Lesson video

Hello, and welcome to this lesson on angles, alternate angles.

I'm Mr Thomas.

I could be happier as always to be taking you through this topic.

I always say time and time again, you're probably getting really wound up with me saying it, but I'm going to say it again, what we're doing this lesson is so, so, so important.

We're learning fundamental fact about some really, really frequently occurring angles that happen.

Now, as always, what I'd like you to do is I'd like you to remove every distraction possible.

That includes turning off those notifications in your apps to do with whatever it may be that you may have that could ping in and disturb you.

It could be your brother, it could be your sister.

The same deal applies, just get rid of them all.

Make sure that we can focus on that math, because that is all that matters right now.

Now with that in mind, let's continue and let's make sure that we do some really good stuff today.

So for your "try this", what I'd like you to do is I'd like you to measure each of those marked angles.

Now you're going to need a protractor for that.

So if you need to get a protractor, go ahead and get one now.

You also want to consider which of them are equal as well.

And then I want you to identify the pairs of vertically opposite angles as a result of doing that.

So pause the video now, get your stuff if you need to, that allows you to access that work and have a go at doing it.

Very good, I'm going to take it that you've done that and you've got the answers ready to go.

So let's go through it then.

Now what I can say, is I can say that A and C are equal 'cause they're vertically opposite.

Now, I don't know what they are without measuring them, and I'm not going to go through measure or how to , I've done that in an earlier video.

But what I am going to do is just say, which ones are equal, 'cause I can tell almost certainly which ones are equal, but I trust you've got that right.

And if you're not too sure about how to measure them, then go back to my previous one about measuring angles.

Now, we've also got B and D, they're equal.

'cause they're vertically opposite.

F and H, they're vertically opposite.

E and G, they're vertically opposite.

I'm sure you're getting an idea now.

J and K, they are vertically opposite and I and L are vertically opposite.

So we're getting the idea there, right? They're vertically opposite, cool.

I'm happy of that Mr Thomas, beautiful.

I'm liking that so far.

So what's really interesting is that, 'cause we can see that certain ones are vertically opposite, A and c, E and G, etc.

Can we see it they are actually the same sort of angle there? That's what we're going to explore today is that actually some of these they're the sure they are vertically opposite, we know that.

But then they're actually vertically opposite, these ones, and they're the same, they're the same, etc.

So that's what makes this really, really interesting is that we've got lots of angles, which can actually be the same throughout.

Really powerful stuff.

Let's continue and see what I mean.

Now for your connect today, you've got a pair of angles at different intersection points with a transversal called alternate, if they satisfy these two conditions, right? First one, lie on different sides of a transversal.

The second, are in the same region.

Remember we learnt about regions in the previous video.

We talk about the internal region and the exterior, the internal or interior or the external or exterior region.

So remember this is called the interior, and this is called the exterior.

So we've got the student here saying both angles are in the interior region.

Now let's identify all the other pairs of angles that meet that criteria.

This is what it looks like.

So these are what we call alternate interior angles.

So those marked on there, they are what we call alternate interior angles.

They are all in the interior region.

And remember one of the fundamental things about the alternate one, is that there on the opposite side of the transversal, we can clearly see that.

And then we have what we call alternate exterior angles.

Now they are on the exterior part, which we can clearly see 'cause we've got them in the blank spaces, rather than in the sort of a crossed part there.

Now, we can see they are on the opposite sides of the transversal, so that make some sort of sense.

We can see that they are.

Looking at them, they're equal.

Just by glancing, we can kind of see they're equal very, very close slash or equal.

And I can tell you now for free that they are equal.

So you've got that.

Let's have a look over.

Now, for your independent task, I want you to combine everything you've learned so far and everything you've learned through angles that far, I'd like you to fill in those blanks as we usually do.

You may need to go back over the stuff we've already done and rewind the video and have a go.

So pause the video, do whatever you need to do in order to fill in that space.

Off you go.

I'm going to take it that you've done that.

And I'm going to go through the answers.

So with that in mind, angles, blank and blank are alternate interior angles.

So alternate interior angles.

Scratching my head for a second thinking, interior means that it's in that sort of like crossed part here and then alternate, so they're equals.

So A and B are going to be equal.

So alternate interior angles.

Angles blank and blank are alternate exterior angles.

So let's take off A and B, that what we've done so far.

The exterior angles, that's going to be C and D, isn't it? It's in that sort of outside space.

So C and D can go there, take them off.

Then it says angles, blank and blank are equal in size.

Actually at this point you could say A and B or you could say C and D, the thing is that we've got C and D in these blank spaces here.

So we're going to put C and D there.

We're all good with that so far.

Hoping it doesn't lock you outside, but we're all good.

Now, angles formed by a transversal that are in the blank region, but on blank sides of the transversal are called blank angles.

Goodness me! That sounds so weird when you put the blanks in, doesn't it? So angles formed by transversal that are in the blank region, but are on blank sides of the transversal are called blank angles.

What could that possibly be? I'm scratching my head thinking about this because there's so much going on there.

Angles formed by transversal that are in the, what would make sense? Did we talk about the opposite region, same region, equal region, alternate region.

I know for fact they're called alternate angles, aren't they? So I can fill that in.

I know that, cool.

But are on the, did we talk about the same region or the opposite region but are on the same side or the opposite side of the transversal? If we look at this, we talk about the same region, don't we? Because we see A and B are in the same region, but we talk about the opposite side of the transversal, don't we? On this side here, and then it's on this side over here.

So it's the opposite side.

Now, if we've got that right, we should have this one being equal, this is, alternate angles formed by parallel lines are equal in size.

And that's definitely true.

We know that should be true.

Hopefully that's clearer now, just need that sort of like reasoning that I've done.

So talking it through if it's making sense of it.

It makes some sort of sense to you guys at home.

So let's go on, we've got our explore task now.

And what I'd like you to do is, for each diagram, I'd like you to identify any pairs of alternate angles and calculate the missing value that you can see there.

So pause the video if you're feeling confident, if you want some support let's know them.

Let's go through some support then for this bit here.

Now I can clearly see that 110 is going to be vertically opposite of D here, so they will be equal.

And I can also tell you that A and C are going to be equal as well.

Think about the straight line just here, what would that sum to, and what would you get to see as a result of doing that? Think about as well, where this is in the region and then where that would be alternate to.

For this bit here, think about what this would be.

What'd that blank space there be? Once you've worked that out, think about, we've got something here, haven't we? What would that be? And then we can use the triangle here to work out what M is.

we can work out what various things are as a result of doing that.

So I'm going to leave you there to explore that a little bit further and see what you can play around with and what sort of different angle facts you can use to get there, because there's a lot of things going on there.

So pause the video now, and then we'll go on to getting the answers in just a moment.

Okay.

Brilliant.

These are the answers that I managed to find.

So like I said, I haven't got every single thing filled out here.

I've only got the absolute skeletons of what A, B, C, etc, are.

Oh, there isn't even, I don't think there's a B, huh? Wow, there is no B, it's an A, C, D, K, I, J, L, M, N and L.

So pretty sure you just need to look at the question a little bit more when you start reading this, Mr Thomas, said to me.

So enough of my rambling, focus on that.

So we've got the things there.

We've got the angles marked there, all around.

And you can think about why we've re-winded the video, why those are the case.

You can see that those, like I said there, they're going to be equal.

They will be equal, etc, etc, etc.

If this one has been hard, I'm using the triangle facts that I just spoke about there, using vertically opposite and then triangle.

Angles in a triangle sum to 180 degrees, the interior angles there.

And it's with that i say again, it's wiz by.

We've got all another episodes done.

And we now know about so much more to do of angles.

We know about those interior, exterior, regions, and we now know how to combine it together with a transversal to get us an, what was it called? Alternate angle.

So good, so good.

Always comes up in exams, always part of problem solving questions that we need to do.

Really important that we're able to do it.

So as always, please have a go at the exit quiz, make sure you've smashed that.

I've designed the questions such that you can really easily, as long as you've been focusing carefully, and you've understood what I've done.

You should be able to do the exit quiz really nicely.

Now as always make sure you tune in for that next episode.

I can't wait to see, I can't wait for you to smash the episode and make sure you do your best work.

So take care for now and see you later.