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  • Hi there, welcome to Math Antics!

  • So far, in our series on geometry, we've learned about points, lines, planes and angles.

  • In this lesson, we're going to learn about another important element of geometry.

  • We're going to learn about polygons.

  • You probably already know a lot about polygons because you see them all the time.

  • Here's some common examples that you might recognize.

  • These shapes are all polygons. That's because a polygon just means a multi-sided shape,

  • and these shapes all have multiple sides.

  • Okay, so that's a basic definition of a polygon,

  • but to really understand what is a polygon and what is NOT a polygon,

  • we need to learn about the specific properties that all polygons have in common.

  • First we need to know the three parts that make up all polygons.

  • And these parts are: sides, vertices, and angles.

  • The sides are just the straight line segments that make up a polygon.

  • And the vertices are points where the sides intersect.

  • And the angles are formed by the intersecting lines.

  • In fact, in Greek, the word polygon literally means "many-angles."

  • So all polygons have sides, vertices and angles.

  • This polygon here has 5 sides, 5 vertices and it forms 5 angles.

  • The next thing we need to know about polygons is that they're 'closed' shapes.

  • Now what does it mean for a shape to be closed you ask?

  • Well, it means that the sides are connected so that there are no gaps.

  • The area inside the shape is separated from the area outside the shape,

  • and there's no way to get from the inside to the outside without crossing a line.

  • It might help to think of a closed shape like a cage.

  • If you put an ant inside the cage, there's no way for it to get out without crossing a line.

  • But if the shape is open, then there is a way out.

  • So these are all examples of closed shapes, and these are all examples of open shapes.

  • And the important thing to remember is that a polygon must be closed.

  • And the last thing we need to know about polygons is that they're 2 dimensional, or flat shapes.

  • And that means that all the vertices must lie on the same plane.

  • If any one of the vertices were to move forwards or backwards,

  • so that it wasn't in the same plane as all the other vertices, then it wouldn't be a flat shape anymore.

  • Flat shapes are also called planar shapes because all of their points are on the same plane.

  • And even though polygons themselves can't be 3D shapes, you can use polygons to make 3D shapes.

  • Like a box, for example.

  • The box is not a polygon.

  • But each of it's flat sides is a polygon.

  • Alright then. We now have a specific definition of a polygon.

  • A polygon is a multi-sided shape that has sides, vertices and angles.

  • A polygon is a closed shape, and a polygon is a 2 dimensional, or flat shape.

  • And now that you know that, it's time to play "Polygon or NOT a Polygon!"

  • Now here's your host: me!

  • Thank you, thank you! Alright. Now the rules of the game are simple.

  • I'm gonna show you a shape, and you tell me if it's a shape, and you tell me if it's a polygon or not a polygon.

  • Are you ready to play?

  • Our first shape is a square! Is a square a polygon?

  • Yes! A square has 4 sides and 4 vertices and it's a closed, 2D shape.

  • So it is a polygon.

  • And next we have, hmmm. I'm not exactly sure what to call this, but, is it a polygon?

  • Nope! It's close, but because it's an open shape, it can't be a polygon.

  • Alright, what about this one? Polygon or not a polygon?

  • Yep! It is a polygon. Even though the sides are not all the same length,

  • it is a closed, 2D, multi-sided shape. In fact, if you count, you'll see it has 7 sides.

  • Ah, how about this one? Is a circle a polygon?

  • Well, it is a closed, 2D shape, but how many sides does it have?

  • Now that's the problem.

  • A circle doesn't have any straight sides, vertices or angles.

  • It's a curved shape, so it's not a polygon.

  • Next we have a star shape, just like me! Is this a polygon?

  • Yup! It has straight sides and vertices, and it's a closed, 2D shape.

  • That means it's a polygon!

  • And what about this one? Right you are, this is not a polygon! It's a dog!

  • Ahh, here's an interesting one.

  • It's a closed, 2D shape that does have straight sides andvertices,

  • but, it also has this curved part here.

  • Can it still be a polygon with that curve there?

  • No! The curved part disqualifies it as a polygon.

  • A polygon has to have only straight sides, so this is not a polygon.

  • And what about this guy here? Is this a polygon? Well, it is just straight lines,

  • but two of those lines cross, and if any lines cross it can't be a polygon.

  • Plus, he has this big open end here. So this guy is definitely not a polygon.

  • And last of all, what about this one?

  • Right you are, this is not a polygon because it's a 3D shape.

  • It's made from polygons, but the whole shape is not a polygon itself.

  • Well, that's all the time we have for this week.

  • Join us next week as we decide: "Is it Bigger than One?"

  • Okay, so after playing that game, you have a really good idea of what a polygon is, and what it is not.

  • The last thing I want to mention is that some polygons have special names depending on how many sides they have.

  • Here's a list of the most important ones to know:

  • 3-sided polygons are called triangles.

  • Triangle are so important in geometry, that they'll get a whole video of their own.

  • 4-sided polygons are called quadrilaterals.

  • Wow! Now that's a fancy math word!

  • But it helps if you just remember that the first part, "quad," means "4."

  • Quadrilaterals are shapes like squares, rectangles, and parallelograms.

  • They'll also get a video of their own.

  • 5-sided polygons are called pentagons.

  • 6-sided polygons are called hexagons.

  • And 8-sided polygons are called octagons.

  • By the way, polygons that have 5, 6, 8, or however many sides like this,

  • are called regular polygons if all of their angles are equal,

  • and irregular polygons if their angles are not equal.

  • Of course, there are a lot more polygons than that, but you probably won't need to know their names.

  • As long as you know what polygons are, and how to identify them, then you're ready to move on.

  • The exercises for this section are pretty easy, so no excuses!

  • Good luck!

  • Thanks for watching Math Antics, and I'll see ya next time.

  • Learn more at mathantics.com

Hi there, welcome to Math Antics!

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