Lesson Video: Vertical and Horizontal Lines | Nagwa Lesson Video: Vertical and Horizontal Lines | Nagwa

# Lesson Video: Vertical and Horizontal Lines Mathematics

In this video, we will learn how to describe and identify horizontal and vertical lines.

16:35

### Video Transcript

Vertical and Horizontal Lines

In this video, we’re going to learn how to describe and identify horizontal and vertical lines.

Wait a second! This doesn’t look like a maths video, all about lines. This is one of those do it yourself videos. How to put up a shelf in a minute. Well, let’s carry on watching. Perhaps we’ll learn something. To build a shelf, you will need some small pieces of wood to make brackets out of, a much longer piece of wood for the shelf itself, all the right tools to put it up with, and a beautiful vase of flowers to put on it once it’s finished.

Step one, fix the brackets to the wall, one, two. They look about right, don’t they? Step two, balance the shelf on the brackets. That’ll do. Step three, place a really expensive vase of flowers right on the end of our — oh, we’ve got a bit of a problem. This shelf is no good at all. What mistake do you think we’ve made? Well, for a shelf to be able to balance books or plates or really expensive vases of flowers correctly, it can’t be sloped or slanted in any way. And if we look at this shelf, it’s higher on the left than it is on the right. There’s definitely a slope on it. And that’s what made our vase of flowers fall off.

We should’ve made sure to begin with that those brackets we put on the wall were perfectly level with each other. We want the line between them to be exactly level from left to right without going up or down at all. And if we do this, the shelf will be what we call horizontal. There’s no chance of anything slipping and sliding along this shelf, is there? It’s perfectly level from left to right; it’s horizontal. We’re not doing too well at our DIY, are we?

Let’s try another how to video instead. Hello there and welcome to how to put up a fence! We’re going to use some sturdy wooden fence posts, a great big mallet to wack them in the ground with, and a coil of wire to make the fence out of. Right, Let’s make a start, shall we?

Step one, decide where your fence posts are going to go. Step two, start banging them in, one, two, three, four. They’ll do. And in step three, we simply need to take our coil of wire and tie it on to make a nice straight fence. This isn’t straight at all, is it? These fence posts are terrible. We can’t fix the wire to these. Can you see the mistake we’ve made?

For our fence posts to stand up and not fall over and for us to be able to tie the wire really straight, they can’t be sloped or slanted to the side in any way. When they were banged in, we should’ve made sure they were perfectly straight up and down, going from top to bottom without leaning to the left or leaning to the right. They should’ve been what we call vertical. And if we’d have fixed them vertically, perhaps the wire that we’d have tied on would have been horizontal. It looks like perhaps this video is about horizontal and vertical lines after all.

But the reason we pretended this was a DIY video to begin with is because horizontal and vertical lines are so important when it comes to making and building things. Let’s imagine you want to build a wall. Perhaps the first thing you might look for is a nice, flat piece of ground. It needs to be perfectly level from left to right. We don’t want it going up or down at all. It needs to be horizontal. And for our wall not to have any risk of falling down at all, we really don’t want it to be sloped in any way. We want it to be perfectly straight up and down. It needs to be vertical.

Now, there’s something interesting about our vertical wall. Look at what happens when it meets the horizontal ground. Can you see what sort of angle it makes? It’s a right angle, a square corner. Whenever a vertical line meets a horizontal line, they make a right angle. Now, it’s important to say two things here. Firstly, not all right angles are made from horizontal and vertical lines. Just because we see a right angle doesn’t mean we can look at the lines that make it and say, “Oh, they’re horizontal and vertical.” But we can say that whenever any horizontal line meets a vertical line, it’ll always make a right angle.

The other thing that is important to say is that the words horizontal and vertical don’t just mean straight. This is a straight line, but it’s neither horizontal or vertical. We can’t even look at a straight line and call it nearly horizontal or vertical. It either is or it isn’t. We have to keep reminding ourselves. A vertical line is perfectly straight up and down. It goes from top to bottom without leaning to the left or to the right. And a horizontal line needs to be perfectly level from left to right without sloping upwards or downwards at all.

And so, if we look at the edges of this video, we can see that it’s made up of two vertical lines and two horizontal lines. Although some of the lines in this triangle are neither horizontal or vertical, we can see that its base is horizontal. And this capital letter T is completely made out of horizontal and vertical lines. It’s even got a line of symmetry. And that line is vertical. There are vertical and horizontal lines wherever we look. And as we’ve seen already, one of the best places to start is looking at a building because without horizontal and vertical lines, many buildings would just fall down.

Let’s answer some questions now where we have to put into practice everything we’ve just learned about horizontal and vertical lines.

Identify whether the given line is horizontal, vertical, or neither.

In this question, we’re given a line. Here it is. Just looks like a normal straight line. But we’re asked to identify something about this line. Is it horizontal? Is it vertical? Or is it neither of them? In other words, is it not horizontal or vertical? To answer the question correctly, we need to really understand what the words horizontal and vertical mean. Let’s remind ourselves.

If a line is horizontal, it’s perfectly level from left to right and doesn’t slope up or down at all. If our line was horizontal, we’d expected it to look like this. Now, if we look at the line we’re given, we can see that it does slope. If this was a road and we had to cycle along it, it would be really hard, a lot different than if the road surface was horizontal. This line is slanted or sloped. So, we know it’s not horizontal.

But is it vertical? What do we remember about vertical lines? A vertical line is perfectly straight up and down, going from top to bottom without leaning to the left or to the right. If our line was vertical, we’d expect it to look like this. But if we look at the line that we’re given, we can see that it doesn’t go straight up and down at all. If our line was the wall of a house, it would really be leaning to the side. This line is not vertical.

We’ve used our knowledge of horizontal and vertical lines to look at this line and say it’s not horizontal or vertical; it’s neither.

How many horizontal lines are in this polygon?

There are some interesting words in this question. Do you remember what the word polygon means? A polygon is just a 2D shape that’s made out of straight sides. So, our question could’ve just used the word shape. And we know the name of this 2D shape, don’t we? It’s a rectangle. So, what we’re being asked is, how many horizontal lines are there in this rectangle?

And you can probably see how many lines there are that make up a rectangle. A rectangle has four straight sides, doesn’t it? But our question doesn’t just ask us how many lines there are. It asks us how many horizontal lines there are. Do you remember what the word horizontal means?

To help us remember, we could think of a word that’s part of the word horizontal. And that’s the word horizon. Do you know what the horizon is? It’s the line we see in the distance where the sky meets either the sea or the land. And although you’d see it wasn’t perfectly straight, if you got up close, it certainly looks straight from a distance. It looks perfectly level from left to right without sloping up or down at all. And remembering the word horizon can help us remember what the word horizontal means. Just like the horizon, it’s a line that’s perfectly straight from left to right and doesn’t slant or slope in either direction.

So, which lines of this polygon are horizontal? Well, this top line or side is horizontal, isn’t it? And there’s also a horizontal line opposite it on the bottom. But if we look at the two lines that make up the sides of our rectangle, we can see that they are straight. And they’re not sloped or slanted in any way. But instead of running from left to right, they run from top to bottom. These aren’t horizontal lines. They’re vertical lines. And so, we can say the number of horizontal lines that there are in this polygon is two.

True or false: A horizontal and a vertical line will form a right angle.

This question is made up of a statement. We’re told that a horizontal and a vertical line will form a right angle. But that statement might not be correct. We need to decide. Is it true? Or is it false?

Now, for us to work out the correct answer, there are a few words we need to remind ourselves of here. There’s the word horizontal, vertical, and also the words right angle. Do you remember what each one of these words means? If something is horizontal, it runs from left to right without sloping. It’s completely level. Can you see which one of the two lines in the picture runs from left to right without sloping? It’s this one here, going across the screen.

Now, there’s one more line in our picture. This doesn’t run from left to right though. That’s because this is a vertical line. This line runs up and down without sloping. This is completely straight from top to bottom without going left or right in any way. So, we can see where our horizontal and vertical lines are.

And our statement tells us that these sorts of lines will form a right angle. Do you remember what a right angle is? A right angle is where two lines meet together to make an angle of 90 degrees, or a square corner. This is why the symbol for a right angle is often a little square drawn in the corner. So, what do you think? If we have a horizontal and a vertical line, will they make a right angle?

Well, if we look at the two lines in our picture, they’re not even touching. They haven’t formed a right angle. But our question doesn’t say, “This horizontal and this vertical line have made a right angle.” It just tells us that if we take a horizontal line and we take a vertical line, they’ll make a right angle. So, to find our answer, all we have to do with our horizontal line is carry on drawing it. There we go. We only needed to add a little bit more. And now our horizontal and vertical lines are touching.

Do they meet at a square corner? Yes, we can see that they’ve made one, two right angles. And if we continue our horizontal line a little bit more, there are more right angles. And this fact is true of any horizontal and vertical lines. Horizontal plus vertical equals a right angle. Horizontal plus vertical equals a right angle. So, although we can make right angles in lots of other ways — can you see this example at the top? Neither of these lines are horizontal or vertical, are they? They’re both sloped, but they still make a right angle. We know that the statement is correct.

A horizontal and a vertical line will form a right angle. This sentence is true.

True or false: The given shape has a vertical line of symmetry.

In this question, we’re given a statement and we need to decide whether it’s correct or not. Underneath the statement, we’re given a picture of a shape. This is the shape that the statement is talking about. Now, did you notice the words “line of symmetry” in the question? Do you remember what a line of symmetry is? If we know that a shape or an object has a line of symmetry, we can think of it like a line or a fold through the middle of the shape. And if that shape is symmetrical, then if it were folded, both sides would fit perfectly on top of each other.

We can also think of symmetry in terms of reflection. We know that a shape or a picture has symmetry when we can take half of the shape and see that it reflects perfectly across the line of symmetry and still looks the same. And as we can see from these little pictures, lines of symmetry can go in all sorts of directions. But our question only talks about one type of line. The given shape has a vertical line of symmetry.

Now, we know that a vertical line is a line that goes up and down. It doesn’t slope to the sides at all. It’s perfectly straight from top to bottom. So, can we draw a line straight up and down from top to bottom somewhere on this shape so that it becomes a line of symmetry?

Well, we know that for lines of symmetry to work, they need to run through the middle of objects. So, if we can find the middle of this shape, which is here, and then draw a perfectly vertical line. What do you think? Is this a line of symmetry? If we folded this shape across the dotted line, do you think one side would fold perfectly on top of the other? If we put a mirror along the dotted line, do you think we’d see that one side is a reflection of the other? I think we would, wouldn’t we?

The line of symmetry in this shape doesn’t run horizontally from side to side and is not sloped in any way. But we can see that the shape has a vertical line of symmetry. The statement in the question is true.

What have we learned in this video? We have learned how to describe and identify horizontal and vertical lines.

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