference between a line segment and a line?

In this Concept, you will learn all about lines and line segments. At the end of the Concept, you will know why James has made the statement that he has.

### Guidance

Previously we worked with numbers and operations. In this Concept, we will begin working with the basics of geometry.

Geometry is a part of mathematics concerned with questions of size, shape and position of figures and with their location in space. This Concept is going to focus on some of the building blocks of geometry.

There are a lot of vocabulary words in this Concept. We use pictures, definitions and symbols to help us to understand things in geometry. Keep your notebook handy to take notes during this Concept!

As we work with the geometric figures below, we will discuss three things about each. We will discuss the description or definition, what the figure looks like and finally how to “name” it.

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

We can name the point Point $A$ . Naming a geometric figure is a way to identify it in a mathematical sentence.

Next, we can learn about a ray . Often we think of a “ray of sunshine.” A ray has an endpoint but extends in one direction indefinitely . Here is a picture of a ray.

Notice that this ray has two points. It has one point, point $A$ , that is the endpoint and one point, point $B$ , which is on the line.

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

Our third geometric figure is a line. We often think of a line as looking like this:

However, in geometry, this would be a line segment . A line segment has two endpoints. Because this line segment does not have arrows on the ends, it means that the ends stop . A line segment is a set of connected points, meaning that while we 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 $A$ and $B$ .

We can name this line segment by using a small line segment above the two endpoints. The symbol is the small line segment $\overline{AB}$ . When you see this symbol, you know that you are working with a line segment.

If the drawing above is a line segment, what does a line look like?

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 and on and on indefinitely. Two of the points have been named on the line. These are the two points that we 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, $\overleftrightarrow{CD}$ .

#### Example A

Which figure has two arrows on the ends?

Solution: A Line

#### Example B

is what kind of figure?

Solution: Line segment

#### Example C

is what kind of figure?

Solution: A Ray

Now back the skateboard park. Have you been paying attention? Here is the original problem once again.

The sixth grade class is working on designing a skateboard park. In the lobby of the school, the following drawing appeared. Cassie and James looked at the design on the way to gym class.

"This is going to be the best," Cassie commented.

"Yes, it will be great to just come to school to skateboard," James agreed.

"The lines for the soccer field have been drawn in," Cassie said.

"You mean "line segments", don't you?" James corrected.

"What do you mean by that?" Cassie responded.

What does James mean? Do you know the difference between a line segment and a line?

When you think about James comment you have to think about the difference between a line and a line segment.

A line segment has definite endpoints, while a line does not have any endpoints.

In looking at the design of the school and specifically the soccer field, you can see that the lines of the soccer field have definite end points. Therefore, the lines are considered line segments and not lines.

### Guided Practice

Here is one for you to try on your own.

Draw a ray, a line and a line segment. Be sure to use a ruler.

Here are three drawings that represent a ray, a line and a line segment. Be sure that your drawings are like these. Then you can continue with the Concept.

### Explore More

Directions: Identify each of the following geometric figures.

1.

2.

3.

4.

Directions: 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?

8. Are there any rays in the picture?

10. Can a building ever be made of lines?

11. Why or why not?

Directions: Define the following terms.

12. Line

13. Line Segment

14. Ray

15. Point

### Vocabulary Language: English

collinear

collinear

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

Dimensions

Dimensions are the measurements that define the shape and size of a figure.
line

line

A line is a straight one-dimensional figure that extends forever in opposite directions.
line segment

line segment

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

Point

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

Ray

A ray is a part of a line that has one endpoint and continues indefinitely in one direction.