Lesson video

Hello, I'm Mrs. Lashley and I'm really looking forward to working with you as we work through the lesson today.

So, by the end of the lesson today, we're going to have worked with alternate angles, but we're going to look at a very special case, which is when the alternate angles are in parallel lines, we then produce equal alternate angles.

Keywords that you'll have met before.

You may wish to pause the video just to read them and refamiliarize yourself, but otherwise, we'll move on to our new keyword for this lesson.

So, we'll be working with alternate angles during the lesson and we're going to come up with this definition as we go, but it is there for you to read if you wish to.

So, our lesson's got three learning cycles.

The first part is just identifying what alternate angles are.

Then, we're going to then specifically look at alternate angles in parallel lines.

And then, finally, we're going to identify the rules.

So, use other angle knowledge that you have, as well as this new alternate angle knowledge that you've just acquired.

So, let's make a start on the first learning cycle, which is identifying what these alternate angles actually are.

So, on the screen, you can see three line segments.

They've got various gradients, various lengths, but they're line segments that we can then arrange into different diagrams. Like this.

So, can you match which one has gone into which position? So, all they've done is translated on the screen to that new arrangement.

Rather than being three separate line segments, those line segments are all together in one diagram, but I could have arranged them like this or this or even this.

So, those three line segments are in each of those diagrams. It's just the positions that gives us the different arrangements.

So, there's the four arrangements that I came up with.

There's still three line segments within each arrangement and one of them is known as the transversal line.

You may have used the word transversal before, so let's just revisit it and make sure we're all happy with it.

So, the transversal line is the one that intersects two or more.

So, because we're only dealing with three here, it's only intersecting two lines, two or more lines at distinct, which means different points.

So, the first three arrangements have now got one of the lines in purple, and that is the transversal.

It's the line that cuts or intersects the two others.

On that last diagram, on that last arrangement, I've not yet put the transversal or not highlighted the transversal.

Can you think about why? Well, that's because actually, they are all transversals, because they all traverse each other in this arrangement.

When we work with different arrangements of line segments, it's useful to think about which one is the transversal line.

Sometimes, all of them can be the transversal and it'll just depend on which part you're working with to which one you want it to be.

So, now, we've got arrangements and we've marked on what we can know as alternate angles.

So, we've got the transversal line, we've got the two other lines in these three-line segment arrangements and some alternate angles have been marked.

Lucas thinks he knows why they are alternate.

So, Lucas thinks from those four diagrams he has a vague idea or a good idea why they are alternate angles.

Do you have any idea why they are the alternate angles in the diagrams? Izzy thinks she does as well, but she would like some non-examples, some marking, some not alternate angles just to reassure her and to check her idea.

So, here we are.

Here are some arrangements that are not showing alternate angles.

So, the marked angles are not alternate to each other.

Lucas had thought that to be an alternate angles or to be alternate angles to each other, they needed to be on either side of the transversal.

But there are some non-examples that also have angles marked on either side of the transversal.

So, from these, Lucas' idea of what an alternate angles were has suddenly failed, because there are some non-examples, some non-alternate angles shown, which are also on either side.

Let's see what Izzy thought.

So, Izzy thought that the two angles had to either be both inside the other two or both on the outside of the other two lines.

Is this conjecture of what alternate angles were still, that still works for the four examples here, but Lucas did have something about something to do with the transversal and it's important that why is there a transversal if it's not going to help us with the alternate angles.

So, both of these line systems have got alternate angles marked.

The one on the left we know as exterior alternate angles.

And the one on the right we would call interior alternate angles.

So, alternate angles can be interior, which is when they're between the lines or exterior, which is one on the outside of the line.

So, that's what Izzy had suggested alternate angles were.

They're on different vertices.

So, if you remember the transversal, the transversal intersects the other two lines at different points, distinct points.

And those points are what we are calling the vertices.

And they do need to be on either side of the transversal.

So, Lucas was right that about alternate angles.

Alternate angles, we do need to have one angle on one side of the transversal and one on the other side, but it's not only about what side of the transversal line they're on, it's also to do whether inside or outside of the other two.

So, together, Lucas and Izzy had identified the definition of alternate angles.

So, a quick check with that one.

Which show a pair of alternate angles? So, pause the video whilst you are having a look at those diagram, thinking about what Lucas and Izzy both said.

Remember that combined, they have the definition.

And then, when you're ready to check, press play.

So, A does show us some alternate angles.

These are interior alternate angles.

B is not showing a pair of alternate angles.

They are on opposite sides of the transversal like Lucas suggested, but they're not both inside or both outside like Izzy suggested.

So, that is why they're not alternate angles on B.

C does show us some alternate angles.

So, we've got that transversal, it's the one that's nearly vertical.

We've got angles on either side and they're also both inside the other two lines.

And lastly, D, D does not show alternate angles, because they're not on opposite sides of the transversal that's cutting through the other two lines.

Hopefully you did well on that, thinking about those two parts of the definition.

For two angles to be alternate, we need them to be on opposite sides of the transversal, and then they either both need to be inside or both outside the other two lines.

You may be thinking about the fact that we've only dealt with three line segments, but are all line systems maximised at three? Well, no.

And a transversal can cut through, can intersect with more than two lines.

So, here, we've got a system where we've got one transversal line segment, we've got three line segments here.

And so, you can see that the transversal is intersecting with more than two lines.

And on the second diagram, it's exactly the same diagram, but our alternate angles are in slightly different places.

So, the alternate angle, the pair of alternate angles can be in slightly different spaces, because it's just whereabouts you focus on.

You just want to focus on two of the lines.

So, on the first diagram, if we ignore that central line, then we've got these two exterior alternate angles.

Whereas on the right-hand one, we're ignoring the bottom line.

Then, we've got another pair of exterior alternate angles.

So, when you've got a more complicated diagram with many more line segments, then it's absolutely fine for you to ignore, not to rub out or to try and erase, but to ignore that and just focus on a certain section of the diagram.

So, here, we've got a different diagram where we've got three line segments being traversed by a transversal.

And again, you can see there are two sets of interior alternate angles, by ignoring the central line and then also ignoring the bottom line.

A check on that, we've got some line systems where you've got three line segments all with one transversal.

So, pause the video to work out which show a pair of alternate angles.

When you're ready to check that, press play and we'll go through the answers.

So, A, we have got an interior alternate angle pair.

So, here, which can sort of ignore that, the middle line of the three and we can see that both angles are within the other two or inside and on either side of the transversal.

B, they are not a pair of alternate angles.

They are on opposite sides of the transversal.

But one would we would say is inside and one would say is outside.

So, we don't have interior alternate nor do we have exterior alternate, because there is one on the inside and one on the outside.

C, it's not a pair of alternate angles, because they're on the same side of the transversal line.

They need to be on opposite sides to be alternate, as well as either inside or outside.

But D does show us a pair of exterior alternate angles.

So, now, you're up to the task where you, for this first question on each of the system as lines, decide if the marked angles, so the ones that you've been given, are alternate or not.

So, pause the video whilst you're working through those six line systems, and then when you're ready for the next question, press play and we'll move on.

Question two is a similar idea, but this one, you need to mark on the alternate angle.

So, you've got one angle and you need to mark the pair, the pairing alternate angle for that line system.

Press pause whilst you're working through those six line systems. And when you're ready for the answers to both questions one and two, press play.

So, here, we've got question one, A, C, E, and F were all alternate angles.

The pair that you were given were alternate angles.

B wasn't alternate, because one was on the outside and one was on the inside and they were not interior nor they were both exterior.

And D was the same reason.

So, they were on opposite sides of the transversal, but one was the inside of the two lines and one was on the outside of the two lines.

Question two, you needed to mark on an alternate angle to the given angle.

So, here now, all the diagrams have got at least two angles marked.

The one that was given for the question and the one you should have drawn on, on D, E, and F, because they were more complicated systems of lines, there were more line segments involved, then you may have put one's alternate angle, but there could have been an alternative.

So, just check that you have got one of the ones that have been given, so they all have the word or, because there was two alternate, depending on which line you ignored when you were looking at the system of lines.

So, we're now onto the second learning cycle and this part is still working with alternate angles like we've just been doing.

So, thinking about angles, a pair of angles that are on opposite sides of the transversal and either both inside or both outside.

But the difference now is that those two lines that the transversal is intersecting with are parallel.

So, here, we've got two line segments and we've also been told that the angle between the two line segments is a right angle.

So, what other angles do we know? So, just pause the video and have a think about that yourself before we go through it together.

Okay, so you may not have done it in the same order as I have, but we know that vertically opposite angles are equal.

So, that other side of where these two lines intersect would also be a right angle.

And we're using the symbol for right angle rather than marking it and writing 90 degrees.

So, we're going to use the notation that's the quickest and most efficient way.

We also know that angles on a line at the same point sum to 180 degrees.

So, therefore, if 90 degrees has already been used up, then there's only 90 degrees left to get from that quarter turn around to that half turn of 180 degrees.

And then, angles around a point sum to 360 degrees.

So, if I've got a one remaining angle out of 360 and I've already used 270 degrees, then there's only 90 degrees left.

You may have filled that in a slightly different way, but the idea is that we actually, by knowing that one of those angles is 90, we know that all three of the others are 90 as well.

So, you've done translation as a transformation previously and if we translate the whole horizontal line down, we create a set of parallel lines.

So, translation doesn't have any rotation to it, it's only going to move it horizontally and vertically.

So, here, we're going to just move that horizontal line vertically down and that would create a pair of parallel lines.

And notice that when that became a pair of parallel lines, we then had the feather marking the arrow to indicate that this is a pair of parallel lines.

And that translation preserves the angle between the line and the transversal.

So, because we've just translated it, there's no rotation, I haven't reflected it, the angles are preserved, the angles are invariant.

So, all those four 90 degrees, all those four and right angles that were on the original horizontal line around that point, I've now moved, have translated down.

We've now got a pair of parallel lines and a transversal.

We know that all the angles that are marked here are 90 degrees, but which ones are pairs of alternate angles? Thinking about what we've just seen and the definition of alternate angles.

Well, A and G, they would be exterior alternate angles.

B and H, another pair of exterior alternate angles.

C and E, so this is an interior alternate angle pair.

They're both on the inside of the two lines.

D and F, interior alternate angles.

And each pair of those alternate angles are equal.

They were all 90 and 90.

So, Laura has decided, well, that just shows that alternate angles are equal when two parallel lines are traverse.

So, when a transversal, when a line that is a transversal cuts through a pair of parallel lines, then the alternate angles are equal.

That's what we've just seen with the right angles.

And Jun has said, Laura, actually, at least that's true if the transversal is perpendicular to the parallel lines, perpendicular meaning to meet at 90 degrees.

So, we've just seen that that is true if the parallel lines are perpendicular to the transversal, if they are 90 degree angles at the point and Laura realises what her mistake there was that, yeah, you can't assume that's true for all.

We haven't seen that to be true for all angles.

So, are alternate angles in parallel lines always equal or is the 90 degrees a special case? So, on the slide deck there is a link to a GeoGebra file where we can have a look at a system of lines where we've got parallel lines and a transversal.

So, I'm going to show you that, and then we'll come back to the slide deck.

So, here, we can see the setup that we just saw, it's been rotated, but the idea is exactly the same that we've got a pair of parallel lines, 90 degrees and a transversal.

So, our transversal is perpendicular to our set of parallel lines.

And so, we've already seen that that means that 90 degrees and 90 degrees that they are equal.

The alternate angles in parallel lines when there are 90 degree angles make them equal.

What we're going to do here is I'm going to move, I'm going to drag the transversal, I'm going to change the gradient of the transversal.

I can also move the parallel lines, make them further apart, closer together.

And we're going to have a look.

Does that change anything? Are alternate angles equal in parallel lines? So, there, we just saw that when I move the parallel line, it's still parallel to the other one.

We had exterior alternate angles that were equal at 90 degrees, and if I dragged it onto the other side, they became interior alternate angles and they were also still 90 degrees.

So, the movement of the parallel line hasn't changed the angle that we've got marked here.

And that's makes sense.

We looked at translating the line and the angles were preserved.

So, now if the transversal is not perpendicular to the parallel lines, does that mean the angles are no longer equal? Well, the transversal was no longer perpendicular to the parallel lines, but the angles were still equal.

So, we saw on the GeoGebra file that actually, the direction of the transversal, the gradient of it didn't affect this equality between the alternate angles.

Here, we've got two lines intersecting and they create angles of 74 degrees.

If I translate that line upwards along the transversal now, the parallel lines have been created.

And because we've translated, the angles have been preserved, so there's still 74 degrees.

And here, we can now see a pair of alternate angles that are exterior alternate angles and we can also see interior alternate angles and everything is 74 degrees.

So, this idea, alternate angles are equal in parallel lines, is holding and we saw that on the GeoGebra.

I can move the second line below it, that's still the same.

Bit further down, bit further down.

So, here, we've seen that this holds true, and so the translation of the line preserves the angle and that is the reason that they are alternate.

It wasn't because they were perpendicular.

That wasn't just a special case of this, it's for any angle.

Then, the parallel line is just a translation and therefore the angles are preserved and we have sets and pairs of equal alternate angles.

So, our alternate angles in parallel lines always equal.

Well, yes, and we can show this using other knowledge that we've already acquired.

So, corresponding angles in parallel lines are equal.

You'll have met that before.

So, here, we've got a pair of corresponding angles.

They're on the same side of the transversal and they're in the equivalent positions around the vertex.

So, we know those two angles are equal.

We also know that vertically opposite angles are equal, and so hence, the alternate angles are equal too.

We can see interior alternate angles there.

And from other knowledge about angles from other facts that we have, we can show that that is why alternate angles are equal in parallel lines.

So, a quick check on all of that about parallel lines.

For alternate angles to be equal, they could lie between two parallel lines, lie on opposite sides of two parallel lines, both lie outside two parallel lines, lie between two non-parallel lines.

So, pause the video and decide which of those statements would be factually correct, and then press play to check.

So, the first one is true if they lie between the two parallel lines.

So, that would be our interior alternate angles.

And if they both lie outside the two parallel lines, that would be our exterior alternate angles.

B, lie on opposite sides is to suggest one is in and one is out.

So, that isn't alternate angles.

And if they were lying between two non-parallel lines, they would be alternate angles, but they wouldn't be equal.

The parallel lines is where this equality element comes in.

So, if alternate angles are equal, then we can determine if lines are parallel.

So, using the fact that alternate angles are only equal if the lines are parallel.

So, are these lines parallel? Well, these exterior, they're both on the outside, alternate angles on either side of the transversal are equal.

They're both marked to be 124 degrees.

So, the lines are parallel.

And then, we could mark our parallel lines with feather marks to indicate that they are parallel.

And if we know they are parallel, so if the diagram has already got the markings to tell you that those lines are parallel, then you can determine the size of an alternate angle.

So, here, we've got interior alternate angles.

We know those vertical lines are parallel to each other.

So, this is equal alternate angles and therefore X is also 68 degrees.

So, a check.

Jacob says from this diagram, this is a pair of interior alternate angles which are equal.

Explain why he is incorrect.

So, pause the video and think about why Jacob's statement is not true for the diagram given.

Press play when you're ready to check.

Firstly, Jacob has called them interior alternate angles and actually both of those angles are marked on the outside of the two lines.

So, they are exterior alternate angles.

So, just a careful.

Just to be very careful there that if we're using the word interior or exterior, we're using it correctly.

And he has also assumed the lines to be parallel.

There's no notation, there's not the feather marks, the arrows to indicate that they are parallel.

So, we can never assume in maths unless we've got numerical values there to suggest that they are equal.

And then, we would know they are parallel or if we've got the notation for parallel lines, then we would know that they would be equal.

But other than that, you can't just assume, because it looks like it that that is to be true.

So, you're now onto task B for this lesson.

Question one and question two are on the screen.

So, first of all, you've got to give the size of the marked angle, and then secondly, you've got to decide if the system has got parallel lines.

Pause the video whilst you're doing that, and then come back for question three.

Okay, so question three, quite a complicated diagram.

Which angles form an equal alternate pairing with angle i.

So, find angle i, and then you need to decide which of the other marked angles form an equal alternate pairing.

Pause the video whilst you're doing that, and then when you come back, we'll go through the answers to questions one to three.

So, questions one, the marked size were all the same, because of the parallel lines, we've got the feather notation there.

So, alternate angles are equal in parallel lines.

So, you were given 76 degrees, therefore A was 76 degrees.

On B, you were given 83 degrees.

It was an exterior alternate angle in parallel lines, therefore they were equal, B was also 83.

And that was the same for C.

On question two, you needed to use the fact that if they were parallel lines, the angles are equal or if the angles are equal, then they are parallel lines.

So, on two, 92 and 93 are not equal.

They're very close to each other as an angle size, but they're not equal, so therefore, there are no parallel lines.

On part B, it was yes.

And so, you can add the feather notation on, that we know that they are parallel.

We've got exterior alternate angles that have been marked as the same size and therefore we've got parallel lines.

And for part C, we have got a more complicated diagram there.

We've got one of those systems where we've got quite a lot of transversals depending on which bit we are focusing on.

But A is an exterior alternate angle to A.

So, we don't know the actual value of that angle, but they're both been marked as angle A.

So, therefore, they are the same, they are equal, and that means they are parallel lines.

Question three, which angles form alternate pairing with angle i? More importantly, an equal alternate pairing with angle i.

Well, o is an exterior alternate angle with i and c is another exterior alternate angle with i.

So, o and c are the correct answers for three.

Now, we're at the last learning cycle, which is known as identifying the rule and that's because you now have quite a few angle facts that you know about.

And the more difficult part, once you start to learn more is being able to recognise when to use which one.

So, that's what this learning cycle is all about.

So, on the diagram, all of the angles that are marked are equal.

Can you think about why? What maths do you know? Why are they equal? How do we know that for certain rather than me just telling you that they are equal? So, angle PQR and angle QTS are corresponding angles in parallel lines.

So, they are equal.

Angle PQR is also equal to angle UTV as they are exterior alternate angles in parallel lines.

So, therefore, they are equal.

And angle QTS is equal to angle UTV, because they are vertically opposite angles which are equal.

So, if PQR, if angle PQR is equal to QTS and angle QTS is equal to UTV, then they are all three of those are equal angles.

So, a check.

Similar to that one, you need to fill in the blanks.

So, which angles and which words for the reasoning do you need to put in the blank spaces? Pause the video whilst you're working through that, and then we'll go come back and go through the answers.

Firstly, angle FED is equal to angle EBC.

Angle GEB is equal to angle EBC as they are interior alternate angles in parallel lines.

And lastly, which two angles are equal, because they are vertically opposite? So, hopefully you can see that, that they're marked on the diagram, they're vertically opposite.

So, now, it's just your labelling.

So, angle GEB is equal to angle FED.

It's worth noting here that the order of your letters may be slightly different to the ones that I've given here.

The main point is that the centre letter will be the same as mine and your other two will be swapped over.

The only place where that might be slightly different is for example, angle EBC, you may have said FBC, because you've started at the very end of the line segment rather than at the vertex E, but you've still described the angle, and that's perfectly fine.

So, just to be mindful that with the answers I'm giving now, you may have given an alternative correct answer and it was just to do with the order that you went round, the sort of direction you went round, whether you went clockwise or you went anti-clockwise and whether you started at the very end of a line segment or you started at the closest vertex for your labelling.

But the part to really check is your centre letter the same as my centre letter and that's where the angle, that's the vertex of the angle and we just describe the line segments for the arms. So, just be mindful with that whether anytime we are using this notation for angles.

So, sometimes, angle problems can be approached in multiple ways and that is absolutely brilliant, but it can at times therefore cause confusion that you might be sat next to your classmate and they seem to have done it in a completely different way to you.

But hopefully, you've both ended up with the same answer.

And this is where justification why and how you got from one part to the next is really important when we come to angle problems, so that we can help understand how we got from one angle to the other using all of this knowledge that we have.

So, here, we've got a question which says, find the size of angle HBE, and HBE has been labelled.

We've also been told the angle DEF is 98 degrees.

So, Sam is going to talk us through their method of how they've got to the angle.

So, angle FED, that was the one that was given as 98 degrees, is equal to angle A, B, H as they are equal exterior alternate angles.

We know they're equal, because we've got a set of parallel lines.

180 degrees minus angle ABH equals angle HBE, remember angle HBE is the angle we're trying to get the size, as adjacent angles on a straight line sum to 180 degrees.

So, Sam is using the knowledge of the angles on a straight line at the same point, always sum to 180 degrees.

So, therefore, 180 minus 98, we know angle ABH is 98, because they are equal exterior alternate angles, gives you angle HBE as 82 degrees.

So, that was Sam's method through this problem.

Let's have a look at Alex's method.

So, the same problem, but Alex has gone about it in a different way.

So, angle FED, the given angle of 98, is equal to angle EBC.

Again, that could have been FBC, but Alex has used the closest vertex as they are equal corresponding angles.

So, that's now marked on the diagram.

That's also 98 degrees, because they're corresponding angles and they're equal because of the parallel lines.

And then, Alex has also used angles on a straight line.

So, angles on a straight line add up to 180 degrees.

So, 180 minus 98 gives us the 82.

So, Sam, Alex went about it in different ways.

Sam used alternate angles, Alex used corresponding angles, but they both ended up with 82 degrees.

There are other ways to approach this problem too, and maybe you were seeing it in a different way to both Sam and Alex.

If we could say 180 degrees minus angle FED equals angle GEF, as adjacent angles on a straight line sum to 180 degrees.

So, we can work out that angle adjacent to the given angle.

So, we now know that that angle is 82 degrees.

We could then say that the angle A, B, C and the angle GEF are equal exterior alternate angles.

So, we can label angle ABC as 82 degrees, and then we could say, well, angle ABC and angle HBE are vertically opposite angles.

So, it's 82 degrees, because vertically opposite angles are equal.

So, we can see this is another way of working around that diagram and still landing with the answer that the angle of HBE is 82 degrees.

However, I'm hoping you can see that this method, not Sam's, not Alex's, but this method is a little bit more long-winded.

You might be like, well, why would you go over there when you could just go directly from 82 degrees to the corresponding angle of 82 degrees? Some are more efficient than others.

Okay, so a little bit of freedom here, but you need to find the size of angle SRQ using alternate angles.

So, just using alternate angles, which is what this lesson's all been about.

Work out the angle, SRQ.

Pause the video whilst you're doing that.

Think about your justification, which is your reasoning as well.

Press play when you're ready to check.

So, you hopefully you've got to the answer that the angle SRQ is 80 degrees.

And using alternate angles, you could say the angle MOR, which was the given hundred is equal to angle QRO as they are interior alternate angles.

And because the parallel lines we know they are equal interior alternate angles.

And then, angle QRO and SRQ are adjacent angles on a straight line.

So, they add to 180, they sum to 180 degrees.

And so, we can do a quick subtraction to work out the 80 degrees.

So, last part of the lesson where you need to do a bit of work thinking about identifying the rules.

So, here, it's not only alternate angles you can use, you can use any of the other angle facts that you already know about.

So, question one has got two parts to it and you need to find the the value of the labelled angles, giving the justifications, so the justifications, the reasons.

So, that's say, an interior alternate angles or equal alternate angles is as much as important as the actual value.

So, pause the video while you have a go at those two, and then when you're ready for the next question, come back and press play.

Okay, so here, we've got question two.

It says, there is a rectangle and an equal actual triangle.

Calculate as many angles as you can.

And again, giving justifications.

It might be that you need to sit and pause on this for a little while.

Reread the question, think about what that actually tells you, label stuff on the diagram.

So, press pause whilst you work on that one.

And then, when you're ready, we're going to come back and go through all of the answers.

So, here's just part A for question one on the screen.

There is a chance that you will have used slightly different reasons or justifications.

So, do check your value, that's important, but also check your justification.

On B, alphabetically, I've done it.

So, E is 101 degrees as adjacent angles on a straight line, sum to 180 degrees.

So, they are adjacent to each other at the same point.

We know the angles on a line add to 180 degrees.

F are vertically opposite angles and G I've said, is corresponding with the given 79 degrees and they are equal, because of the parallel lines.

We do need full reasons.

You can't just say corresponding angles, because we've seen or you would've seen that corresponding angles don't have to be equal.

But when there are parallel lines, that's when they become equal.

So, we need to say equal corresponding angles or corresponding angles in parallel lines to justify why they are equal.

So, question two, question two, you get very little information except there is some implicit information.

It's a rectangle, you know stuff, you know angles about rectangles and it's an equilateral triangle.

You know about the angles in an equilateral triangle.

So, actually, there is a way into this problem and that's by starting with rectangles and equilateral triangles.

So, equilateral triangles have 60 degree angles.

That is by definition, that all the angles are equal.

So, they are 60 degrees.

Rectangles have got right angles, 90 degrees.

So, we can just add them onto our diagram.

And remember that this question was calculated as many angles as you can, giving your justifications.

So, it doesn't matter if you didn't manage to get all of them.

See how many you did as we go through.

Adjacent angles on a straight line sum to 180 degrees.

So, the angle that's next to the 90 would be 90, 'cause 90 add 90 is 180, and the two angles on the outside would be 120 degrees, because 120 and 60 makes 180.

Alternate angles are equal, vertically opposite angles equal, and corresponding angles are equal.

So, because rectangles have got sets of parallel lines, then we can start to think about corresponding and alternate angles within that section of the diagram where the edge of the equilateral meets the rectangle.

You may have done it in slightly different order.

Obviously, you may not have gone through the angles in the same way that I did, but just check your justifications and check the angles on your diagram.

So, well done today.

We've got to the end of the lesson on alternate angles.

So, alternate angles are a pair of angles, both between or both outside two line segments that are on opposite side of the transversal that cuts them.

If the two line segments are parallel, then the alternate angles are also equal.

Unknown angles in the systems, including the parallel lines, can be found using alternate and corresponding angles.

So, as we move into diagrams with parallel lines, you now can start thinking about alternate angles as well.

Well done today.

I've really enjoyed working with you through this lesson.