Math Antics - Polygons
mathantics
https://www.youtube.com/watch?v=IaoZhhx_I9s

Transkript (automatisch erstellt)

0:06 Hi there, welcome to Math Antics! So far, in our series on geometry, we've learned about points, lines, planes and angles.
0:14 In this lesson, we're going to learn about another important element of geometry. We're going to learn about polygons.
0:20 You probably already know a lot about polygons because you see them all the time. Here's some common examples that you might recognize.
0:28 These shapes are all polygons. That's because a polygon just means a multi-sided shape, and these shapes all have multiple sides.
0:37 Okay, so that's a basic definition of a polygon, but to really understand what is a polygon and what is NOT a polygon,
0:45 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.
0:54 And these parts are: sides, vertices, and angles. The sides are just the straight line segments that make up a polygon.
1:03 And the vertices are points where the sides intersect. And the angles are formed by the intersecting lines.
1:11 In fact, in Greek, the word polygon literally means "many-angles." So all polygons have sides, vertices and angles.
1:20 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.
1:30 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.
1:37 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.
1:47 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.
1:56 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.
2:05 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.
2:15 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,
2:23 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.
2:34 And even though polygons themselves can't be 3D shapes, you can use polygons to make 3D shapes. Like a box, for example.
2:43 The box is not a polygon. But each of it's flat sides is a polygon.
2:49 Alright then. We now have a specific definition of a polygon. A polygon is a multi-sided shape that has sides, vertices and angles.
2:59 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!"
3:10 Now here's your host: me! Thank you, thank you! Alright. Now the rules of the game are simple.
3:18 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?
3:26 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.
3:38 So it is a polygon. And next we have, hmmm. I'm not exactly sure what to call this, but, is it a polygon?
3:48 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?
3:59 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.
4:12 Ah, how about this one? Is a circle a polygon? Well, it is a closed, 2D shape, but how many sides does it have?
4:22 Now that's the problem. A circle doesn't have any straight sides, vertices or angles.
4:28 It's a curved shape, so it's not a polygon. Next we have a star shape, just like me! Is this a polygon?
4:38 Yup! It has straight sides and vertices, and it's a closed, 2D shape. That means it's a polygon!
4:47 And what about this one? Right you are, this is not a polygon! It's a dog! Ahh, here's an interesting one.
4:56 It's a closed, 2D shape that does have straight sides andvertices, but, it also has this curved part here.
5:05 Can it still be a polygon with that curve there? No! The curved part disqualifies it as a polygon.
5:14 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,
5:25 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.
5:36 And last of all, what about this one? Right you are, this is not a polygon because it's a 3D shape.
5:43 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.
5:50 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.
6:02 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:
6:12 3-sided polygons are called triangles. Triangle are so important in geometry, that they'll get a whole video of their own.
6:21 4-sided polygons are called quadrilaterals. Wow! Now that's a fancy math word!
6:27 But it helps if you just remember that the first part, "quad," means "4." Quadrilaterals are shapes like squares, rectangles, and parallelograms.
6:37 They'll also get a video of their own. 5-sided polygons are called pentagons.
6:43 6-sided polygons are called hexagons. And 8-sided polygons are called octagons.
6:50 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,
6:59 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.
7:08 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!
7:19 Good luck! Thanks for watching Math Antics, and I'll see ya next time.
7:24 Learn more at mathantics.com