Lesson Video: Straight Lines, Line Segments, and Rays | Nagwa Lesson Video: Straight Lines, Line Segments, and Rays | Nagwa

# Lesson Video: Straight Lines, Line Segments, and Rays Mathematics • 3rd Grade

In this video, we will learn how to identify points, lines, rays, line segments, and endpoints.

15:54

### Video Transcript

Straight Lines, Line Segments, and Rays

In this lesson, we’re going to learn how to identify points, lines, rays, line segments, and endpoints. Let’s start with a line and a question. When is a line not a line? Well, this might seem like quite a strange question to be asking. But hopefully by the end of this video, you’ll understand that the answer to this question is “when we’re speaking mathematically.” Because you know maths has its own vocabulary, its own language of words and terms that mean very special things.

A good example of this is the word “sum.” Perhaps you’ve heard people use the word “sum” to mean calculation. I did a whole page of sums today. Well, we know that if we’re speaking mathematically, the word “sum” means something very definite. When we find the sum of some numbers, it’s to do with addition; we add them together. So, if we’re speaking mathematically, we can’t really use the word “sum” to mean any calculation. It has to mean addition.

And did you know, if we want to use the language of maths properly, what we would normally describe as a line in everyday life isn’t actually a line. Let’s use an example to find out more. And as we do, we’re going to learn some other words to do with lines, and each one is going to be part of this language of maths.

This is Archie. He’s waiting for a bus. And as you do when you wait for a bus, he’s standing still at an exact position. We could even label this position. We’ll call it 𝐴. And in the language of maths, do you know the word we use to describe an exact position like this? It’s a point. There are lots of points we could draw, but only one point that Archie’s standing at. And that’s point 𝐴. Now let’s imagine time goes on and a few more people join the queue. One of them is Archie’s good friend Bert. Bert’s standing at an exact position too. It’s another point, B for Bert, so let’s call this point 𝐵.

Now what if we get a ruler and we join up point 𝐴 with point 𝐵? It sort of represents our queue of people, doesn’t it? Now normally you might say that something that looks like this or this or this is a line. As we’ve said already, in this video, we’re going to be talking the language of maths. And so this line isn’t a line. It’s part of a line. It’s what we call a line segment.

Because this can be tricky to understand, let’s write down what we actually mean by a line segment. A line segment, as we said already, is part of a line with two endpoints. Here’s another new word for us. What do you think an endpoint is? Well, it won’t surprise you to learn that an endpoint is a point on the end. These are at the end of line segments. So point 𝐴 and point 𝐵 are endpoints. And this teaches us something very important about lines in maths. A line goes on forever. The idea of something going on and on and on forever is quite difficult. But in maths, this is what we mean by a line. And because we can see that what we’ve drawn here starts and then stops at two different endpoints, we can see that it doesn’t go on forever. This is just part of a line that goes on and on and on. It’s a line segment.

Now let’s imagine that this bus doesn’t turn up and more and more people join the queue after Bert. The queue just goes on and on and on and on. In fact, they never ever stop. It just keeps on going forever. Now we’ve reached the end of our screen here. But how can we show that this goes on and on and on because at the moment it looks like we’ve got another endpoint. Why don’t we draw an arrowhead at the end? There we go. Now we’ve shown that it doesn’t end. It carries on going forever.

But do you know, in maths, we still can’t call this a line. Although the arrow at one end shows that it does carry on forever in one direction, we can see that what we’ve drawn does actually have an endpoint. It’s the point where Archie is standing at the front of the queue. He’s still standing at a fixed endpoint. And there’s a word for what we’ve got here, another word to add to our maths vocabulary. What we can see here is a ray. Let’s think about the Sun’s rays for a moment. They start at an exact position. They come from the Sun, don’t they? But the Sun’s rays travel in straight lines and go on and on and on from that starting point. It’s a useful way to remember what the word “ray” in maths means. We start from a point and then keep on going on and on and on and on.

Now so far everyone’s standing very politely in this queue waiting for the bus. So Archie turns around to say hello to Bert. But unfortunately, just as he does this, while his back’s turned, somebody pushes in and then someone else and someone else. We’ve run out of room again. So, to show that our queue is going on and on and on in this direction, let’s draw another arrowhead. And you’ll be pleased to know we’ve just drawn a line, because in maths a line is a straight path. You can see what we’ve drawn is straight, can’t you? It’s a straight path that continues in both directions, not just in one direction like a ray, which doesn’t end. It just goes on and on and on and on and on and on. We’ll stop there, but you know what we’re trying to say.

Just before we answer some questions based on these words that we’ve learned, let’s just go over them again. Let’s get rid of the queue and just draw this on a blank page. If we draw two dots on a page and label them 𝐶 and 𝐷, what have we got? These are two points, aren’t they? They’re two exact positions: point 𝐶 and point 𝐷.

Now if we take a ruler and we join point 𝐶 up with point 𝐷, what have we got? Well, what we’ve got has two endpoints, doesn’t it, one here and one here? What we’ve drawn starts and stops. We’ve drawn a line segment. It’s part of a line, and it’s got two endpoints. We could call it line segment 𝐶𝐷. It goes from 𝐶 and stops at 𝐷.

What else can we do? Well, what if we extend our line segment past point 𝐷 on and on and on? And to show that it goes on and on and on, we’ll put an arrow. What we’ve drawn now only has one endpoint. We can’t really say what’s happening at the other end because there is no other end. It just keeps on going on and on and on. What we’ve got here is still part of a line. It’s a ray. We know that rays start from a point and continue in one direction. And because we start at point 𝐶, we go through point 𝐷 and carry on going, we could call this ray 𝐶𝐷. So, if this is ray 𝐶𝐷, what’s this? We can see it’s still a ray, but this time the endpoint is point 𝐷. And our ray continues through point 𝐶 on and on and on. So it’s still a ray; it’s just continuing in the opposite direction.

Finally then, what if we show that what we’ve drawn goes on and on in both directions? It doesn’t have any endpoints. We know that a straight path that continues in both directions and never ends is called a line. And we could call this line 𝐶𝐷 because it passes through points 𝐶 and 𝐷.

Now how well do you think you’ve learned these words? Let’s answer some questions now where we have to practice our knowledge of what they mean.

Which of the following figures is a straight line?

In this question, we’re given five pictures or figures. And we’re told that we need to find which one of them is a straight line. Now perhaps before we start, we can see that one of these figures is definitely not a straight line. Figure (e) is curved, isn’t it? So we can be sure that (e) isn’t the right answer. But what about the others? Let’s go through each one and look at how they’re different.

Figure (a) is a shape. It looks like the letter H, doesn’t it? Figure (b) definitely looks like we could call it a straight line. And figure (c), in fact this looks almost the same as figure (b), except it has two arrowheads, one on either end. But then (d) also looks like a straight line. This time it’s only got one arrowhead.

Well, to answer this question, we need to think about what the word “straight line” means in maths because it means something very definite. In maths, a line is a straight path that continues in both directions and does not end. If we think about figure (b) for a moment, we can see that it definitely starts and stops. It’s a certain length, isn’t it? It has what we call two endpoints. Now, if a line goes on and on and on in both directions, we can see that this is only part of our line, doesn’t go on and on at all. Figure (b) is a line segment. And although we might have said that the shape in figure (a) is made up of lots of straight lines, we can see now that each one starts and stops. This shape is made of lots of line segments.

It looks like our answer is either going to be figure (c) or (d). Which one of these is a straight path that continues in both directions and doesn’t end? Well, if we look at figure (d) for a moment, we can see that it does have a start point. At the other end, it goes on and on. We can tell this because we can see an arrowhead. But it doesn’t go on and on in both directions. It’s only in one direction. This is what we call a ray. And so if we look at figure (c), we can see arrowheads at both ends. This is a straight path that does continue in both directions. It doesn’t matter which way we travel. It’s going to go on and on and on. The figure that is a straight line is figure (c).

Select the correct name for this object. Is it a point, a line, a ray, a line segment, or an angle?

The object that this question is talking about is this here. Notice how we can’t just say “this line here,” because although we might look at this and say it’s a line, we’ve actually got five different answers to choose from. So perhaps it isn’t a line. In everyday life, we’d call it a line. But this is a maths question. And sometimes words in maths have very definite meanings. Let’s go through each of our possible answers and see what each one means. Then perhaps we’ll be able to say what the name of the object is.

Our first word is “point.” We know that a point is an exact position. There’s a point here, here, here. There are points along our object. And there are endpoints at either end of our object. But we can’t use the word “point” to describe the whole object. This isn’t a point.

Is it a line? Well, it definitely looks like a line. And as we’ve said already, in everyday life, we would describe it as a line. But in maths, the word “line” means something very definite. It’s a path that has no endpoints. It keeps on going in both directions. Now, if our object had arrowheads at either end, we’d see that it didn’t have any endpoints and it carried on going in both directions. We then could say it was a line. As we’ve said already, our object does have two endpoints. We can’t use the word “line” to describe it.

What about the word “ray”? A ray has one endpoint, and it continues in one direction. It looks like this. Can you see the orange arrow that’s pointing to the word “ray”? That’s a ray too. It has an endpoint, and it continues in one direction. Our object doesn’t continue in any direction. It has two endpoints. So we know it can’t be a ray.

Is it a line segment? A line segment is part of a line. It has two endpoints. In other words, it starts and it stops. Well, our object starts and stops, doesn’t it?

Just to check the last word, we know we don’t have an angle either. An angle is the number of degrees of turn that are measured between two rays. And these two rays begin from the same endpoint. Our object has two endpoints. It starts and it stops. Although we might be tempted to call it a line, we know the correct name for this object is a line segment.

Which is the starting point of the ray?

We have four points to choose from: 𝑁, 𝐴, 𝑋, or 𝐶. This question talks about a ray. And in order to answer the question, we need to understand what a ray is. In maths, a ray is the name we give for part of a line. It has one endpoint, and it continues in only one direction. So, on our diagram, can you see the ray? It’s this path here. It’s part of a line with one endpoint. And this arrowhead at the other end shows that it continues in only one direction. This arrowhead is a way of showing us that the ray is going to continue all the way to the edge of the video screen, off the screen, and on and on and on.

So now that we know what a ray is, which one of our four points is the starting point of the ray? Well, we know the answer can’t be 𝑁 or 𝐶. These points are nowhere near our ray. Point 𝐴 is a point on the ray, but it’s not where our ray begins. It might sound strange, but the starting point of our ray is the endpoint. It’s point 𝑋. Let’s draw over it in blue to show what’s happening. We’ll start at point 𝑋. And our ray continues in a straight line through point 𝐴 and on and on and on. The starting point of the ray is point 𝑋.

What have we learned in this video? We’ve learned how to identify points, lines, line segments, endpoints, and rays.