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Lines, Line Segments, and Ray

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Lines, Line Segments, and Rays | Exercise | Education.com

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Lines, Line Segments, and Rays will help students practice this key fourth grade skill. Try our free exercises to build knowledge and confidence.

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the different between lines and segments...

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Clil_ activity on 21 November, she is smart!!

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Questions:
•    What is geometry?
Is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
•    Is geometry Art or Math? Both
•    What do we use geometry for? To draw and create shapes, objects, etc.
Tools:Ruler, set of squares, compass and technical pens.
Geometric
Layouts

Parallel lines: Two lines in a plane that do not intersect or touch at a point are called parallel lines. Line m has everywhere the same distance to line.

Perpendicular lines: The segment AB is perpendicular to the segment CD because the two angles it creates (indicated in orange and blue) are each 90 degrees. If a line is perpendicular to another as shown, all of the angles created by their intersection are called right angles.

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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 segment a line a line and array and array and this is kind of the pure geometrical versions of these of these things and so a line segment is actually probably what most of us associate with a line in our everyday lives so a line segment is something just like that for lack of a better word a straight line but what 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 the segment is based on the fact that it has a ending point and the starting point our starting point and an ending point a line if you're thinking about it in the pure geometric sense of a line is essentially its 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 a line would look like this and to show that it keeps on going on forever and 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 our right over here so obviously yeah you know I've never encountered something that just keeps on going straight forever 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 array is something in between array has a well-defined starting point so that's its starting point but then it just keeps on going on forever so then so the Ray might start over here but then it just keeps on going then it just keeps on going so that right over there is array 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 on our classification right over here so let me get the module let me get the module going let me let me where did I put it where did I put it there you go all right so what is this thing right over here well there's two arrows on both ends so it's implying that 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 out correct next question all right now what about this thing well once again arrows on both sides 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 so it goes or one written think about it goes on forever and 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 in 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 that that gives you enough to work your way through this module and you might notice when I did this 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

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Lines, line segments, & rays (video) | Khan Academy

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If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

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1. watch the videos
2. search the key words
3. write the definition for each geometric shapes
4. Do the excercises in each videos
5. sketch on your excercise book (or app notability) any geometric shapes
6. Games. in a small team search any element in nature that are like shapes elements, for exemple: lines, segments, ray, plane,  but also square, circle and the other.

Win the team thas will have search a much more elements

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- [Instructor] What I wanna do in this video is give an introduction to the language or some of the characters that we use when we talk about geometry. And I guess the best place to start is to even think about what geometry means, 'cause you might recognize the first part of geometry. Right over here you have the root word geo, the same word that you see in things like geography and geology, and this refers to the earth. This refers, my E look like a C right over there, this refers to the earth. And then you see this metry part. And you see metry in things like trigonometry as well. And metry, or the metric system, and this comes from measurement. This comes from measurement, or measure, measurement. So when someone's talking about geometry, the word itself comes from earth measurement and that's kind of not so bad of a name, because it is such a general subject. Geometry really is the study and trying to understand how shapes and space and things that we see relate to each other. So, you know, when you start learning about geometry, you learn about lines and triangles and circles and you learn about angles and we'll define all of these things more and more precisely as we go further and further on, but it also encapsulate things like patterns and three-dimensional shapes, so it's almost everything that we see, all of the visually mathematical things that we understand can in some way be categorized in geometry. Now, with that out of the way, let's just start from the basics, a basic starting point from geometry, and then we can just grow from there. So if we just start at a dot. That dot right over there is just a point, it's just that little point on that screen right over there. We literally call that a point. And I'll call that a definition. And the fun thing about mathematics is that you can make definitions. We could have called this an armadillo, but we decided to call this a point, which I think makes sense because it's what we would call it in just everyday language as well. That is a point. Now, what's interesting about a point is that it is just a position that you can't move on a point. If you were on this point and you moved in any direction at all, you would no longer be at that point, so you cannot move on a point. Now, there are differences between points, for example, that's one point there. Maybe I have another point over here and then I have another point over here and then another point over there. And you want to be able to refer to the different points, and not everyone has the luxury of a nice, colored pen like I do, otherwise they could refer to the green point or the blue point or the pink point, and so in geometry, to refer to points, we tend to give them labels, and the labels tend to have letters. So, for example, this could be point A, this could be point B, this would be point C, and this right over here could be point D. So if someone says, "Hey, circle point C," you know which one to circle. You know that you would have to circle that point right over there. Well, that so far, it's kind of interesting. You have these things called points. You really can't move around on a point, all they do is specify a position. What if we wanna move around a little bit more? What if we wanna get from one point to another? So what if we started at one point and we wanted all of the points, including that point that connect that point and another point? So all of these points right over here. So what would we call this thing, all of the points that connect A and B along a straight, and I'll use everyday language here, along kind of a straight line like this? Well, we'll call this a line segment. In everyday language, you might call it a line, but we'll call it a line segment, 'cause we'll see when we talk in mathematical terms, a line means something slightly different. So this is a line segment. And if we were to connect D and C, this would also be another line segment, a line segment. And once again, because we always don't have the luxury of colors, this one is clearly the orange line segment. This is clearly the yellow line segment. We want to have labels for these line segments. And the best way to label the line segments are with its endpoints, and that's another word here. So a point is just literally A or B, but A and B are also the endpoints of these line segments, 'cause it starts and ends at A and B. So let me write this A and B. A and B are endpoints, another definition right over here. Once again, we could have called them aardvarks or end armadillos, but we, as mathematicians, decided to call them endpoints, because that seems to be a good name for it. And once again, we need a way to label these line segments that have the endpoints, and what's a better way to label a line segment than with its actual endpoints? So we would refer to this line segment, over here, we would put its endpoints there. And to show that it's a line segment, we would draw a line over it, just like that. This line segment down here, we would write it like this. And we could have just as easily written it like this, CD with a line over it would have referred to that same line segment. BA, BA with a line over it would refer to that same line segment. And now you might be saying, "Well, I'm not satisfied just traveling in between A and B." And this is actually another interesting idea. When you were just on A, when you were just on a point and you couldn't travel at all, you couldn't travel at all in any direction while staying on that point, that means you have zero options to travel in. You can't go up or down, left or right, in or out of the page and still be on that point. And so that's why we say a point has zero dimensions, zero dimensions. Now all of the sudden we have this thing, this line segment here, and this line segment, we can at least go to the left and the right along this line segment. We can go towards A or towards B. So we can go back or forward in one dimension. So the line segment is a one-dimensional, it is a one-dimensional idea almost, or a one-dimensional object, although these are more kind of abstract ideas. There is no such thing as a perfect line segment, because a line segment, you can't move up or down on this line segment while being on it, while in reality, anything that we think is a line segment, even you know, a stick of some type, a very straight stick, or a string that is taut, that still will have some width, but the geometrical pure line segment has no width, it only has a length here. So you can only move along the line, and that's why we it's one-dimensional. A point, you can't move at all. A line segment, you can only move in that back and forth along that same direction. Now, I just hinted that it can actually have a length. How do you refer to that? Well, you refer to that by not writing that line on it. So if I write AB with a line on top of it like that, that means I'm referring to the actual line segment. If I say that, let me do this in a new color, if I say that AB is equal to five units, it might be centimeters, or meters, or whatever, just the abstract units five, that means that the distance between A and B is five, that the length of line segment AB is actually five. Now, let's keep on extending it. Let's say we wanna just keep going in one direction. So let's say that I start at A, let me do this in a new color, let's say I start at A and I wanna go to D, but I want the option of keep on, I wanna keep on going, so I can't go further in A's direction than A, but I can go further in D's direction. So this little, this idea that I just showed, essentially, it's like a like segment, but I can keep on going past this endpoint, we call this a ray. And the starting point for a ray is called the vertex, not a term that you'll see too often. You'll see vertex later on in other contexts, but it's good to know, this is the vertex of the ray. It's not the vertex of this line segment, so maybe I shouldn't label it just like that. And what's interesting about a ray, it's once again a one-dimensional figure, but you could keep on going in one of the (murmurs), you can keep on going to or past one of the endpoints. And the way that we would specify a ray is we would say, we would call it AD and we would put this little arrow over on top of it to show that is a ray. And in this case, it matters the order that we put the letters in. If I put DA as a ray, this would mean a different ray. That would mean that we're stating at D and then we're going past A, so this is not ray DA, this is ray AD. Now, the last idea that I'm sure you're thinking about is, well, what if I could keep on going in both directions? So let's say I can keep going in, let me, my diagram is getting messy. So let me introduce some more points. So let's say I have point E and then I have point F right over here. And let's say that I have this object that goes through both E and F, but just keeps on going in both directions. This is, when we talk in geometry terms, this is what we call a line. Now, notice, a line never ends. You can keep going in either direction. A line segment does end, it has endpoints, a line does not. And actually, a line segment can sometimes be called just a segment. And so you would specify line EF, you would specify line EF with these arrows just like that. Now, the thing that you're gonna see most typically when we're studying geometry are these right over here, because we're gonna be concerned with sides of shapes, distances between points. And when you're talking about any of those things, things that have finite length, things that have an actual length, things that don't go off forever in one or two directions, then you are talking about a segment or a line segment. Now, if we go back to a line segment, just to kind of keep talking about new words that you might confront in geometry. If we go back talking about a line, that time I was drawing a ray, so let's say I have point X and point Y. And so this is line segment XY, so I could denote it just like that. If I have another point, let's say I have another point right over here, let's call that point Z, and I'll introduce another word, X, Y, and Z are on the same, they all lie on the same line if you would imagine that a line could keep going on and on forever and ever. So we can say that X, Y, and Z are colinear. So those three points are co, they are colinear. They all sit on the same line and they also all sit on line segment XY. Now, let's say we know, we're told that XZ is equal to ZY and they are all colinear. So that means this is telling us that the distance between X and Z is the same as the distance between Z and Y. So sometimes we can mark it like that. This distance is the same as that distance over there. So that tells us that Z is exactly halfway between X and Y. So in this situation we would call Z the midpoint, the midpoint of line segment XY, 'cause it's exactly halfway between. Now, to finish up, we've talked about things that have zero dimensions, points. We've talked about things that have one dimension, a line, a line segment, or a ray. You might say, well, what has two dimensions? Well, in order to have two dimensions, that means I can go backwards and forwards in two different directions. So this page right here, or this video, or this screen that you're looking at is a two-dimensional object. I can go right, left, that is one dimension, or I can go up, down. And so this surface of the monitor you're looking at is actually two dimensions, two dimensions. You can go backwards or forwards in two directions. And things that are two dimensions, we call them planar, or we call them planes. So if you took a piece of paper that extended forever, it just extended in every direction forever, that in a geometrical sense was a plane. The piece of paper itself, the thing that's finite, and you'll never see this talked about in a typical geometry class, but I guess if we were to draw the analogy, you could call a piece of paper maybe a plane segment, because it's a segment of an entire plane. If you had a third dimension, then you're talking about kind of our three-dimensional space. In three-dimensional space, not only could you move left or right along the screen, or up and down, you could also move in and our of the screen. You could also have this dimension that I'll try to draw. You could go into the screen or you could go out of the screen like that. And as we go into higher and higher mathematics, although it becomes very hard to visualize, you'll see that we can even start to study things that have more than three dimensions.

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Terms & labels in geometry (video) | Khan Academy

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Instructor] What I wanna do in this video is give an introduction to the language or some of the characters that we use when we talk about geometry. And I guess the best place to start is to even think about what geometry means, 'cause you might recognize the first part of geometry.