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Hello, and welcome to this lesson on angles, corresponding and allied angles.

It's our final one this series, I'm really excited to be able to present it to you today.

So, make sure you've got that pen and paper that you need in order to write down whatever we're doing today.

Make sure you've got that quiet space so that it's distraction-free, as well.

So without further ado, let's take it away with Mr. Thomas's lesson.

So, if you'll try this, what I'd like you to consider is, which of those dotted lines below are parallel? Can you justify why they're parallel? So, pause the video now, and have a go at that task for the next five minutes.

Off you go.

Excellent.

Did you get the answers that I've got just coming up now? There we go.

Very good.

Did you get those? So, it's going to be A and D because if you see, A and D, if I fill that in there, what I get is 74 degrees.

Right? I can also see that, because they've got 74 degrees, that they are going to be equal there.

So A and D.

What about B and H? Well, B here and H here, I can fill this bit in as being 120 degrees.

So I know they're on the same angle there, so I know they are going to be parallel.

I can then say that C and F will be equal, as well.

If I see C here, I can see that it corresponds, so it's got, sorry it's vertically opposite with 95 there.

So it's going to be filled in as 95, and I can see they're going up to the same angle.

Very, very good if you managed to get that, well done.

Hi guys, it's Ms. Jones here, and I'm just coming in to introduce two key terms that you're going to need for the rest of the lesson.

We're going to think about what we mean by corresponding angles and allied angles.

So we've got here a diagram showing a pair of parallel lines this time, and we've got a transversal passing through them.

Now, we could say that these two angles, that you can see highlighted, are corresponding.

They're angles that are on the same side of the transversal.

You see here, they're both above that transversal in this diagram, but they're in different regions.

So this one's on the exterior of those parallel lines, this one's on the interior.

Now, the reason that we want to be able to identify corresponding angles is because we know that corresponding angles are the same value.

So we can say this angle is equal to this angle.

Allied angles, slightly different, again on the same side of that transversal, but these are in the same region.

So we can see here that this one is external, and this one is external.

And we might say that, actually, this angle would be allied angle with this angle here.

Now what's interesting about allied angles is that this angle would add together with this angle to make 180 degrees.

And we can see this makes sense because this angle would be equal to this angle here.

We could see that would make 180, so that if we add this angle with this one, that should also equal 180 degrees.

Okay, I'm going to pass you back over to your teacher and you can have a go at identifying some corresponding angles and some allied angles.

So what I want us to think about now is to identify pairs of corresponding angles and then allied angles, and then combine this knowledge together to be able to say something is equal to something and then something add something is equal to 180.

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

Off you go.

Awesome.

Let's go through it then.

So we've got.

So what I want us to consider now is to identify pairs of corresponding angles and allied angles, and then use those to form some sort of number sentences, right? So we can say that corresponding angles would be, which one? So it would be G and C, wouldn't it? So I can say G is equal to C, they lie on the same side of the transversal in different regions, aren't they? So G is equal to C.

I could also say F is equal to B.

I could also say H is equal to D, and I could also say that A is equal to E.

What other ones have I got? Well, let's try and do the allied angles now.

I could say that B plus G is equal to 180.

I could also say that C plus F is equal to 180.

I could also say that H plus A is equal to 180.

I could say that E plus D is equal to 180.

So I've given you a few odd ideas there of what you could do in order to get those equations formed.

So, really good if you've managed to spot those without me having to do them, first of all, well done.

So for your independent task today, what I'd like you to consider is the filling in the blanks there.

So, pause the video now and have a go doing that task for the next eight minutes, please.

Off you go.

Very good.

Let's go through it then.

So angles on the same side of the transversal but in different regions, so same side of the transversal but in different regions.

So that's on the same side and then on different regions, aren't they, are called what? Do you remember what they were called? They were called corresponding angles, weren't they? Very good if you got that.

So corresponding angles, good.

Angles on the same side of the transversal and in different regions, sorry, in the same regions are called what angles? Well, that's an example of it there, and that is of course going to be allied, isn't it? Very good if you got that.

If you're not getting this, then rewind the video to have a look back and think about why that might be the case.

We can then say corresponding angles formed in parallel lines are blank inside.

Well we can say, in size, we can say they're equal.

Very good if you got that.

And then allied four angles formed in parallel lines, blank to blank.

Well, I've said sum to 180 degrees, don't they? Let's consider the diagram now.

We can then say angles blank and blank are corresponding angles.

Well, we've just given an example of that being the diagram of you to fill out corresponding.

So that's going to be A and B, aren't they? We can then say C and D are allied angles, or we can say A and B are going to be equal 'cause of the corresponding nature of them, and then angles C and D sum to 180 degrees.

So very good if you managed to get that without me having to help you, very, very good.

Well done.

So for your explore task today, what I'd like you to assume is that the dotted lines can be rotated.

So the angles can vary.

So you can see that I've got these little rotation sides there, they can rotate, so they can vary.

Which of the following statements imply the dotted lines are parallel? So pause the video now, I'm going to give you seven minutes to think about that and to come up with a statement, say with a true, false, or maybe sometimes they are true, in some cases.

Okay, let's go through it then.

So, I could think, for example, for the dotted lines to intersect, well, they'd have to be parallel.

They wouldn't be parallel, right? If they intersected, they wouldn't be parallel.

What about A is equal to E? Well, if that was equal then of course, that probably would suggest they're going to be parallel, wouldn't it? Yeah.

So, as a result, then, we can then come up with these statements here.

And we can say, like it says, the dotted lines intersect does not imply they're parallel 'cause they meet, don't they? A is equal to E would imply they are parallel 'cause they're, those angles there, those corresponding angles there would be equal and therefore they would be, they would be parallel.

Alternate angles are equal implies that corresponding angles are equal.

Yes, that would imply that.

B and H being equal would also imply that they are parallel.

This is a very interesting case, though.

Allied angles are equal.

Well, if they are, if they are 90, 'cause then you've got the angle separated over, equally over both of them.

So that's a really interesting point to consider.

Very, very good if you've got all of that, in particular, that final point there.

So with that, that brings us to the end of our session today.

So really, really amazing work that you may have completed there.

I'm really happy that you managed to keep up and take on board all that we've done today.

Make sure you smash that exit quiz and you prove to me just how much you've learned and equally that you have a very safe day and take care.

Bye-bye.