Introduction to Geometry

Lesson Plan - Get It!

Audio:

Before you begin this lesson, it would be a good idea to review the vocabulary words you will be working with.

Click on each word to find its definition in A Maths Dictionary for Kids Quick Reference:

• geometry
• point
• line segment
• ray
• line

Take a look at the literal meaning of the word geometry. The word itself actually comes from two words: "geo," which means Earth, and "metry," which means measurement. Quite simply, geometry is the study of measurement of items in and on the earth.

Geometry was used by the Greeks, Babylonians, and Egyptians to design their buildings and even their artwork. All of their designs began with the simplest of ides in geometry: the point, the line, the line segment, the ray, and the vertex.

When discussing points, you need to remember that a point is a specific spot on Earth. If you were standing on a point and then you moved, you would no longer be on that same point. You would be on another point. This is a good way to remember that points do not move. See the illustration below for a visual explanation:

Here is a point. It is just a spot somewhere on Earth. It could be on your table, in the air, on your nose — it could be anywhere! Right now, let's pretend it is on your front lawn.

This is you standing on the point. It is important to remember, points do not move, so if you were to walk around you would no longer be on that point.

Pretend that you see another point and want to walk over to it. Again, you would leave the one point and go stand on a new point.

What if you saw another point? And another point? You could walk to each of them; just remember that when you reach them you are standing on a new point.

• How do you tell the difference between points?

Remember, they are everywhere, all around us.

In the above pictures, you should have noticed that each point was a different color. However, that is not how it really is with points.

All of the points around us are invisible. However, when you want to design something, you draw a picture. On your picture you represent what you are designing with points. It is necessary to label each point in your design so you can successfully build your project.

Let's imagine you are designing a fort that you are going to build in your back yard. The illustration below shows how you can begin your design with four points:

Notice that each letter used to label each point is capitalized. That is important to remember. When you are working with points in geometry and you have to label them, make sure you use capital letters.

In the illustration above, you are walking from point A to point B. Now that you have given each point a label, it will be easier to build your fort. You will be able to add the materials to connect the points and build the floor of your fort.

In your design, you can connect each point by drawing a line from one point to another. The lines would illustrate that, when building your fort, you will need to connect 4 boards to begin building the floor of your fort. This is where line segments come in handy!

When you draw a line from one point to another, it is called a line segment. Notice that each line, in your design, has a beginning and an end. That is what makes them line segments.

Your fort design is really beginning to take shape!

Just like naming or labeling the points, you can name or label the line segments, too! Let's pretend that you want to put a door at the front of your fort and a window at the back. In your design, you could draw a door on line segment DC and a window on line segment AB.

When you are writing your directions on how to construct your fort, you will need to write the line segments like this:

Notice the line drawn above the capital letters. That tells you that you are talking about a line segment.

• Can you name all 4 of the line segments in the picture above? I am sure you can!

Let's pretend that you want your fort to have a porch and that you want that porch to be attached to the right side of the fort. Let's also pretend that you want your porch to be even with the back of your fort but the rest of the porch will go past the front of your house.

You will need to go back to your design and change your line segment BC into a ray. A ray has a beginning point on one end. The other end of the ray could go on and on forever.

You know your porch is not going to go on and on forever, but drawing a ray in your design will remind you where you want your porch to go and that it is going to go past the front wall of your fort:

Take a look at your fort design.

• Do you see the difference between a line segment and a ray?

The ray has a definite endpoint, which in this example is point B, and an arrow on the other end that tells you it continues through point C and on forever. Of course, a ray needs a label, too.

Labeling a ray is similar to labeling a line segment, except that you will need to put an arrow above the letters instead of a line. Also, the letter under the end point of the arrow is the point where the ray begins, and the letter under the arrow is the point through which the ray continues.

Below is the label for the example above:

If you labeled this ray CB instead of BC you would not be talking about the same ray. Ray BC means it starts at point B and goes through point C. Ray CB means it starts at point C and goes through point B.

• See the difference?

Your fort design keeps looking better and better!

Now, let's pretend that you want an area on the other side of your fort for your friends to park their bikes. You may even want to use a board that is attached to the bottom of your fort to be the place where they lock their bikes.

In your design, you could just change line segment AD into a ray just like ray BC. However, you have SO many friends you would need a bigger area for all of their bikes to be parked!

Instead of making line segment AD a ray, you could make it a line! That way, the area to park the bikes will go past the front and the back of the fort.

A line has arrows at both ends. This means that it could go on and on in each direction. Of course, you know that your bike parking area will not go on and on in both directions forever; however, when you put the line in your design, it will remind you that the parking area is going to extend past the front and the back of your fort.

You would write the line AD like this:

Unlike rays, it does not matter which letter comes first when you are labeling or naming a line.

You have now learned how to draw a design for a fort using figures from geometry!

Take out a piece of paper and a pencil and draw your own design using points, line segments, rays, and lines.

You can also watch the video Line Segments, Lines, and Rays (below) to get a better understanding: