 In this video, I'm going to very quickly go over a couple of vocabulary words here. Some of these you might already know, but it's always good to go over these, especially with the new notation that you're going to see. Parallel lines, perpendicular lines, skew lines, and parallel planes. These are the four that I'm going to go over very quickly. Now, if you look over here, if you look over here, we're going to do this with a cube. Okay? So we're going to look at parallel lines and perpendicular lines and all sorts of different stuff with this cube. Now, those here, we have these red arrows. These red arrows right here, those mean that those lines are parallel. Okay? These are some of the parallel notation that we use, so AB and EF are parallel. And then also, these double arrows down here kind of mean the same thing. It just means a different set of parallel lines, EH and FG is a different set of parallel lines. Okay? Now, this down here in the corner by H, that's the same, that's what you would normally think. That's a right angle. It's a 90-degree angle. And then same thing up here with B. This right here is also a 90-degree angle. It doesn't quite look the same here, but again with a three-dimensional object, we're looking at the top of this box, okay, top of this cube. And so it's skewed just a little bit, but what it means is still the same, is that it's just going to be a 90-degree angle just like the one down there. Okay? So we're going to use this cube to go over a couple of these different vocabulary words. So here we go. Parallel lines, it's just like what you normally think. Parallel lines are lines that do not intersect. They do not intersect. Okay? Now again, this is a vocabulary word you've used many times in different math classes. It's nothing, anything different. Okay? Now, what we're also going to look at here is some of the little bit of notation that you might see that might be a little bit different, might be new to you. Okay? So I'm going to choose two lines that are going to be parallel. Now A and B, or excuse me, AB and EF are obviously parallel. Let's choose something else. Something like CG and DH, okay? Those ones there on the bottom, those ones are in fact parallel, so I'm going to use those. So DH, that segment, is parallel, is parallel to CG. Okay? Now notice the symbol that I use here. This is our parallel symbol. Two vertical lines going up and down. That's our parallel symbol. It's kind of a shorthand for parallel. That's what we commonly use. Okay, next, next we have perpendicular lines. Okay? So perpendicular lines are when two lines intersect, draw a quick picture here. When two lines intersect, they form a 90-degree angle. Well, in fact, to be a little bit more precise, four 90-degree angles are formed. One here, there's one over here, there's one there, and there's one there. Okay? So all four of those angles are actually 90 degrees. Okay? So we've got to be a little bit more precise when we go through our definition here. So a perpendicular lines are lines that intersect to form, now this is where that new stuff comes in, four 90-degree angles. Okay? Using a little bit more notation here, this is the angles, angle symbol right there, angles, okay, for plural. All right? So lines that intersect to form four 90-degree angles, so being a little bit more formal with our definitions, giving out a little bit more information, not just that it intersects to form 90 degrees, we form four 90-degree angles, just a little bit of extra there. Okay? So let's look at a couple of lines that could be perpendicular. Okay, this time I will just use the obvious ones here. So H, C, and H, E are in fact perpendicular, so I'm going to use those as my example. So E, H, that segment, is perpendicular to HG, is perpendicular to HG. So notice that this symbol in the middle looks like an upside-down T, okay, it looks like two perpendicular lines, that is in fact our perpendicular symbol that we use, okay, that's our perpendicular symbol. Just like Parallel's got its own symbol up here, perpendicular's also got its own symbol. Okay. Next on the list, skew lines, skew lines. So when we're dealing with three-dimensional objects like this cube over here, there are certain lines that actually do not interact with each other at all. So these lines we call skew lines, okay, so an example of something that doesn't interact with each other, an example like EH, okay, there's one segment here, and then over here, CG, these two lines have nothing to do with one another. This one goes up and down, this one goes back and forth, forward and backwards. They don't intersect, they're never going to cross each other. They're not parallel, they're not the same distance apart. They really don't interact with each other at all. So skew lines are actually very different. Now again, these can only happen in three-dimensional space, so it can only happen with a three-dimensional cube like this, okay. So skew lines are lines, let's use a different color here, let's use a different color, change things up a bit. Okay, these are lines, lines that are not parallel and, and are not, oh wait, I should rewind there, they do not intersect, and do not, intersect is a, is a verb, so I got to use do, not, intersect, do not intersect, okay. An example of this, as we stated earlier, it would be EH and CG, EH and, use my ampersand symbol here, this means and, and CG, that segment there, okay. So that gives you an example. Now again, there are many, many examples of these, even within this cube that we have here, but I'm just giving one example, keep this nice, short and sweet. All right, last but not least, we have parallel lines, or excuse me, not parallel lines, parallel planes, just like parallel lines up here, it's going to be basically the same definition, except for we're talking about planes, and again, we're going to go over the notation just a little bit. So these are planes, planes that do not intersect, two planes that do not intersect. So this would be like lines on a highway, or excuse me, not lines on a highway. We're talking about two planes. This would be like the top of a table, and the floor. Those are two planes that don't intersect, okay, they're both parallel. That's an example, a real-life example of one. All right, anyway, now an example of two planes in this figure. Now what we have to do is we have to define the planes first. Now to do that, we need three points for a plane. One point makes a point, two points make a line, three points make a plane, okay. Notice the logical progression of the numbers of points making the different shapes. So anyway, what we need to do is we need to figure out some points to use for our faces, for our planes. So in this case for our cube, we have a front face and a back face and a left face and a right face and a top face and a bottom face. We've got lots of different faces, lots of different planes to use. Okay, so for this example, I'm just going to use the front face here, because it's staring us right in the face. And we're going to use the back face, way back there, okay. Notice these dotted lines here, I forgot to mention that earlier. These dotted lines here represent the backs that we can't see. Those are the lines that we can't see. Those are behind everything, can't quite see those. Anyway, so this front face, notice the points here, E, F, G, H. Those are the four points that make up that face. But again, I only need three of them to define a plane. So I'm just going to use E, F, G, just stay with the alphabet. So E, F, G is a plane and it is parallel. Now that's the front face, now I want the back face. Back face is A, B, C, D. As I said before, we only need three points. I'm just going to use A, B, and C. I'm going to use, get rid of that, A, B, and C. So the plane, E, F, G and the plane, A, B, C, they are in fact parallel. This would be our front face and the back face of our cube up there. Okay, that's just a little bit of vocabulary that goes along with the section that we are learning. Again, that vocabulary is parallel lines, perpendicular lines, skew lines, and parallel planes.