Numbers and numerals

Axioms and arrays

Factors and multiples

Order of operations

Positive and negative numbers

Expressions, equations and inequalities

Angles

Classifying 2-D shapes

Constructing triangles and quadrilaterals

Coordinates

Area of 2-D shapes

Transforming 2-D figures

Prime factor decomposition

Conceptualising and comparing fractions

Manipulating and calculating with fractions

Ratio

Percentages

Different number systems

Sequences

Forming and solving equations

Forming and solving inequalities

Linear graphs

Accuracy and estimation

Algebra and problem solving

Ratio (8.6a)

Ratio, real life graphs, and rates of change

Direct and indirect proportion

Univariate data

Bivariate data

Famous maths problems

Angles and parallel lines

Angles in polygons

Bearings

Volume and surface area of prisms

Area review

Circles

FDP review (9.1a)

Probability

Sets and Venn Diagrams

Solving linear simultaneous equations algebraically

Solving linear simultaneous equations graphically

Angle review (9.5a)

Constructions, congruence, and loci

Pythagoras's theorem

Ratio review (9.7a)

Similarity and enlargement

Surds and trigonometry

Quadratic expressions (9.9)

Quadratic equations (9.10)

Indices and standard form

Growth and decay

Finance

Maths

Y8 Maths

Key Stage 3

Year 8

UNIT

In this lesson, we will be reviewing intersection points and the ways in which changing to transversal angles will change the position of the intersection point.

Angles on parallel lines review: Revisiting intersections

﻿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.

In this lesson, we will be looking at transversal angles and what they have to be so that the lines do not intersect.

Angles on parallel lines review: Revisiting transversal angles

﻿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.

In this lesson, we will be looking at identifying alternate and corresponding angles on parallel lines.

Angles on parallel lines review: Revisiting alternate and corresponding angles

﻿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.

In this lesson, we will be calculating missing angles using transversals and parallel lines.

Angles on parallel lines review: Finding missing angles

﻿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.

Complete the sentence: A transversal line _____________.

Complete the sentence: Transversal angles ___________.

What is the size of angle a?

Which of these pictures show parallel lines?

Will these lines intersect? If so where?

Complete the sentence: Alternate angles are ___________.

Angle h and angle d are ________________.

The shaded region is the _______________.

What are the missing words in this sentence: Corresponding angles are found on _______________ side of the _____________ in _______________ regions.

Complete the sentence: Alternate angles on parallel lines ___________________________.

Which pair of angles are corresponding?

Unit Overview: Angles and parallel lines

Lessons:

Angles on parallel lines review: Revisiting intersections

Angles on parallel lines review: Revisiting transversal angles

Angles on parallel lines review: Revisiting alternate and corresponding angles

Angles on parallel lines review: Finding missing angles