Lesson video

Hello and welcome to another video.

In this lesson, we'll be finding missing angles on parallel lines.

My name is Mr. Maseko, make sure you have a pen or pencil and something to write on before you start this lesson.

Okay.

Now that you have all those things, let's get on with today's lesson.

First I try this activity, pause the video here and give this a go.

Okay.

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

First, you were to identify the corresponding angles.

Let's think back to last lesson, what was the definition of a corresponding angle, Good! They're on the same side of the transversal that's one.

What's the other thing? there in different regions and at different intersection points.

Okay.

So same side of the transversal so if we just look up here, different regions, so one has to be in the exterior and one has to be in the interior.

So.

if you look at this, we can say angle F and angle.

B F and B, those are corresponding.

Same side of the transversal, different regions.

You could have also had G and C.

H and D, E and A.

Alternate angles, what are the definition of alternate angles? Good! Different sides of the transversal.

So next thing, different intersection points.

Good! Last thing, same region.

Good! Different sides of the transversal.

Same region, different intersection points.

So one's going to to be up here and one's going to to be down here.

But they have to be in the same regions.

If we look in the interior region, remember that inside.

So we can see that angle C and angle E they're on different sides of the transversal in the same region on different intersection points, so C and E.

you could have also had B and H, you could have had F and D or you could have A and G.

you have your interior alternate angles and you have your exterior alternate angles.

vertically opposite angles, those are on the same intersection point.

That's a difference between corresponding and alternative, and vertically opposite.

Corresponding and alternate at different intersection points, whereas.

vertically opposite at the same intersection point.

So looking at one intersection point, and you see that B and D, those are vertically opposite.

You could have had A and C, E and G or H and F.

A really well done if you got any of those.

So the first thing we want to look at is for parallel lines, corresponding angles are always equal.

Now why do corresponding angles have to be equal for the lines to be parallel? Well, let's explore and see.

let's pick these two angles.

So this angle here, where is its corresponding angle? Good, on the other intersection point and at different regions.

So in the exterior region, we can see that this is the corresponding angle.

Now what happens if those angles are different? Right now, they're the same and the lines are parallel.

Well, if they're different.

Well, let's change this first angle.

Let's make it smaller! What happens with that angle becomes smaller? So see, that's the angle now.

Do you see now that the lines are now tending towards each other.

Can see that the distance between the lines is decreasing and at some point they will end up intersecting.

So that's why those angles have to be the same to keep the lines the same distance apart all the way through, meaning that they will never meet.

So corresponding angles have to be equal on parallel lines.

So, if this angle was 120 degrees, the corresponding angle would have to be? Good! It also have to be 120 degrees.

Okay! Now let's look at our other type of angle, which was our alternate angles.

Now, again.

Remember where we find alternate angles? Same region, different sides of the transversal.

Different intersection points, same regions.

If we just look at the interior region, different sides of the transversal.

Now, again! Alternate angles on parallel lines just the same way as corresponding angles.

They have to be equal.

Why? Well, you can explore by trying to change one of them.

If you change one of these angles, again, you'll be able to see that your lines will start tending.

See if I do this now, that angle is quite small.

You can see that the distance between the lines decreases up until the point where they will intersect.

So like corresponding angles, alternate angles have to be equal in order to keep the lines parallel.

Now, this is a really important thing because it helps us to figure out other angles in a diagram like this.

One we know that corresponding angles are equal and alternate angles are equal.

Pause the video here and give this activity a go.

Okay.

Now that you've tried this, let's see what you come up with, well it says that angle B is 120 degrees.

So how big would angle E be? Well, what other angles do you know that are 120 on this diagram? Well, you know that angle F is 120.

Why? Because it's corresponding.

How do we know its corresponding? How do we know? Same side of the transversal, different regions.

Same side of the transversal, different regions.

Different intersection point, corresponding angle.

So they are equal on parallel lines.

Well, you know that H also has to be equal.

Why would H be the same as well? Well, it's vertically opposite to F and same thing with D is vertically opposite to B.

Now we want to figure out angle E.

well, we know about F is 120, so E is on a straight line with F.

So it would have to be? Good! 60 degrees.

Because angles on a straight line add up to 180.

Now there's something really important here.

If you look at this, see those two angles in the interior region on the same side of the transversal.

Those two angles in the interior region on the same side of the transversal.

What do they add up to the end up to? They add up to 180.

Will that always be the case? Hm, try it out with other power lines and see what you find out.

But those two angles are called co-interior angles.

So those two angles are called co-interior angles.

And you'll find that on parallel lines, those two angles always add up to 180.

Hm! Now for this independent task, look at these diagrams and work out the angles labelled A.

Pause the video here and give this a go.

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

Well, A on the first diagram should have been 91 degrees.

Why? Because it is corresponding to 91.

Hm, okay corresponding.

You just have spotting patterns.

Same side of the transversal, different regions.

Okay.

What about A, on the second diagram? Good.

It's 100, because it's meant to be it is alternate to 100.

See! Different sides of the transversal, different sides of the transversal.

Some region alternate.

So this was alternate.

This one was corresponding.

What about angle A in that third diagram? Well, if you look at this we have different sides of the transversal, different regions.

It can't be alternate.

It, it can't be alternate and it can't be corresponding.

but what can we figure out? Well, there's multiple ways you could go about this.

You can find out what this angle is, or you can find this one, this angle is corresponding to 88, or it is 88.

This angle is alternate to 88.

So it is 88.

It doesn't matter which way you go about it.

You can find any of those angles.

And then, you know that angle A is on a straight line with 88 degrees.

So that is 92, using your rules for alternate and corresponding angles.

Now, some of you may have noticed or I can figure out this angle because it is co-interior to the 88.

And that angle will then be 92.

Meaning the vertically opposite angle is also 92.

See, there are multiple ways to figure out these angles.

All you have to do is just remember your corresponding angles, your alternate angles and your vertically opposite angles.

You cannot add co-interior angles to that as well.

And you could go the same way with this one, or we've got 95.

Well, we know that this angle there, that would be 85.

Why? It's on a straight line with 95.

And that angle is alternate to angle A because it's on different sides of the transversal, in the same region.

So angle A is 85.

Good! Really well done for getting through this.

Now, for this explore task.

Work out as many angles as you can.

You're practising using your alternate angle rules, vertically opposite angles and corresponding angles.

Just work out as many angles as you can.

pause the video here and give that a go.

Okay.

Now that you've tried this, lets see what you have come up with.

Well, let's see.

if we just focus on this transversal first.

So this transversal we can have, well, this angle is alternate to this angle.

How do I know it's alternate that angle? You know this now, different sides of the transversal, same region at different intersection points.

So that angle is 40.

Okay.

And then, if that angle is 40.

It's on a straight line with 140.

This angle here is vertically opposite, so, to 45.

So that is 45.

Well, now we've got that second transversal.

The one that's still dotted.

You can see that we have this angle and this one up here.

Those are on the same side of that transversal, in different regions.

So they corresponding, so this one has to be 45 also.

And the angle, that is on a straight line with that is 135.

Okay.

Are there other angles that we still haven't figured out? Well, we have this angle here or this angle is in a triangle with 40 and 45.

Angles in triangle add up to 180.

Goods! So that angle has to be 95 because 95 was 45 plus 40 gives you 180.

And this angle also has to be 95 because it's vertically opposites.

So, do we have any more angles? Well, we've got the two angles that complete the circle with the two 95.

Well, we know around the point it has to equal what? Good! around the points it has to equal 360, we already have two 95s.

So 95 add 95, that is 190.

Well done! So what are you left with? You're left with 170 to split between two angles.

So both of them have to be? Good! Both those angles are 85.

Now really well done, If you got some of those answers and even more so if you've got all of those answers.

Now, if you want to share the work that you did today.

Ask your parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak.

Now, this was our last lesson on revisiting parallel lines, and I know that you've made some great progress.

I will see you again next time.

Bye for now.