Lesson video

Hello and welcome to this lesson on revisiting alternate and corresponding angles on parallel lines.

My name is Mr. Maseko.

Before you get on with this lesson, please make sure you have a pen, a pencil and something to write on.

Okay, now that you have those things.

let's get on with today's lesson.

First try is activity.

Given that the two bold lines are parallel, which transversal angles are equal? Remember the transversal angles are the ones that are made at the intersection points between the transversal and the parallel lines.

So there's a transversal and these two lines are parallel.

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, if you can remember back to last lesson, we're investigating what happens if we change some angles and if they're to stay where the lines remain parallel or not.

And we noticed that those two angles have to be the same for the last three parallel, because if those two angles were different.

So let's say that angle was slightly off.

So the thought angle was just a bit different.

You see how those lines are no longer parallel, if those angles are different.

So the angles are for the same.

So this angle, which is the same as this angle, and remember vertically opposite angles are also equal, so those two angles would also be the same.

And then this angle is the same as this, which is the same as this, which is the same as this.

So when we have a transversal intersecting two lines, in this way, there are two regions that are really important to us.

We have a region called the exterior region and that's the region not shaded in, and that's the region outside the parallel lines, so there's your exterior region.

And then we have that interior region, which is inside the parallel lines.

So the transversal that's crossing our two parallel lines, or just any two lines, we make two regions and exterior region and an interior region.

Now it's really important because you notice that those transversal angles be made, some of them are in the exterior region and some of them are in the interior region.

And now let's look back to which angles were the same.

Remember we said this angle in the exterior region is the same as this angle in the interior region.

Well the same thing here.

That angle and exterior is the same as what this angle in the interior.

Now, this relationship between angles in the exterior region and the interior region to make those lines parallel is really important.

And those angles that are equal have names.

The first halves of angles we'll look at, is what we call alternate angles.

Note alternate angles, so this is our transversal line.

Now alternate angles are on opposite sides of the transversal.

So one angle would be on this side and the other one will be on this side.

They are at different intersection points.

So we can't have, so let's say we have this angle and this angle, they can't be alternate, even though they're on different sides of the transversal, they are on the same intersection points.

So they are not alternate.

So alternate angles have to be at different intersection points.

So one will be here and the other one will be over here.

Another really important thing is that they are in the same region.

Different intersection points in the same region on opposite sides of the transversal.

So pause the video here and identify all the alternate angle pairs you can.

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

Well, if we look at this angle here, so this is an angle in the exterior region.

So we need an angle on the opposite side.

So we are looking at the opposite slide.

So down here, on a different intersection point.

So it has to be on this intersection point on this side.

But on the opposite side.

So in the same region, so this angle there, so this angle is alternate to this angle.

Do you see what's happened in the same region and they're on opposite sides of the transversal.

So they are alternate angles.

Another pair you could have had, is this angle and this angle.

Same region different sides of the transversal.

They are alternate angles.

Now, if these lines are parallel, what can you state about those alternate angles.

On parallel lines, those alternate angles are always equal.

On parallel lines those alternate angles are always equal.

Now the next type of angle we're going to look at is corresponding angles.

Now for corresponding angles, unlike alternate, they are on the same side of the transversal.

But they're not in the same region, they're in different region and remember, they're also at different intersection points.

That's a similarity between alternate and corresponding.

Alternate angles at different intersection points, corresponding angles are also at different intersection points.

But corresponding angles are on the same side of the transversal.

So here's a transversal and they're in different regions.

So pause the video here and identify as many pairs of corresponding angles as you can.

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

Well, if I pick this angle, we have an angle in the interior region.

So if I go to the second intersection points, I want an angle on the same side and in a different region.

So on the same side, in a different region, it would be this angle.

So those two angles are corresponding.

I can do the same thing with this angle.

And that has to be the same as this one.

Same thing with this angle, there has to be the same as this one.

And then I'm going to label this one X as to be the same as that's fine.

So those are all different pairs of corresponding angles.

And we've already seen from our investigation of intersection points that those angles have to be the same for the lines to be parallel, because if it changes, the line will start going in a different direction and you end up intersecting with the other line.

So like alternate angles, corresponding angles are also always equal.

Now for this independent task, it's all about identifying alternate and corresponding angles.

So pause the video here and give this a go.

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

Angle b and h.

Angle b and angle h.

They are on different sides of the transversal in the same region, coz they're both in the exterior region.

So they are alternate.

Angle d and f, different sides of the transversal, same region.

So they are also alternates.

Angle h and d, same side of the transversal.

They're both on the same side and different regions, so these ones are corresponding.

I'll just write in short.

G and c, same side of the transversal, different regions.

So again, there's a call responding c and e, angle c, angle e different sides of the transversal, same region, so these are alternates, I'll just write alt.

Okay.

So really well done if you got all of these.

Now, here's an explore task, given that the line segments, a, b and CD a parallel, show that the interior angles of a triangle sum to 180 degrees, and give your reasons.

If you want a clue, keep watching the video.

But if you want to try this on your own, pause the video in three, two, one.

Okay, for those of you that want a clue, first you've got to look at this.

What do the angles on a straight line sum to? Good, they sum to 180 degrees.

So these three angles, a, b and c.

So a plus b plus c sum to 180 degrees.

Now using those rules, you just figured out four corresponding angles and alternate angles, can you identify other angles that would be the same size as angle a and other angles that would be the same size as angle c.

Pause the video here and give that a go.

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

Well, if we look at this, let's look at angle a, we have angle a, here's a transversal, and these are parallel lines, what angle is the same as a? Well, we can have a corresponding angle there that is on the same side of the transversal, but in different regions.

So there's a corresponding.

That angle is the same as a.

And we can also have this one.

This is also the same as a, because if you look at other vertically opposite angles are the same, or you've altered angles are the same because alternate angles, different sides of the transverse all in the same region, alternate angles.

So this angle, this base angle of the triangle is a, and using the same reasoning you would have figured out that this base angle of the triangle is c.

And if you look inside the triangle, we have the angles, a, b and c, and we've already seen that angles a, b and c add up to 180 degrees.

So we've just shown that angles in the triangle add up to 180.

If you would like to share your work, ask your parent or carer to share your work on Twitter, tagging at Oak National and hashtag LearnwithOak.

I will see you again next time for a final lesson on angles on parallel lines.

Bye for now.