The definition of a 'parallel line' is...

Is it possible to draw a hexagon with three pairs of parallel sides?

Is it possible to draw a triangle with a pair of parallel sides?

If I draw a pair of lines and they both form a 70 degree angle with the horizontal, are they parallel?

If I draw a pair of lines and one line forms a 20 degree angle with the horizontal, and the other forms a 20.01 degree line with the horizontal, are they parallel?

Exploring intersections

﻿Hello, and welcome to this online lesson on angles, transversal angles. Now, before we start, as always, I want you to clear away any distractions that could distract you. Such as your brother, your sister, your pet, whatever it could be. I want you to find a quiet space as well in which you can work. Remember, if you're watching via your phone, make sure, like I have, I've got all my apps switched off, and that I'm ready to go, and I can focus. If you're watching via a desktop or something similar, make sure your phone is switched off just so you can concentrate extra well. 'Cause, as always, we're doing some really powerful maths and we want to be able to focus. So, without further ado, let's get stuck in and get on with Mr. T's lesson. So, for the Try this, I'd like you to look at the intersection below that's formed by two straight lines that are crossing over. Like that. So, work out the missing angles. And can you think of any facts you can write down about of the four angles formed by two straight lines crossing, as a result of that? So, you may know this knowledge already. I'm about to go through it, we'll see what happens. Pause the video now and have a go. Okay, great, I'm going to assume you've done that, so let's have a think about what these are. So, looking at this, it looks to be that that 75-degree angle crosses over, and this is also going to be 75 degrees. And you'd be correct in saying that. That is 75 degrees. Do you know why? Why is that? You may have some idea. Do I hear, do I hear a vertically opposite angles are equal? Of course, I do. So yeah, we can say that these are vertically opposite angles. So, vertically opposite angles, angles, are equal. So that's one reason we can provide. Now, what can you also notice? Well, this, of course, this jagged part I'm shading on here forms part of a straight line. That's 75 degrees. So, what do we know about angles in a straight line? What do they sum to? Got angle on a straight line, what's that sum to? 180 degrees, right? So, 180 degrees in total means I need to do 75 plus something gives me 180. Well, that something is going to be, of course, 105 degrees. So, I know that one's going to be 105 degrees. Now, what I can say is that's going to be vertically opposite this one. So, that's actually going to be 105 degrees, as well. So, that, of course, is vertically opposite angles. I'm going to shorten that to VO, VO, let's just go with VO, vertically opposite. And from there, there's one other fact I can use for this whole thing. What is going to be, do you think? Let's get really creative. What do I notice? What's that that I've just coloured in there? It's a point, right? So, I can say that angles around a point sum to, well, if I add them all together, what do I get? I get, mmm, 360 degrees, right? Sum to 360 degrees. So, that's another angle fact I can use. So much information, such a small diagram. This is why angles are such an interesting topic. So, I'd encourage you to get really, really creative with that, and form other little things you can do from that. But that is so powerful. Such a small amount of information, but actually, it's incredibly powerful. Let's move on then. So, if you connect here, we've got angles formed at each point of intersection with a transversal. For the dotted lines, the shaded region is called the interior. So, just doing that little bit more on there, and annotating it slightly, we can take this whole area here as the interior. And, of course, this part here is the interior still. Interi, goodness me, my computer's lagging a lot. That's the interior there. And the white region is called the exterior. So, that's called the exterior, just there. And then, this bit is over here, this bit is here, and this bit is here. So, that's really powerful. We've defined certain regions that we have there. This part here being the interior, and that part up there being the exterior. Now, what the heck is a transversal, I hear you asking. Well, Mr. Thomas, what is it? Of course, it's this line here. So, this line that I'm sort of wiggling in at the moment, that is what we call our transversal. Yeah, so that is what we call a transversal, that line going through, all right? So, quite a lot of things you've taken on board there. With that in mind, I'd like you to have a go at the Independent Task. So, filling in those blanks as you see appropriate. You may want to go back in the video over what I've just said in order to access that, and to do that to the best of your ability. So, pause the video now, and have a go, and we'll go through the answers in just a moment. Okay, great. Let's go through the answers, then. So, there's actually quite a lot going on here. Now, I think almost immediately, you should be able to answer this one here. This is called the what region? The didn't hear you, say it louder, what is it? It's the interior region, right, very good. So, that's the interior region. Cool, what about this bit here, the white, sort-of blank part here? That was the, sort of like the outside. And another word for outside would be what? Ex terior, right? So, the exterior. Talk about, like, exterior of houses, the outside part. We're just talking about the exterior region in angles here. So, that's that bit done. What's the line that goes through, what did I say that was? That was called the transversal, right? Say it once more, it's the transversal. Transversal, there we go, good. So, transversal for that one there. Beautiful. So, we call the space between two lines the interior region. The space outside the lines is called the exterior region. Cool, we know that already. If a third line crosses these two lines, we call it a transversal, cool. Each of the intersections formed has two pairs of blank opposite angles which are always equal. What did I say those angles were called? They were called something opposite angles. I've already said it, what is it? It's going to be vertically, vertically opposite angles. So we can fill that in now. And just leaves this little badge to finish in, which is the angles. Now, you've got 130 and 50 here. Now, you could be really strategic here and see, well, which one's the larger angle. Well, of course, that one's the larger angle. Therefore, that would be 130 degrees. Vertically opposite angles are equal, so that's 130 degrees. So, this one down here would be 50 degrees as a result. And the reason for this being 50 is what? Why is that 50 degrees? That is because it's a, yeah, you got it, vertically opposite angle. So, we can tick those off now, and we're done. Yes! Very good, well done. Let's move on. So, we've now got an Explore task that I'd like you to have a go at. And I want you to copy the diagrams below, and in each of them, I want you to shade the interior region. Then label the transversal. And then mark on two different pairs of vertically opposite angles. So, pause the video now if you're confident with doing that. If you're not, then by all means, listen in for a thorough explanation and support. Okay, cool. Let's go on with some Support though. So, we've got the interior region. Well, interior refers to what's like inside. Like, you talk about I'm in the interior of my house, right? I'm sort of, I'm between some walls. I'm caged in, right? So, with that in mind, we can say that this area here would be the interior region, wouldn't it? Right? The transversal, remember, refers to one of those lines. So, think about what line that would be. And then vertically opposite angles, well, I'll give you one pair. It would be this one here, wouldn't it? And this one. So, that would be a pair of vertically opposite angles. So, with that in mind, I think you should be able to complete that first one, for sure, and maybe the second one, as well, as a result. So, have a go. Pause the video now and have a go at that, please. Okay, excellent. I'm going to take it that you've had that support, and you're really happy with it, and you're happy to move on to the answer. So, this is what I'm calling the answer. Now, I've marked on a pair of vertically opposite angles here. That's your first one, that's your second one, and then this is the transversal just here. Transversal just here, of course, pair, and then pair here, and this is the interior throughout. I'm just going to shorten it to INT. So, we've got a really powerful diagram there that says a lot of things, and I'm really happy if you managed to do that. Now, unfortunately, and quite unbelievably, that's us at the end of the lesson. I can't quite believe it, it's gone so quick, right? And you've learned so much already. You learned about interior, exterior, and transversal, vertically opposite. All sorts of things to angles that are really, really important, right? So important you understand that terminology. So, well done. I just want to remind you to do that exit quiz. Absolutely smash that learning out of the park. Make sure you doing a really good job with it, yeah. Prove to everyone how well you've done. Get those five questions right, and move yourself onto the next lesson I'm going to be doing. All right? Now, all that's left to say is to take care, and I'll see you in that next episode. Bye-bye.

The space BETWEEN two lines is called the...

The space OUTSIDE two lines is called the...

If a third line crosses these two lines, as in the previous questions, this is called the...

The point at which two (or more) lines cross is called the...

Two lines cross and form an intersection. One of the marked angles is 75 degrees. The vertically opposite angle to 75 degrees would be...

Transversal angles

In this lesson, we will learn how to explore intersections formed with two lines and a transversal, and understand how to identify vertically opposite angles.

Maths

Y7 Maths

Key Stage 3

Year 7

Angles

Geometry

THEME

UNIT

Describing and comparing angles

Measuring and drawing angles

Partitioning angles

Finding unknown angles

Alternate angles

Corresponding and allied angles

Which of the following best represents the definition of the word 'angle' in mathematics?

A full turn represents how many degrees?

If Angle A is greater than Angle B, how can I express this mathematically?

You are given that: 360 - R = S. Which of the following statements is correct?

Alternate angles only appear in the interior region.

Allied angles are equal.

If I have an equilateral triangle and a square around a point, what is the remaining angle left?

Lesson overview:Transversal angles

Core Content

Angles: