Topic D: Foundations
- [Voiceover] What I wanna talk about in this video is shapes with four sides, and the mathy word for shapes with four sides is quadrilateral. Quadrilateral. And any time you see quad as part of a word, it's a good, it's a good sign that you're dealing with the number four somehow. So a quadrilateral is something that has four sides. So that is a quadrilateral, this is a quadrilateral, this is a quadrilateral. They all have four sides. This is a quadrilateral. even this is a, let me make it look even weirder, even this is a quadrilateral. So what's not a quadrilateral? Well, a triangle would not be a quadrilateral. It has three sides, one, two, three. So let's cross that out. A pentagon that has five sides, that would not be a quadrilateral. It has one, two, three, four, five sides. A circle that has, I guess you could say, no sides, it's just one big curve, it's a circle. That's not going to be a quadrilateral. If you had six sides, seven sides, a hundred sides, none of that is going to be a quadrilateral. So now let's think about the different types of quadrilaterals, or the different categories of quadrilaterals. So one is the parallelogram. So a parallelogram is a quadrilateral, and as we learn more math, we'll learn other ways of thinking about this. It's a quadrilateral where opposite sides are parallel. And parallel is just another way of saying that they're going in the same direction. So what do I mean by that? So something like this, something like this, would be a parallelogram. Why? Because this side is opposite to this side, and they're pointed in the same direction. They're going, they're going, if I were to draw an arrow, if I were to draw an arrow here, those arrows are pointed in the same way. So those two sides are pointed, are parallel, is the word we say. And these two sides, these two sides right over here are parallel. So this is a parallelogram. So what are other examples of parallelogram? Well even your classic square, even your classic square, is a parallelogram. And we'll talk more about what makes a square special. It's a special type of parallelogram because this side is going in the same direction as that side, and this side, and this side, whoops, let me do that in yellow, and this side is parallel to that side. So what's not a parallelogram? Well, something like, something like this would not be a parallelogram. You might say, "Wait, "I see two opposite sides are parallel." You might say, "Look, this is parallel to this." But then you would see that this is not parallel to this. One way to think about some things that are not parallel is if the lines kept going, they would cross each other at some point, while these lines, these lines right over here, they're never going to cross each other. So this one right over here is not a parallelogram. It has one set of opposite sides being parallel, but not the other. Another example of something that is not a parallelogram would be this one right over here, because none of the opposite sides are parallel. So parallelogram, opposite sides are parallel. So now let's talk about, let's talk about more types of four sided shapes, or quadrilaterals. So the next one we'll talk about is the rhombus. So the rhombus is a type of parallelogram. The opposite sides need to be parallel, but that's not, by itself, that doesn't make it a rhombus. The opposite sides need to be parallel, and all the sides have to be equal. So for example, this that I'm drawing, that is a parallelogram, but it is not a rhombus. It's a parallelogram because that side, these opposite sides are parallel. If they kept going, they would not cross each other. And these two opposite sides are parallel. So it's a parallelogram, but it's not a rhombus because the blue sides are longer than the yellow sides. So that is not a rhombus. A rhombus would have to look like this. A rhombus would have to look like that. So opposite sides are parallel and all the sides are the same length. And now you might say, "Well maybe a square is a rhombus," and I want you to think about that. Is a square a rhombus? Are all the sides the same length, and are the opposite sides parallel? Well we already said that the opposite sides of a square are parallel. A square is a parallelogram. And all the sides of a square are the same length. So a square is a rhombus. So one way to think about rhombuses, or rhombi, is they're squares, and you could kind of view them as kind of a pushed over version of squares, if a square was moving really, really, really fast in a cartoon, that's what my brain thinks of when I think of a rhombus. So now let's think of rectangle. And you might have heard the word rectangle in the past, but let's think a little bit more about what makes a rectangle. So a rectangle is going to be a parallelogram, but that by itself does not make it a rectangle. So for example, this right over here is a rectangle. Why is it? Well it's definitely a parallelogram. This side and that side are parallel. They'll never intersect. And this side and this side are parallel. They're never, they're never going to intersect if you kept going on and on and on, or they're never going to cross each other. But what makes it a rectangle? It's definitely a parallelogram, but what makes it, why do we use the word rectangle? Well one way to think about it is they way that they come together at the corners. So in a rectangle, the things come in to, I guess you could call them square corners. And that's called a right angle. That's called a right angle right over there. So this is what makes a rectangle. It's a parallelogram where all the corners are right angles. You could put a little square there, if you wanna think about it that way. So for example, this right over here would not be a rectangle. Why? Cause you can't, if you put a square here, notice. That does not, a square doesn't fit in the corners the way that it fits right over here. That you have, the square does not fit over here. This is a parallelogram, but not a rectangle. A rectangle is a parallelogram that has square corners. But what about our square? Is a square a rectangle? Well let's draw it out. Well let's think about it. A square, opposite sides are parallel. We've already said it's a parallelogram. And a square has, the corners are square. That's where when people say make a square corner, that's where it comes from. The corners are square. They are at right angles. So the square is a rectangle. So the square is a really interesting quadrilateral, because a square falls in to all of these categories. The square, a square is a square, it's a rhombus, it's the type of rhombus where the corners are right angles, or you could say where the corners are square. This one right over here is not a square, this one is square. They're both rhombuses, or they're both rhombi. A square is also a rectangle. It's a parallelogram where the corners are right angles, where they are square. A square is definitely a parallelogram, and everything we've talked about is a quadrilateral.