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Lines, line segments, & rays

Learn the difference between lines, line segments, and rays.  Created by Sal Khan.

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Video transcript

What I want to do in this video is think about the difference between a line segment, a line, and a ray. And this is the pure geometrical versions of these things. And so, a line segment is actually probably what most of us associate with a line in our everyday lives. A line segment is something just like that. For lack of a better word, a straight line. But why we call it a segment is that it actually has a starting and a stopping point. So, most of the lines that we experience in our everyday reality are actually line segments when we think of it from a pure geometrical point of view. and I know I drew a little bit of a curve here, but this is supposed to be completely straight, but this is a line segment. The segment is based on the fact that it has an ending point and a starting point, or a starting point and an ending point. A line, if you're thinking about it in the pure geometric sense of a line, is essentially, it does not stop. It doesn't have a starting point and an ending point. It keeps going on forever in both directions. So a line would look like this. And to show that it keeps on going on forever in that direction right over there, we draw this arrow, and to keep showing that it goes on forever in kind of the down left direction, we draw this arrow right over here. So obviously, I've never encountered something that just keeps on going straight forever. But in math-- that's the neat thing about math-- we can think about these abstract notions. And so the mathematical purest geometric sense of a line is this straight thing that goes on forever. Now, a ray is something in between. A ray has a well defined starting point. So that's its starting point, but then it just keeps on going on forever. So the ray might start over here, but then it just keeps on going. So that right over there is a ray. Now, with that out of the way, let's actually try to do the Khan Academy module on recognizing the difference between line segments, lines, and rays. And I think you'll find it pretty straightforward based on our little classification right over here. So, let me get the module going. Where did I put it? There you go. All right. So what is this thing right over here? Well, it has two arrows on both ends, so it's implying that it goes on forever. So this is going to be a line. Let's check our answer. Yeah, it's a line. Now it's taking some time, oh, correct, next question. All right, now what about this thing? Well, once again, arrows on both sides. It means that this thing is going to go on forever in both directions. So once again, it is a line. Fair enough. Let's do another one. Here we have one arrow, so it goes on forever in this direction, but it has a well-defined starting point. So it starts there, and then goes on forever. And if you remember, that's what a ray is. One starting point, but goes on forever. Or one way to think about it, goes on forever in only one direction. So that is a ray. So let's do another question. This right over here, you have a starting point and an ending point, or you could call this the start point and the ending point, but it doesn't go on forever in either direction. So this right over here is a line segment. There you go. So hopefully that gives you enough to work your way through this module. And you might notice, when I did this module right here, there is no video. And that's exactly what this video is. It's the video for this module.