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Hello, and welcome to this lesson about angles in polygons, building shapes from triangles.

We're going to do another part, but this is basically an introduction to this topic.

So please take a moment to clear away any distractions, be that your sister, your brother, your pet, whatever it may be that's distracting you, including your phone.

If you're watching on your phone, by all means, that's great, but make sure all those app notifications are silenced so that you aren't getting distracted.

We're going to do some really powerful math, so make sure we're really, really focused throughout.

Right, so when you're ready to begin, let's get going.

I'd like you to have a go at the Try This.

We're thinking Cala makes shapes by combining congruent, remember what congruent meant? Exactly the same, right? So exactly the same equilateral triangles.

She says, "With two triangles, I can make a rhombus.

With three triangles, I can make an isosceles trapezium".

What shape can she make with four triangles or five triangles? Have a go at that task now.

Okay, so the sorts of shapes she can make are the following: she could make, for example, the isosceles trapezium, which I'll mark as isosceles IT, so that's the isosceles trapezium she can make.

She could of course make that rhombus, which I'm just going to mark with R.

If we thought about it a little bit further, what else could she make? Well, she could make What's that if she uses six, six, six, six equilateral triangles there, she could make a one, two, three, four, five, six-sided shape.

She can make a regular, you got it? Regular hexagon, right? She made all sorts of different shapes.

So that's just a few of the ideas that she could make, right.

She made all sorts of shapes from that.

Let's move on.

So for our Connect, we want to work out the internal angles of that rhombus.

So if we want to work out the internal angles of the rhombus, what we could say is we've got 60 degrees here, we've got 60 degrees there, and we have 60 degrees just here.

So of course we've got a total of 180 degrees there, right? So the total is going to be 180.

Let me just box that off, right.

And the same thing for here as well, of course.

So 60, 60, and 60.

So what we have here is 180.

So we've got a four sided shape, an example of a four sided shape, which of course is a quadrilateral, right? And we've got the total angle was in that summing to 360 degrees, right? So I can do 180 plus 180 and I get 360 as a result.

So I know 360 the total interior angles of my quadrilateral.

So the total interior angles of my quadrilateral, total interior angles of a quadrilateral sum to 360 degrees, okay.

Pause the video.

I'll give you a moment to write that down.

Fantastic.

Right.

Let's move on.

So what I'd like you to think about is to think about finding all the angles in those triangles below, and then commenting on the total interior angles using notation given.

So for example, I could say that this is the quadrilateral, A B C D.

So I know I'm referring to quadrilateral ABCD, cause I've got A to B, to B to C, to C to D, and then back again, of course, I get a quadrilateral.

So I know that the interior angles, of course, for there would sum to.

you can fill out the rest.

You could also think about how you're going to label this.

So you could also fill it out as A, B, C, D, E, and you could find out different things about that.

Of course, the same applies for this one here.

I'll leave that one for you to decide.

So pause the video now and have a go at doing that task.

Okay, excellent.

Let's have a go at going through that then.

So the quadrilateral ABCD that I identified, if I write this out again, there's going to be 360 degrees, isn't it? That's what that sums to.

So 360 degrees.

So I'm thinking, well, I could also mark it as E, like I have just a moment ago.

And I could say, for example, the triangle ABE is equal to, what would that be equal to? 180 degrees, of course.

Right? I could also think about BEC, and that of course is a triangle, so I know that would be 180 degrees as well.

I could also say that I've got ABC here, and that could be equal to 180 degrees.

I could also say that if I had it up to maybe D, E and then F there, I could say, I've got AEFD is going to be 360 degrees.

Right? I can see, I can mark on that that is going to be looking like this.

And as a result, I get another rhombus-like shape.

So I can see that that would be 360 degrees.

All sorts of different combinations that we can have there.

Excellent.

Let's move on.

So for your Explore task, what I'd like you to consider is that you've got an equilateral hexagon, and equilateral octagon are going to be built out of equilateral triangles.

So I want you to try and find the internal, internal angles of those shapes.

So what other equilateral polygons can you make from equilateral triangles? I'm going to let you think about that for a moment.

If you need some support by all means carry on, but if you don't please pause the video now.

Okay.

So I'll take you may need some support where you want to go through the answer, in which case let's consider it.

So we've got the following: We've got this one, two, three, four, five, six-sided shape, so that's going to be the hexagon.

Now I know that each of these equilateral triangles has 180 degrees internally within it, so I can fill that out.

So of course, foUr lots of a 180 are equal to what would that be? 720 degrees, right? So 720 degrees.

So I know the internal angles within that hexagon sum to 720 degrees.

What about this one over here? This is quite odd looking shape.

It looks like sort of like a seahorse of some description, right? So that's what we're going to call an equilateral octagon, over here.

So that's going to be 180 degrees.

One, two, three, four, five, and six.

So it made up a six different, sorry, six identical equilateral triangles.

So six times 180, give you a moment to figure that one out.

What would that be? Have you got answer? So six times 180, that's going to give us 1080 degrees internally within the equilateral octagon.

So an octagon sums to 1080 degrees internally.

So I'll let you play around with other equilateral polygons, but hopefully you may start to notice a pattern, and that's what we're going to explore in the next lesson that we have together.

So, I just want to say fantastic work with today's lesson.

Very, very good.

I also want you to just revel in the fact you've learned quite a lot from that.

There's quite a lot of things that are quite complex there.

So we're going to explore that in the next lesson that we're going to have.

So remember, you can always share your work by tagging @OakNational on Twitter, and you can send a picture to your teacher as well, as long as you have got your parent or carer to ask permission to do so.

So that's it from me for today's lesson.

I just want to bid you farewell.