Lesson video

Hello, and welcome to this lesson on revisiting transversal angles.

Now this is a recap lesson of things that we did in year seven.

My name is Mr. Maseko.

Before you go on with today's lesson, please make sure you have a pen or a pencil and something to write on.

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

First, try this activity, 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.

What's the relationship between angle B and angle D if the lines intersect to the left of the dotted line? So if these lines, so this is angle B, and this is angle D, and we want the lines to intersect on the left of the dotted line.

So we want those lines, so we want something that looks like this.

So we want this scenario to happen.

So the lines intersect on the left of the dotted line.

Well, what's happened? You can tell that angle B is what? Is greater than angle D, for the lines to intersect on the left of the dotted line.

Well, what's the relationship between B and D if they don't intersect or if they don't intersect? So let's say that they're they're constantly the same distance apart.

Well you can say that angle B is equal to angle D, well if those angles are the same, then those lines will not intersect.

Now I want to delete this.

What's the relationship between B and C if the lines don't intersect? what we've already said, remember for them not to intersect that angle has to be the same as this angle.

So the lines are parallel.

So B and D have to be equal.

So then what would the relationship should B and C be? If B and D are the same, what's the relationship between B and C? Well, let's see if we can come up with an answer.

First thing, here's a diagram.

Can you work out all the missing angles? 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, we know that angles on a straight line equal, so on a straight line, they equal 180 degrees and more, on a straight line, that is half a turn.

so 180 degrees.

So we already have 75 degrees.

So this angle there, has to be 105 degrees, and we can do this for this straight line also, that's 105.

Meaning that this angle there has to be 75 degrees.

And then this angle there, has to be 105 degrees.

So if you look using that one angle, for angles on a straight line, we were able to find all the angles around that point.

What do you notice? Well, if you look, there are two pairs, there's a pair of angles that's the same.

There is a pair of angles that is the same.

So that pair is the same.

And the 75s are the same.

So you have this diagram and you have angles that are the same in this way.

And we call those, these are vertically, so these are vertically opposite angles.

And vertically opposite angles are always the same.

Vertically opposite angles, if you look, we use that rule.

We just use the rule for angles in a straight line, and we notice that the vertically opposite angles, the vertically opposite angles were equal.

And that's a rule that we can follow all the time.

Anytime you have two lines that intersect the vertically opposite angles are always equal.

Now we want to use this rule to answer the question that we asked in the first slide.

What's the relationship between B and C if the lines do not intersect? Remember we already, we already came up with the relationship between B and D.

We said that for the lines not to intersect, B must equal D so that those lines don't intersect.

Well, if B and D are the same, so we can say that B is the same as D.

And we know that vertically opposite angles are equal.

We know that C is also the same as D.

If B is the same as D and C is the same as D what can we say about B and C if the lines don't intersect? Well, we can say B has to be the same as C.

Now those angles that are found on parallel lines when they have a transversal across them.

So you see this line that crosses both those parallel lines, we call that, a transversal.

Now the angles that are made at those intersection points, those are transversal angles.

So give me some values for these angles, if these lines are parallel.

These lines are parallel.

So tell me, let's say this angle and this angle, what could they be? Okay, so D could be anything.

So D it could be 100.

If D is a 100 F, well F also has to be a 100, because those two angles would have to be the same.

Otherwise, if they weren't, imagine F was let's say 120.

Imagine F was 120.

Do you see what's happening? If F was 120, those lines would not be parallel 'cause you can see that they're getting closer and they will end up meeting somewhere.

Not let me delete this.

So D and F would have to be the same in order for those lines to be parallel.

Okay? What else can you see? Well, A and E would also have to be the same.

So if you said any numbers for A and E that were the same, like 50 and 50, that would have also been fine.

And E would have to be the same.

Now, like when you're investigating when we're investigating intersection points.

Remember when we changed the angles we saw when the angles were different, the lines intersected and the width became the same, and those angles were always.

Huh? Those angles, Now we'll investigate more what these angles are called, but you can see which angles need to be the same based on what would happen if you change them.

Like, if we change that 50 degrees and made it smaller, for example, this line would cross this space, you've made the 50 degrees smaller, but you can see that the distance here is not different from the distance there.

So those lines are no longer parallel.

Remember with parallel lines, the distance between them stays the same.

So you can use this to investigate which angles would have to be equal just by, if you move one line, see what happens when that angle changes, and you'll notice that B and H have to be the same.

And then C and G also have to be the same.

So this is what we should have noticed, but angle A, E, C and G were all the same would all have to be the same.

Why? Because if A is the same as E and A is also the same as C and E is the same as G cause they're vertically opposite, then all those angles are the same, same goes for B, D, H, and F.

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

Pause the video here and give this a go.

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

Well, we know that angle A is 30 degrees.

Now these lines are parallel, so which angle is the same as angle A? Well, we know that E has to be the same, because if those angles were different, those lines would not be parallel.

Well C is the same as A, so that's 30 degrees.

And look, C is also the same as E.

And if you look G is also the same as E so that's also 30 degrees, because these are vertically opposite.

Well, what about the other angles? Well, all these other angles you see lie on a straight line with a 30 degree angle.

So that's 150, that's 150, which makes sense, 'cause we knew that D and F have to be the same.

H is 150 and B is also 150.

What can you see? On a pair of parallel lines, there are only what? Two transversal angles.

So we only have, we've got four 30 degree angles and four, 150 degree angles.

Oh, this is important.

Now, realising which ones are the same and the patches of which angles have to be the same is really, really important.

And we'll explore this more in further lessons.

Now, for this task, work out as many angles as you can.

These lines are parallel.

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.

Well, let's deal with the angles on a straight line first.

If that's 110, this would have been about 70 degrees as this would have also been 70.

And then this is 110 degrees, it's vertically opposite.

Now, if you look at this, that's 140, vertically opposite, that would be 40 degrees, and this would also be 40 degrees.

Oh, okay.

We're getting somewhere now.

Now, if you look this parallel, this line is parallel to this line and this is the transversal that makes the 70 degree angle.

And remember what we said on parallel lines, there are only what, two distinct angles.

So we know that up here, there has to be a 70 degree angle and a 110.

Which one is it? Well, we know that this one would have to be 70 and that's 110, that's 110 and that's 70.

Okay.

So now what? We now want to figure out the angles on this transversal line.

How could we do it? Well, if we look inside this triangle, we have a 70 degree angle, a 40 degree angle.

Angles in a triangle add up to what? 180.

70 and 40 gives us 110, which means this angle is 70.

If that's 70 degrees, which means this is 110.

Again, we're now following the same rules around the transversal there's only two distinct angles, and you can tell which ones have to be same, 'cause you change one and then you will see which way the line travels.

And you'll see that if this angle here, if this angle is not 110 degrees, then those lines will meet either on this side of the line or on this side of the line.

And again, so that's what, this one will be 110 and that should be 70.

So look, from just knowing two angles in this diagram and our ideas about parallel lines and the angles that have to be the same, we were able to figure out all the other angles on this diagram, 110, and this is 70.

Now we will explore more of this in the next few lessons, but for now, thank you very much for participating in today's lesson.

And if you want to share any of your work, ask your parent or carer to share you work on Twitter, tagging @OakNational and #LearnwithOak.