Lesson video

Hello, and welcome to this lesson about "Angles in Polygons, Building shapes from triangles, Part two".

So this is the second part of two in the "Building shapes from triangles" series that I'm doing.

I'm Mr. Thomas.

I couldn't be happier about doing your lesson today.

Yes! Right, so please take a moment as usual, to clear away any distractions.

As I always say, like your brother, your sister, or your pet, or actually, anything to do potentially with your phone as well, so make sure those apps or notifications are silenced, and that you've got all the breathing space that you need through a.

A nice well ventilated spacey room, if you can, okay? We're about to do some really powerful math, so you need to make sure that we can really concentrate and that we can really really get involved.

So let's get stuck in straight away.

So have a go at the "try this" now.

So how many sums to 180 degrees can you find in this diagram? I've got Cala and Yasmin have suggested two already.

So they've got 180 is equal to F plus J, and A plus B plus C plus F is equal to 180.

Have a go at the rest of them, and see if you can find loads and loads that we can analyse.

Pause the video and have a go, please.

Okay, brilliant.

So when I was going through this, I was thinking, well, we've got quite a few that we can think of.

We've got, for example, F plus J, like Yasmin who said that, which I'm going to highlight here.

So she's got that angle there that's already been done.

We've got Cala's angle, which is A plus B plus C plus F, so A plus B plus C plus F.

So those four tics that I have there.

You could also think of D plus E, so this one here.

That would, of course, give you 180 degrees, 'cause angles on a straight line sum to 180 degrees.

You could also think of H plus I plus L.

That would work, 'cause that's a triangle as well.

So H plus I plus L is equal to 180 degrees.

And then you could also think, hmm, I've got E, plus G, plus H.

Because angles in a straight line land on, sum to 180 degrees.

So I've got that as well.

There are also many other odd combinations that you may have thought of, and they're absolutely valid, as long as it is on a straight line or angles within a triangle, interior angles in a triangle summing to 180 degrees.

Then that's perfect, okay? Well done, give yourself a tic.

Let's move on then.

So what I'd like you to kind of think about now is categorising them.

So we're going to think about the interior angles that we've got here, summing to 180 degrees.

So we have been through a few of them already.

Have a go now at categorising those videos, those videos? I'm on about.

Those angles that you have, just that.

So pause the video and have a go at categorising those angles.

Very good.

Okay, so you should be able to categorise them.

Now, you may have been a bit confused.

You may have thought, "Okay, cool, Mr. Thomas, I'm happy with this.

I get the interior angles one, I get this one.

What's the idea of compounding triangles?" Well, what we mean by that is, you may have seen the prompt that I have down there, which is C, this one here, plus I, plus K, plus L.

And do you see, if you draw all of those inclusive angles there, and draw the triangle that associates from it, you get one really really big triangle? So when you combine many triangles together to make an even bigger triangle, that's what we call a compounding triangle.

So you may have also had, for that one, you may have said, "Well that previous one that we had, A plus B plus C plus F, would form a compounding triangle, okay?" We've got that triangle here, and we've also got this triangle here.

So it's going to be A plus B plus C plus F.

And of course, for a few of them, we've already covered them, so D plus E would give the angles in a straight line summing to 180 degrees.

And then the interior angle, is like we said, A plus B plus D.

And we've also got C plus E plus F.

So they all work.

So have a go and just correct your work if you've got any of those wrong.

If you got them all right, superb, I'm very happy indeed.

Let's carry on, then.

So we've now got our independent task.

And what I'd like you to do is I'd like you to find the sum of each of those following angles.

So we've been through a few of them already for sure, but there's one or two that you may not be 100% sure on.

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

Excellent.

I'm going to take it for the fact that you're moving on that you're ready to go through the answers.

So here you go, here are your answers.

A plus B plus D, we've already been through that, that is equal to 180 degrees.

D plus E, that's a straight line, so 180 degrees.

A plus D plus F plus J.

Hmm, Mr. Thomas, that might be a bit of a weird one, okay.

Let's go through that, then.

So you've got A here, and you've got B, D, and then F plus J.

Do you see that is a triangle over here? So I'm just going to mark that with T.

And then a straight line over here, S.

So it's going to be 180 for this component here, and then a straight line, 180 for that bit there.

So that, of course, gives us, when we add them together, 360 degrees.

So G plus H plus I, plus J plus K plus L.

Well, let's go over to it.

So G, star it.

So G plus H plus I plus J plus K plus L.

So do you see that if you drew all those together, you get a quadrilateral? So angles in a quadrilateral sum to 360 degrees.

You could also say it's one triangle here, T, and then another triangle here, T, which would give you two triangles, which sum to 360 degrees.

So it's all sorts of ways that you can see this, which is the beauty of this topic.

So we now know that is correct.

A plus B plus C plus D plus E plus F.

Sounds like we're just going through the alphabet, right? So, what that's going to be is, that's going to be the triangle over just here, so A plus B plus C plus D plus E plus F, is going to be these two triangles here, the ones that I've got circled with T, and then the circle T.

So that's going to give us two triangles, which gives us another sum, 360.

And what about C plus I plus K plus L? So C is going to be.

Let's mark this now with.

What shape should I use? What shape shall I use? Let's mark it with a plus symbol.

So it's going to be C, plus I, plus K, plus L.

Well, we can see, if we connect that altogether, we get one angle, two angle, three angle, four angle.

Well, they all sum to make us a triangle, don't they? So that one there is going to be 180 degrees quite naturally.

Now Cala, she's working out E plus G plus H plus L.

She says that E plus G plus H is 180 degrees, and H plus I plus L is 180 degrees.

So the total is 360 degrees.

Do you agree with that? Now, she's made a really really silly mistake.

What she's done is she's done E plus G plus H, so she's done this part.

And then she's done H plus I plus L.

Do you see that she's double counted H? What's going on there? What's she done, right? She's made a really silly mistake.

Really simple, really silly mistake to make.

So just beware that you can do that, okay? So actually, we don't agree with her.

So no, I disagree with Cala.

With Cala, because she has double counted H.

You'll really have to excuse my terrible handwriting.

But I hope yours is even neater than mine, and that we can move on from my terrible handwriting, of course.

So, let's move on.

Let's go on to the Explore task now, final task.

So we need to find more statements.

Some might not even be sums to 180 degrees.

As we've seen with our previous task, right, by substituting equations to find even more angles.

So pause the video now.

If you need some support, I'm more than happy to provide it in the next slide.

Amazing, let's go on then.

So one possible idea I had was A plus B plus D.

So we can see that that of course, we've had that a few times, that would be 180 degrees.

I was going to put in brackets because of the triangle.

And then minus C plus J plus K.

Now do you see, if you add C plus.

I'm sorry, G plus J plus K.

So, G plus J plus K, that would be a triangle, right? So you're just subtracting the triangle.

So we're just subtracting all the angles again within the triangle.

Now, if you subtract one triangle, 180 degrees, from another triangle, 180 degrees, well that, of course, is going to give you a sum of zero.

So we can then start to think, well we've got.

If we do G plus H, plus I, plus J, plus K plus L, and that is two triangles which would sum to? 360 degrees, very good.

So that would be 360.

And then we could maybe even subtract.

Let's go with this.

A, D, and B, from our.

Equation that we've got set up here.

So that would be 180, because of a triangle.

I'll leave that in here.

Quadrilateral, there's a reason there.

So I have 360 minus 180, well that would give me, of course, 180.

We're getting quite used to these now, so you should be able to answer those pretty quickly.

So there's all sorts of different possibilities you could have.

I could be here for hours and days on end, just finding little tiny intricate things that you could do there.

So there's all sorts of things you can do there, as you can see, okay? So I really hope that you've learned a lot as a result of today's lesson, and that brings us to the end.

So what I want to say as always, is that you're doing an amazing job to be able to keep up with that, it's really really good.

I'm sure you're on track to do really well as time progresses with this.

We're going to move on to something slightly different in the next part.

We're going to be trying to make sure that we can combine the knowledge altogether to progress even further.

So don't forget to do that post quiz, just to check to see how much you've learned.

It's really important that you do that so you can see how well you're doing, and I can also see how well you're doing as well.

I want to make sure that you're learning lots as we go on.

And then remember, if you can, as always, take a picture of your work and ask your parents or carer to share with your teacher, so they can see all that fantastic learning that you've done today.

And you can always Tweet @OakNational if you'd like to as well.

So all that's left for me to say is goodbye, and to see you in our next lesson.

Take care, bye bye.