(upbeat music) Good morning, my magnificent mathematicians.

I am so excited to be with you this morning.

We are going to have so much fun today learning more about math and growing our brains.

Today, I want us to review all the basic concepts of geometry.

Now, the word geometry comes from a Greek word that means to measure the Earth.

Geo means Earth and metron means measure.

But when I think about geometry, I don't think about measuring the Earth.

I always think about art.

Can you guess why?

All of geometry is based on three concepts: the point, the line, and the plane.

And from those three basic concepts, we get nine geometric elements.

Now I have Hayden here with me today, and he says that he's up for my geometry art challenge.

Hayden just finished middle school, and next year he'll be taking a whole class on geometry.

Hayden, how are you feeling?

I'm feeling great.

Susanna: You think you've got this?

Yeah, I think I got this.

But I need one thing.

Our magic whiteboard.

OK, Hayden.

So here are the rules.

You have to use all nine elements from the list to create one piece of art.

Now, you can use any of those elements more than once.

Just make sure you use all of them.

And if you win the challenge, you will earn one of your favorite things: a pack of hot chips.

Hayden, are you ready?

Yes.

Susanna: OK. Let's get started.

Now, while Hayden is drawing, we're going to review what all of those elements mean.

First, we have a point.

Now, a point is just a location.

Technically, a point doesn't have any dimension.

That means it doesn't have width.

It doesn't have length and it doesn't have depth.

It only has location.

And it tells us a very specific point in space.

But even though it doesn't have length or width or depth, we have to draw it somehow.

So we use a dot.

Second is a line.

A line is a set of points that extend infinitely in both directions.

To show that it goes on forever and ever, we put a line with arrows at both ends.

Our next element is a ray.

A ray begins in a specific location with a point and then it extends infinitely in one direction.

I tell my students to think about a ray of sunshine where the sun is like the starting point and the ray of sunshine shoots out from the sun and it goes on forever and ever.

We draw a ray with a starting point, and then we make sure to put an arrow on the other end.

Next, we have a line segment.

Now, a line segment is only part of the line, and it has two distinct endpoints.

To draw a line segment, we start with a point and we end with a point.

OK. Now let's talk about our three different types of angles.

So an acute angle is an angle that measures less than 90 degrees.

When we're not talking about geometry, the word acute can mean sharp, like an acute pain, something that hits you suddenly and doesn't last a long time.

Maybe that will help you remember that an acute angle looks like a sharp point.

Our next angle is a right angle.

A right angle measures exactly 90 degrees.

When two lines intersect each other at 90 degrees, and they're perpendicular to each other, they form a right angle.

And we show that by drawing a square down at the angle's vertex.

OK, our last angle is an obtuse angle.

This is an angle that measures more than 90 degrees.

The word obtuse actually comes from a Latin word that means dull or blunt.

So if the acute angle is sharp and has a small measure, the obtuse angle is dull and has a much larger measure.

We draw it by connecting two rays at a vertex point.

OK. One last definition that we mentioned at the beginning as one of the three basic concepts of geometry.

A plane.

A plane is a flat surface that extends infinitely.

You can think of it like a chalkboard or a sheet of paper.

And that's it for our definitions.

Are you ready to check on Hayden?

Let's see if he's going to win his geometry art challenge.

Hayden, this looks really great.

I love your drawing.

I'm going to go down the list, and then you show us where that element is in your art.

OK?

OK. First, where is a point.

We have our points all throughout the mountains.

Susann: Great job.

Hayden: Just scattered across.

Susanna: OK, what about a line?

Hayden: We have our line right here at the bottom with all the trees.

Susanna: And I see your arrows at both end Hayden: Yes.

Susanna: What about a ray?

Hayden: We have our rays as the trees, and they're all going up.

Susanna: Great job.

What about a line segment?

Hayden: We have our line segments throughout right here.

Susanna: With their endpoints.

What about an acute angle?

Hayden: Our first acute angle is this mountain.

Susanna: Uh huh.

And what about a right angle?

Hayden: Right here.

And then also the birds.

Susanna: Those are exactly 90 degrees.

Great job.

And what about an obtuse angle?

Hayden: Our obtuse angles right here and right here.

Susanna: And those are greater than 90 degrees.

Hayden: Yes.

Susanna: Oh, great job.

And you're going to get your prize, your bag of hot chips.

OK, that's all we have for today.

I hope you have an amazing day, and I'll see you next time on Rise and Shine.

Bye.

(upbeat music) (light music)