Lesson video

Hi, how are you today? I hope you're having a good day.

My name is Miss Coe, and I'm really excited to be joining you for this maths lesson.

In this maths lesson, we're going to be looking at geometry.

Now, you might wonder what geometry means.

Geometry is all about shape, so I'm really excited to say that this lesson is all about exploring different shapes.

I really hope you'll enjoy learning about this as much as I will enjoy teaching you.

By the end of this lesson today, you will be able to say that you can identify parallel lines and extend lines in polygons to determine, or work out, if sides are parallel.

In this lesson today, we have just one keyword.

I'm going to say it, and I'd like you to say it back to me.

My turn, parallel.

Your turn.

Great job.

Let's just double-check we know what that word means.

Parallel lines are straight lines that are always the same distance apart.

They never get closer together or further apart.

In this lesson today, we're going to focus on identifying parallel lines in shapes and in other situations, and we have two cycles.

We're going to start by identifying parallel lines generally, and then we're going to really focus on extending parallel lines in polygons to determine whether or not they are parallel.

If you're ready, let's get started with the first cycle of our lesson.

In our lesson today, we are going to meet Aisha and Sam, and they are going to be providing lots of examples for us to think about and asking us some questions along the way.

Let's start here.

A rectangle is a special type of quadrilateral, and it has two pairs of parallel sides.

Let's focus on the pair that we've shown.

Remember, we show parallel lines using small arrows pointing in the same direction.

If we draw the lines without the rectangle, are those lines still parallel? Hmm.

I wonder what you think.

Let's take a look.

Here they are without the rectangle.

What do you think? Are those lines parallel? This is a pair of parallel lines, so they are still parallel.

The lines are the same distance apart.

They don't get closer together or further apart.

So parallel lines don't need to be in shapes in order to be parallel.

They just have to fit that property, do they stay the same distance apart? Time to check your understanding.

Select the pairs of parallel lines.

So we have A, B, and C.

Look really closely at those three pairs of parallel lines and decide the ones that you think are parallel.

Pause the video here.

Welcome back.

How did you get on? Let's take a closer look at A.

Remember, parallel lines stay exactly the same distance apart.

They don't get closer together or further apart.

A fits that bill completely.

This is a pair of parallel lines.

It doesn't matter that they're not horizontal or vertical.

As long as they stay the same distance apart, they are still parallel, and we've marked them with our arrows pointing in the same direction.

Let's look at B.

I can clearly see that the lines in B get closer together.

If I look on the left-hand side, they are further apart than they are on the right-hand side.

B is not a pair of parallel lines.

What about C? C is a pair of parallel lines.

It doesn't matter that they're close together.

They stay the same distance apart, so these are a pair of parallel lines.

Well done if you identified A and C being a pair of parallel lines.

Sam is exploring drawing parallel lines.

Let's see what she gets up to.

Sam says, "I am going to draw a third line on this drawing.

I think the lines are still parallel." There is the third line that she has drawn.

What do you think? Are the lines still parallel? Yes, they absolutely are.

The lines are all parallel to one another because they stay the same distance apart.

And she can use strips of paper to show this.

Let's take a look.

Here, we've placed a strip of paper between the top and the middle line, and if we move that strip of paper to a different position, we can see that they are the same distance apart.

Similarly, with the middle and the bottom line, if we have a smaller strip of paper, we can show that distance, and again we can move it along and see that it is the same distance apart.

And then if we look at the top and bottom line, we can do the same thing.

We can move them around and show that they stay the same distance apart.

So we can say that more than two lines can be parallel to one another.

So Sam is still exploring with the same two original lines, and she's going to draw a different third line on this one that she still thinks will be parallel.

Here we go.

She has drawn another third line onto this drawing, and she thinks the lines are still parallel.

What do you think? Hmm.

Yes, these lines are still parallel.

Even though the first two are closer together than the other ones, all of them remain the same distance apart from one another.

And we can see again here, if we used a strip of paper, we can see that these two lines are still the same distance apart, these two lines remain the same distance apart, and we know that the original two lines were the same distance apart as well.

So we know that the important factor here is that the lines have to stay the same distance apart.

You can have two lines that are really close together, but as long as that gap remains the same, they are still parallel.

Sam is going to draw another different third line on this diagram, and she still thinks these lines are parallel.

Let's see what she does.

Hmm.

There's her third line.

What do you think? Is this line still parallel to the others? Yes, it is.

So this time, her line is longer than the other two, but that doesn't matter.

It also starts and ends at a different place to the other lines, but that doesn't matter.

The only thing to think about is whether the lines stay the same distance apart, and in this example they do, so these lines are still all parallel to one another.

Time to check your understanding.

I'm going to show you some different lines drawn on this diagram.

Which of the lines is parallel to the other two lines? I'd like you to have a close look and explain your choice.

So here is option A, here is option B, and here is option C.

Which of these lines is parallel to the other two? Take a close look.

Perhaps discuss with a friend, if you have one nearby.

Pause the video here.

Welcome back.

What did you think about lines A, B, and C? Were they parallel to the others? Well, if you look at A, we can see that it is parallel to the other lines.

It is shorter, but it still stays the same distance apart from the top line and then from the bottom line, so it is parallel.

There is one other parallel line in this example.

Can you spot it? That's right.

Line C is parallel.

It is below the original lines, but it is still the same distance apart of the other ones.

Line B is not parallel to the others because you can see that it is getting closer to the lower line and further away from the top line.

Well done if you spotted that A and C were parallel and reasoned why.

Let's take a look at a quadrilateral.

This is a trapezium, and you may have seen this quadrilateral before.

It has exactly one pair of parallel sides.

And remember we can show the parallel sides by using the arrows to indicate them.

If we draw the lines without the trapezium, are the lines still parallel? Hmm, I wonder what you think.

Here are the lines drawn without the trapezium.

What do you think? Are the lines still parallel? Well, hopefully, by now, you've realised that absolutely they are.

They might be different lengths, but they still stay the same distance apart.

Therefore the lines are parallel.

Sam is exploring parallel lines with this pair of parallel lines.

She's going to rotate the lines, or turn them, and she still thinks they are parallel.

Let's look and see what she does.

There we go.

What do you think? Are the lines still parallel? Yes, Sam is absolutely right.

The lines haven't got any closer together or further apart.

They are still parallel.

It doesn't matter how she rotates them.

As long as she doesn't rotate the individual lines, they will still be the same distance apart.

She's going to add a third line to these two lines, and she thinks it is still parallel.

Here is her third line.

What do you think? Is it still parallel? Hmm.

Well, yes it is.

Sam's line is longer and thicker than the others, but it is still parallel to the other two.

It still remains the same distance apart.

The thickness of the line doesn't matter.

It just has to be the same distance apart.

Well done, Sam.

Some really nice examples there.

Time for your first practise task.

I would like you to draw a pair of parallel lines.

Use a strip of paper to check that they are parallel, so remember they need to be the same distance apart.

Then I would like you to add a third line and show that it is parallel to the other two.

Then I would like you to draw three lines that are all parallel.

Can you draw an unusual example that you think no one else will have thought of? Good luck with those three tasks.

Pause the video here, and I'll see you shortly for some feedback.

Welcome back.

How did you get on? Did you think really carefully about what made your lines parallel? So remember, your lines may have looked different to mine.

I decided to do a longer line and a shorter line.

These are still parallel.

They stay the same distance apart.

They don't have to be the same length, remember.

If I add a third line, this line is parallel to the other two lines.

It stays the same distance apart from both lines.

I can check that or show that by using strips of paper.

I can see that these strips of paper are the same lengths, and no matter where I place it between those top two lines, it stays the same distance apart.

And I can do the same with the middle and lower line.

I can show that they stay the same distance apart.

For Question 3, I asked you to draw some unusual examples of parallel lines.

You might have drawn lots of different things here, but here is one unusual example.

Can you think about why it's unusual? Well, that's right.

We've got two lines that are very close together but are still parallel because they are the same distance apart, and then we've got one that feels very far away, but it is still parallel to the others.

It stays the same distance apart of the others.

I've also made it a bit unusual by including a very thick line along with two thinner lines.

Remember the thickness of the line doesn't matter.

Let's move on to the second cycle of our learning where we are extending parallel lines in polygons.

This is a trapezium, and hopefully you've seen trapeziums before.

It has exactly one pair of parallel lines.

We've marked those parallel lines using the arrows.

Sometimes, though, it can be hard to tell if lines are parallel.

In this particular trapezium, one of the parallel lines is really very short.

So sometimes we can be unsure as to whether the lines really are parallel or not.

In examples like this, we can extend or stretch the lines to check if they are parallel.

So to do that, we use a ruler.

So we use a ruler to extend the line, and we line the ruler up with where we want to extend.

So in this case, we want to extend that short trapezium side to check that it is parallel to the side opposite.

So we're gonna line it up really, really carefully, and then we're going to draw a long line.

It doesn't have to be the same length as the line you're comparing.

Just make it as long as you can.

So we have drawn a line there.

What we have done is extended that side.

We can now see that the lines are parallel.

They stay the same distance apart.

And we could use a strip of paper if we needed to to show that wherever we place that strip of paper along the line, those two lines stay the same distance apart.

If our extended line is parallel to the side we're thinking about, then that means the short side is also parallel.

The sides of the trapezium are a pair of parallel sides, and we've proved that by extending that line.

Time for a quick check of your understanding.

I would like you to explain the steps of using a ruler to extend the marked sides on this quadrilateral to see if they are parallel.

Pause the video here and have a go.

Welcome back.

Hopefully you said something like this.

Take a ruler and line it up with the short side that you want to extend.

So we've lined it up with that very short side of our quadrilateral.

The next step is to draw a long line.

Remember that it doesn't have to be the same length as the side you're comparing.

Those are the key two steps to be able to extend a side to see if they are parallel.

And I can see from this that these two lines are parallel.

Earlier in their learning, Aisha constructed a pentagon using construction sticks.

You might have used construction sticks before.

They are straight sticks that can be used to make different polygons.

Aisha made this pentagon.

She wasn't sure at the time if the sides that she has shown here are parallel to one another, and it's okay not to be sure sometimes.

But now she says that she's going to draw her shape in order to investigate further, and hopefully she can apply some of her learning to check to see if these are parallel or not.

She's drawn around her shape, and now she thinks the sides are parallel, but she wonders if she can find a way to check.

Aisha starts by rotating, or turning, her shape like this.

Now the two lines are vertical, she says, and that's easier for her to think about.

So we can now see that the vertical sides are the ones that we're thinking about.

I think they look parallel, but I'm not sure I can tell just by looking.

She's still not sure, so she can extend the lines of her shape to check.

She's going to use a ruler and line it up with the shorter side and draw a longer line, like this.

She does it with both sides so that she can be super clear about whether the sides are parallel.

Then she's going to use a strip of paper to see if the lines are the same distance apart.

What do you think? Do you think these sides are parallel? Well, let's have a look.

Here is the strip of paper, and if we move it along, we can see that the lines stay the same distance apart.

So yes, these two lines are parallel.

They stay the same distance apart.

So that means the sides of the shape are parallel too.

We can show that, remember, by drawing arrows pointing in the same direction.

Great work, Aisha.

I really liked how you used your new learning to check something that you weren't sure about earlier in your learning.

Time for your second practise task.

For Question 1, I would like you to see if these shapes have any pairs of parallel lines.

You might want to make some predictions before you start.

Any that you're not sure about, I'd like you to extend the sides in order to check.

Remember you can mark any parallel sides that you find using arrows.

For Question 2, I'd like you to think about this tricky problem.

Sam adds a quadrilateral to Aisha's shape and makes a compound shape.

So she starts off with Aisha's pentagon and draws a quadrilateral on top of it.

Sam says that the side marked A is parallel to the side marked B.

Sam is correct about this.

I would like you to explain why.

You might want to draw some lines on this problem and think really carefully about it.

Good luck with those two tasks, and I'll see you shortly for some feedback.

Welcome back.

How did you get on? Let's look at Question 1.

Shape A has one pair of parallel sides.

Did you manage to spot them? Here are the pair of parallel sides, and we can extend the lines to check that they are parallel.

They stay the same distance apart.

We can use a strip of paper if we need to to show that they are the same distance apart.

Shape B has one pair of parallel sides as well.

Did you spot them? It's this pair of sides.

If we extend the lines, and we can use a piece of paper to show that they stay the same distance apart, those two sides are parallel.

Well done if you spotted that.

Shape C doesn't have any pair of parallel sides.

You might, however, have thought that these two sides were parallel, but when we draw the lines, we can see that the extended lines get closer together, so these sides are not parallel.

Well done if you spotted all of those shapes.

For Question 2, Sam added a quadrilateral to Aisha's shape to make a compound shape.

Sam is correct when she says that the side marked A is parallel to the side marked B.

I asked you to explain why.

Now, remember, Aisha's shape had a pair of parallel sides, A and the side in the middle of the compound shape now.

That might give you a bit of a clue to why.

So we know that side A is parallel to the side there in the middle, which we're gonna label side C to help us out.

There we go.

The sides of the two shapes are the same when they joined.

So the quadrilateral that Sam added to Aisha's original shape is the same.

It's the same side.

So that side is also parallel to side A.

Side B is parallel to side C.

You may have drawn some lines to show that.

So that means that side B has to also be parallel to side A.

Now, that was a really tricky problem that took a lot of reasoning, so well done if you managed to say why sides A and B were parallel.

We've come to the end of our lesson, and we've been really focusing on identifying parallel lines.

Let's summarise our learning.

Parallel lines are always the same distance apart.

Parallel lines, though, can look different and still be parallel.

And you can see from the example there that we could have thicker or thinner, longer or shorter lines.

The important thing is that they remain the same distance apart.

And we've also seen that more than two lines can be parallel to one another.

We can also check to see if lines are parallel by extending the lines and making sure they're the same distance apart.

Thank you so much for all of your hard work in this lesson today.

I've really enjoyed it, and I hope to see you in another maths lesson soon.