Lesson video

Hello, and welcome to today's lessons about bearings within parallel lines.

For today's lesson, all you need is a pen and paper or something to write on and with.

If you could please take a moment to clear away any distractions, including turning off any notifications.

And if you could try and find a quiet place to work, where you won't be disturbed, that would be brilliant.

Okay, when you're ready, let's begin.

Okay, so for the try this of test today, we're going to be looking at Binh's statement here and we will decide if is always true, sometimes true, or never true.

So let's pause the video and have a go.

Pause in three, two, one.

Okay, welcome back.

Now, I don't know what you've decided, but let me show you kind of my thinking here.

So, what angle do we want? Well, we want to know this angle.

That angle will tell us the bearing of A from B, okay? Now, those angles, those angles are equal.

Do you remember what those angles are called? They are called corresponding angles and corresponding angles are equal.

So we can use this fact to help us work out bearings problems. Now, is it true, is Binh's statement true? Well, that is equal to 180.

So, Binh's statement is only true if this angle here is equal to that angle there.

So, we'd have pink angle on a pink angle, and that only ever happens if the pink angle is 90 degrees.

So Binh's statement is sometimes true.

I'm going to need, I want you to remember this fact that we can use our corresponding angles to solve bearings problems. There is another angles in parallel line fact that we can use.

Watch this one.

Extend the line, find that corresponding angle and then this angle.

Well, those two form a straight line, so they must add up to 180.

Because that pink one is the same as that pink one.

These two also must add up to 180, and they are called co-interior angles, co-interior angles.

Sometimes people call them allied angles and you can call them allied angles if you want, if that's what you're used to.

But I prefer co-interior, so I'm going to call them co-interior, okay? And co-interior angles add to 180.

So we can use corresponding angles, and we can use co-interior angles to solve bearings problems. Find the bearing of A from B? Okay, that is not the bearing from B, that's from A because it's A.

So we're going to draw a north line from B.

Now, we want this angle here, okay? We want that angle there.

And there's two ways that you can do it.

You can extend this line and find that angle, which is 110 because those two are corresponding, and then plus 180.

Gets you to get this calculation.

Or you know that these two angles here and here must add up to 180, which means that, so this is 70, so far is 70 then the bearing is 360 subtract 70.

That is an awful 70, I do apologise for that, which equals 290.

Okay so our answer is the same both ways.

So, whichever you prefer, using the co-interior or the corresponding angles you can do, right? So have a go, pause the video in three, two, one.

Welcome back, hopefully you did your north line and I'm going to do my favourite way, which would be those two add up to 180.

So that's 130, and then do 360 minus 130 which should give you 230.

And then if you did it the other way, you extend that line.

Guess that angle is 50, so then you do 50 plus 180, which is also a bearing of 230.

Next one, so it's from B, so we're at B.

Okay, now, we want to know this angle here.

And this is why I prefer the co-interior one, the other one, the corresponding angles, it was about the same difficulty, but this one is slightly easier for the co-interior.

These two add up to 180.

So 180 subtract 52, and that should give me 128, okay? So that is on a bearing of 128.

You've to pause the video and have a go.

Pause in three, two, one, okay? So hopefully, you have drawn in your north line from B and you have used co-interior angles.

You could have done it the other way if you wanted, but as long as you've got a bearing of 040, well done.

Okay, next one.

Find the bearing of A from B? So from B that means we are at B.

Okay, so we want to know what that angle is there.

What could we do? Well, we can use the fact that these add up to 360 so that should give me 52, so this angle there is 52.

Now, because that's 52, I can use my co-interior angles, 180 subtract 52 and that should give me 128, okay? Your turn, pause the video in three, two, one.

Okay, so first thing we're going to do is draw our north line from B and we want to identify what angle we want to work out, which is this one.

Now, I can use my angles around a point add up to 360 to find that that equals 120.

Now, those two are co-interior, which means they add up to 180.

So that means that that angle is 60.

The angle is 60, so the bearing is 060, okay? You must remember three figures, okay? So now it's time for some independent practise, all right? But be careful.

I've written be careful here, because it's from B, right? From B.

Some of them are in there and they may trick you, okay? Be very careful about where you are starting from.

So pause the video to complete your task, resume once you're finished.

Okay, so here are my answers.

I would like you to mark your work.

So pause the video and mark your work.

Pause in three, two, one.

Okay, so hopefully you've got most of them correct.

The final thing for today is our explore task.

So I would like you to pause the video to complete your task, resume once you've finished.

Okay, so now let's go through this, all right? Let me go talk through how I did it.

Well, the first thing we've got to find is this bearing here.

So that's from A and that's 085.

So I'm going to mark that on my diagram.

Now, this pink angle is a corresponding angle with this one, so that is 085 as well.

This angle is 180, what's this angle? Well, that angle is, can you see that alternate angle there? That's going to be 50.

Look at this angle, well, they add up to 180 and they add up to 180.

Well, that's interesting.

Look 50, 85, 50, 85.

That means that that there is 45.

That's interesting how those two are the same as those two.

Okay, let's work out another angle.

What is this? That one, they add up to 180, so that would be 130.

What do those two add up to? Interesting.

And hopefully, you can write some bearing statements as well.

So the bearing of B from C, the bearing of A from C, the bearing of C from A, the bearing of C from B etc.

Okay, but I just wanted you to, I just wanted to show you those angles and draw your attention to them.

Because these patterns are super interested.

And you might want to now continue to explore and draw some more triangles within parallel lines, and see if these statements, these little findings that we've got here are always true, okay? Can you come up with a convincing argument that these are always true? And that is it for today's lesson.

So, if you'd like to, please ask your parent or carer to share your work on Twitter, tagging @OakNational and @LearnwithOak.

Thank you very much for your participation and hard work.

We are done, and I'll see you next time.