Lesson video

My name is Miss Darwish and for today's lesson, we going to be looking at two types of triangles.

They are equilateral triangles and right angled triangles.

And we going to be comparing them today.

But before we get started, if you can just take yourself to a nice, quiet, peaceful environment, ready for today's lesson.

Okay so the lesson agenda for today, we going to be looking at triangles in general, and then we're going to have a look at equilateral triangles followed by right angled triangles.

And then at the end of course as always, there will be a quiz for you to do.

Okay let's start.

So you're going to need for this lesson, something to write on something to write with, paper and pen or pencil, and you will need a pair of scissors for today's lesson.

So if you want to just pause, go and get those things and then come back and we'll carry on with the lesson.

Okay, hopefully you've got your items that you need for today.

So in front of you I have three triangles, I want you to have a think, what's the same between these triangles? What's the same? Have a think what's the same if you want to jot anything down feel free to.

Once you've had a think about what's the same, what's different between these triangles? What's different? Okay, should we have a look together? Let's have a look.

So let's start with what's the same.

Obviously they are all triangles.

They have three straight sides, which makes them a triangle.

And they also have three vertices.

So there're three sides, three vertices, right? Hopefully you got those.

Okay, they don't have any parallel lines.

Remind me, what's a parallel line? Where two lines do not meet or any of the sides of a triangle.

Does a triangle have two sides that don't meet or don't touch? No, all three sides of a triangle touch.

A triangle does not have any parallel lines.

Okay, what's different? The sizes are different if I was to measure all the triangles they're quite different in size and also the orientation.

That means the position of the triangle.

They're oriented differently, they're in different positions, okay? They're not in the same position.

Okay, let's have a look at some regular shapes.

So in front of us, we have a regular triangle and a regular quadrilateral.

So a regular shape is a shape where if I was to measure the sides with a ruler, they would all measure the same.

It has equal sides and not just sides, the angles as well.

If I was to take my protractor and measure the angles, they would all measure the same.

So we've got an example of a regular triangle and a regular quadrilateral.

Now the regular triangle has a name.

It's called a equilateral triangle.

If I just go back remember the regular quadrilateral is called a square that would be a square, okay.

Let's focus on the triangle.

So a regular triangle, let's just recap where all the sides measure the same and all the angles measure the same, that type of triangle we wouldn't say regular triangle, we would call it an equilateral triangle.

Can you say that? Equilateral triangle, well done.

So we've got an example of an equilateral triangle.

Now the angles in an equilateral triangle have to be 60 degrees.

The angles, the interior, that means the inside angles of a triangle, all add up to 180.

So 60 add 60 add 60 is equal to 180 degrees.

Or we could say three lots of 60.

Three times 60 is equal to 180.

So what are angles inside an equilateral triangle? 60 degrees, but any triangles and angles add up to 180.

It doesn't matter what type of triangle it is, they all the angles inside a triangle add up to 180.

But just an equilateral triangle has a 60 degree angle, a 60 degree angle and a 60 degree angle.

Three lots of 60 degree angles.

Okay, have a look at these triangles.

If I told you one of them was an equilateral triangle, which one would you say it was and why? Have close look, so I'm going to tell you now, one of these triangles is an equilateral triangle which one and why? Definitely not the blue one, the turquoise colour, why not? Because two of its angles are different.

Yes, one angle is 60 degrees but the other angle is 50 degrees.

Definitely not an equilateral triangle.

It's definitely not that one because one of the angles is 90 degrees.

And if it was an equilateral triangle, the angles would be 60 degrees each, well done.

Now it is that one because all the sides have the same measurement, three centimetres, three centimetres, three centimetres.

And it cannot be the green one because two of the sides are different lengths.

So well done if you said the yellow triangle.

Okay now, bit of a game that we're going to play today.

So can these be rearranged to make one large equilateral triangle? Let me explain, in front of you, you have four small, equilateral triangles, correct? Now, I'm going to show you we to do this together.

We're going to rearrange them.

That means we're going to move these small equilateral triangles to make one equilateral triangle.

Do you think can do that? Let's have a, let's just start with one triangle.

So we got one equilateral triangle.

We got three more to position.

Let's have a think about the side first of all.

Okay, we're making the side a bit longer.

if the triangle where are going to put the second one then? Where do you think the next two might go? Remember you can move the orientation of the triangle and you can place it in a different place.

Where do you think the next one would go? Well the next two would go doesn't matter which one first.

There's a third one and can you see where the fourth one would go? Well done, so what we've done here is we've taken four small equilateral triangles, and we've created one larger equilateral triangle, quite cool.

Okay, we can see that the side, we can check that the sides are actually equal in length.

And we can see that that side of the triangle is equal to two of the small equilateral triangles.

And there's the other side that we can check again.

The other side of the triangle is equal to two of the smaller equilateral triangles.

Now here is a larger equilateral triangle.

How many equilateral triangles is it made up of? Count them for me? Well done if you said nine.

So before we could see that we could make an equilateral triangle from four smaller ones.

And now we can see that we can make a large equilateral triangle from, nine smaller equilateral triangles.

But this time, one of the sides or each side sorry, is the length of three small equilateral triangles.

So we got three small equilateral triangles.

The triangle we saw before had two.

Okay, let's have a look at right angled triangles now.

Here's an image of a right angled triangle.

This is another right angled triangle.

What's the same and what's different? It's basically the same right angled triangle, but I'm just moving the orientation.

Remember that word orientation, can you say it for me? Orientation, good.

Just moving the position of it.

Sometimes when we see a triangle that looks like this, it's quite obvious we can see the right angle.

But if I was to show you lots of right angled triangles and the orientation was a bit different, sometimes you might have to just try and sway your head slightly just to spot where that right angle is.

Okay, so this is also a right angled triangle.

This is also right-angled triangle.

You see what I mean by moving the orientation? Okay, going to play a game.

Can you find a right angled triangle? I'm going to give you six seconds.

I want you to point at the screen now and giving you longer.

Okay, and six, five, four, three, two, one, which one's is a right angled triangle? Well done if you got that right, let's have another go.

Six seconds, point to the one you think is six, five, four, three, two, one.

Which one do you think it is? Well done if you got that right.

Let's do another one.

Can you find the right angled triangle in six, five, four, three, two, one.

I tricked you, or did I not trick you? Did you realise that actually it was both there and you see the 90 degrees in both of them.

They are both right angled triangles.

Well done if you said both.

Okay, let's have a look at this triangle.

We know two of the angles, one of the angles is 40 degrees.

The other angle is 50 degrees.

What can we call this type of triangle? And how do you know, what kind of triangle is it and why? Okay, the first thing I would personally do is to check what the third angle is.

50 degrees, 40 degrees, what will the third angle be? We know in a triangle in any triangle it doesn't matter which type of triangle, all of the interior angles, the angles inside add up to 180 degrees.

So if we did 180 degrees take away 40 take away 50, that would give us the missing angle.

And the missing angle is 90 degrees.

So we did 40 add 50 it was 90 and take it away from 180 we are left with 90 degrees.

So this is a right angled triangle because the missing angle was a 90 degree angle.

Well done, if you said that.

Okay, now it is time for you to pause the video and get on with the independent task.

This is actually one of my favourite tasks so I really, really do hope you have some fun with it.

And then when you are ready, come back and we will go through the answers.

Okay, hopefully that was okay.

You didn't find it too tricky.

Let's go through the answers together.

Let's see what you did.

Okay, so you had some smaller equilateral triangles to cut off and try and place them together.

So you should have something that looked like this.

And remember of course, with the triangles, feel free to move them around, change the orientation.

So is this what your equilateral, your large equilateral triangle looks like? So each of the sides of the large equilateral triangle should be the same as three of the small equal lateral triangles.

Now you could also have 16 smaller equilateral triangles to create one really large equilateral triangle.

And of course, each of the sides would be the same as four smaller equilateral triangles.

The triangles that I've used, sorry, I've done a mixture of white and yellow triangles just to make it obvious.

Just to make it it's just to help you count them.

So 16 small equilateral triangles and before we had nine small equilateral triangles, just to make one.

So let me just move myself out of the way.

We can have an equilateral triangle from just one, or we can have four smaller equilateral triangles to make one large equilateral triangle.

Or we could have nine small equilateral triangles to create one large equilateral triangle.

Or we could have 16 smaller equilateral triangles to make one larger equilateral triangle.

So you've got one, four, nine, 16.

What do you think the next number might be after 16? How else, how many triangles can you have? Can you see a pattern with the numbers? Okay, let's have a look together.

So these numbers are actually called squared numbers.

You might have spotted that pattern well done if you did.

So we've got one times one is equal to one, two times two or two squared is equal to four, three times three or three squared is equal to nine, four times four or four squared is equal to 16.

So now let's see if you've got that question right when I asked you how many smaller equilateral triangles, can make the next number after 16? Five times five or five squared is equal to 25.

Can I make a large equilateral triangle from 36 smaller ones? Yes, why? Because six times six is equal to 36.

Okay, if you would like to share your work with Oak National, that would be brilliant.

But please ask your parent or carer to share your work for you onto Twitter.

And don't forget to tag @OakNational and #LearnwithOak.

I would absolutely love to see your equIlateral triangles and maybe you've made, you've used a hundred small equIlateral triangles to make one large one or maybe 144.

If you want to make the biggest possible one, just lay it out on your living room floor.

That will be great, but I would really, really love to see these.

So I just want to say well done for all of the work that you've done today, and I hope you get on with the quiz or okay.

Just a way to say good luck with the quiz and a really, really big, well done for the brilliant, amazing work that you have done today with me.