Lesson video

Hello and welcome to this lesson on intersections.

Now this will be a recap lesson on what we did when we were in year seven.

Now, my name is Mr. Maseko.

Make sure you have a pen or a pencil and something to write on before you start this lesson.

Okay, now that you have those things, let's get on with today's lesson.

First try this activity.

Now how would you change the angles so that the intersection point.

So, this point, moves further away from the horizontal line or moves closer to the horizontal line.

So how would you change those angles? Pause the video here and give this a go.

Okay, now that you tried this, let's see what you've come up with.

Well, if we look at this diagram, we want to take this point and we want to move it closer to the horizontal line.

So what can we do? Well, if you look, if we change the angle of this line.

See, we've now taken the intersection point and we've moved it closer.

So what's happened to the angle of that second line? We have changed it so that it intersects on that second line, so it intersects on this line as a lower point.

So now the angle's smaller so any angle that is less, or say the angle is less than 60 degrees for the second line.

That's fine.

As we move your point closer to their horizontal line.

Let me erase the stuff we've written so far.

See, if we take the second line and we make the angle that bit smaller, so instead of it being.

So let's say we make it 90 degrees for example.

That should be a straight line.

You see how that point is now further away from the horizontal line? If we've taken this line and we've decreased the 120 degree angle, we've moved further away.

So we could also say what the angle is less than 120 degrees, that moves further away.

Now this idea of what happens when we change these angles and what happens to the intersection point for those lines is what we'll explore further throughout this entire lesson.

Now, Xavier says if angle a is less than angle b, that lines would intersect below the horizontal line.

So these are horizontal.

Do you agree with that statement? Now draw a diagram to support your answer.

Pause the video here and give that a go.

Okay? Let's see what you come up with.

All you have to do is look at that second line, and let's see what happens when we increase that angle.

As we increase the angle, the line is moving this way.

What's happening to the intersection point? So each time we increase the angle.

See now the intersection point is doing what? So every time we increase the angle.

So you see your line is moving clockwise.

So every single time we increase that angle, so this angle is increasing each time.

See what's happening, that intersection point is doing what? Is moving below the horizontal line.

It first starts going further and further up, and then at some point it won't be intersecting above the horizontal line, and at some point that intersection point will end up being below the horizontal line.

And this is the diagram that we could have drawn to show this.

Now, what if we want these lines to not intersect? What could we do? We don't want them to intersect, what could we do? Pause the video here and give that a go.

Okay, now that you've tried this, let's see what you'll come up with.

Well, we don't want these lines to intersect, and we've seen that if we change this angle and we increase it, we move this point further away from the horizontal line.

And you saw that we can change the direction that that line is travelling in.

So every time we increase the angle, we can increase it to a point where those lines never meet.

Now what should we increase it to? We got it, we'd have to increase that angle to 120 degrees, and if you look, if that angle was 120 then these two lines, you see the distance between them stays constant all the way through, meaning that those two lines will never meet.

Now you see when those two angles are the same, those two lines will never meet.

We say that those lines are parallel.

So, solve like train tracks.

So these two lines are parallel, the distance between them stays the same all the way through, and these lines never meet.

And this happens when these angles are the same.

So you could have either changed the 60 degrees to 120 or you could have changed the 120 degree angle, you could have changed that one to 60 degrees.

You'd have made a pair of parallel lines, and those are lines that never meet.

Now, looking at these lines here, will they meet? So will they intersect? If they do intersect, where will the intersection point be? Pause the video here and give that a go.

Okay, now that you've tried this, let's see.

Well if we look at this diagram first, will those lines ever meet? Well, no, these ones won't meet 'cause if you look those two angles, those two angles are the same, so these two lines are parallel.

You can see that the direction that we are travelling in is the same, and the distance between them stays the same all the way through.

Now if we look at this diagram, you can tell that these angles, so this line as it moves down, the distance between the two lines gets smaller and smaller.

Now it's very minor but because this angle is just slightly bigger than this one, that distance would keep decreasing as you get further below the horizontal line, that distance would decrease until they meet somewhere below that horizontal line.

Because as you get further up, those lines, the distance between them will just get further and further apart.

So these two lines will meet and they will meet below the horizontal line.

Now here's an independent task for you to try.

So, pause the video here and give this a go.

Okay? Now that you tried this, let's see what you have come up with.

Well, you should have noted that these lines, this was where parallel, that those two aren't parallel, you can tell that they're getting closer and closer and they will intersect somewhere down there.

And if you now draw a parallel line to this, well just pay attention to what happens with the line.

Every time you go one down, you got two across, one down, two across, one down, two across.

So you got to do the same thing.

So, when you draw a line, your line is going to look the same as this one, every time you go one down, you got two across, and one down, two across, one down, two across.

So that line I've just drawn is parallel.

And that's also how you could have told that these lines were parallel because look, when you go one across, you go one up, one across, one up.

Here, one across, one up, one across, one up.

Whereas here, if you look for that first line you go one across, two up, whereas here you go one across and one and a bit up.

So that's how you can tell that those lines aren't parallel and these ones are parallel.

So now we're matching the descriptions.

Well the ones that don't intersect are the ones with the same angle.

Okay, if you look at this diagram now, we're trying to decide if they intersect above or below the horizontal line.

And you've got to pay really close attention to how the line is moving.

And if you just extend this line, you can tell with a ruler that these lines look like they're going to meet below that horizontal line, whereas if you looked at these lines, if we expand them upwards, you can see that they're getting closer and closer up there and they will meet above the horizontal line.

So that's above and this one there, that is below the horizontal line.

Now here's an explore task.

Suggest values for angles a and b so the intersection point lies within each of these regions.

And I'll suggest a value for a and b that would make the two lines parallel.

Pause the video here and give this a go.

Okay, now that you've tried this let's see what you're going to come up with.

Your answer should be something like this.

In order to be in region six, all angles have to be acute, what does that mean? That means they have to be less than 90 degrees, but angle a has been less than angle b, and you can tell because if angle a is less than angle b, that's how this is going to help him.

And then these are all the other scenarios that you could have had.

You could have had when both are obtuse 'cause you can see, to move the intersection point down there, both of those angles have to be obtuse.

Well see, and angle a if you look at it, angle a has to be less than angle b.

So values that we could have had for each of these regions, we said here that angles had to be, what? They had to be less than 90 degrees, those are our angles.

But then a had to be less than b, so you could have had a being 40 degrees and b being 50 degrees, for example.

And you can just follow those rules.

For obtuse angles there, bigger than 90 degrees but here a is less than b and up here both obtuse, a is greater than b, here both acute a is greater than b.

Here you want acute b and an obtuse a, and here obtuse b and an acute a.

So if your answers fit in with this, really well done.

And remember for two lines to be parallel, a must equal b.

Those two angles are the same, those lines would never meet.

Okay, I really hope you've enjoyed today's lesson and if you want to share your work, ask your parent or carer to share your work on Twitter tagging @OakNational and #LearnwithOak.

I will see you again next time.

Bye for now.