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If a regular octagon was split into 8 equal parts, each equal angle at the centre would be...

You are given that: a + a + a + a = 180. What is the value of a?

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

If each of the angles on a straight line are 50, 60, x and y, what is x?

Finding unknown angles

﻿Hello, and welcome to this lesson about angles, Exploring intersections. I'm Mr. Thomas, and as always, I'm really happy to see you and I can't wait to get started. So remember as always with all of my videos, I just want you to take a moment to carry away any distractions you may have. As always, you may be your brother your sister or your pet. Just move out them out of the way temporarily. We can deal with them in a moment. So make sure you've got your phone silenced and that you've got any app silenced as well. And that we're all ready to go, We've got those notifications turned off and we're in a quiet spot where we can concentrate. As always we're going to be doing some really, really powerful maths. I wouldn't want you to miss out on that. So without hesitation, let's keep going. So have a go to try this, you've got four statements there. What I'd like you to do is I'd like you to draw those and to see if they're true or false, so if they can be proven or not, so you can draw a quadrilateral with two pairs of parallel sides. Is that possible? A pentagon with two pairs of parallel sides, is that possible? A triangle with one pair of parallel sides, is that possible? And then a hexagon with exactly three parallel sides. Again, is that possible? So pause the video now, have a go at drawing those and proving if they are possible. Okay, let's go through it then. So we've got a quadrilateral with two pairs of parallel sides. You've got two options you could have for this one, you could have a square 'cause that is one pair of parallel sides, tendon, and then parallel here with this one here. So that's one possible one, or you could have a rectangle that would also work. So that would be your parallel side one and then parallel side two, so two pairs there. So that could also work, A Pentagon with two pairs of parallel sides. I'm going to come back to that one in a moment and you'll see why, a triangle with one pair of parallel sides. Well, if I try and do a pair of parallel sides, I can't do anything with that, can I? that's not possible. To connect those parallel sides, I'm going to need three, but then I've still got this sort of like hanging here. So its not possible. So it's actually not possible for a triangle. My letter D hexagon with exactly three parallel sides. Well that one there is very simply going to be a regular hexagon. I can have the one parallel sides, two, three. So that parallel sides is with that one, that one with this one, and then this one you've got to really excuse the poor drawing here, but you get the idea. So you've got three parallel sides for that one there. So that one works as well. Pentagon with two pairs of parallel sides. I can almost guarantee you didn't get this one, it's really tricky. I have to think about this for quite some time, but it is possible actually. That's the really satisfying thing about this. If we draw a shape that looks something like this, and then I connect it looking like this, I've got one pair of parallel sides so far, there we go, a bit of a tongue twister. I can then create another path by doing this. And do you see that I can actually. If I continue that a little bit further, I can connect that together, and I haven't got any parallel sides of this one here, but I've still got two pairs of parallel sides. So that one actually works. What a cool shape, right? It looks like a little bit like a fish, 'cause it got so many like fins attached to it with these arrows, right? So all sorts of things going on there. So really good that you're able to play around with it and even better if you can understand that if you've got that wrong, very good. Let's keep going. So we've got a connect here, and what I want you to think about here is we're going to play around with lines and basically saying whether they can intersect or not, or maybe not intersect, etc. Now, one of the key things we need to remember throughout this whole thing is that parallel lines are defined as lines that do not intersect. So highlight it, do whatever you need to do with this, just make sure you understand that parallel lines are defined as lines that do not intersect. So these for example are not parallel lines 'cause they intersect, they crossover each other. Now what I've got done here is I've got a little task for us to complete, which is to sketch different examples of diagrams for each of the other two cases. I've got an angle here that of course is the less than sign a is less than b. So I can see if I said that was for example 30 degrees, it may or may not be 30 degrees, I don't know, and this one is 80 degrees again I'm just approximating. Then we can see that they do intersect. Now if I was to be strategic here and think, well, a has got to be greater than b in the next case, I can then try and draw that case out. So I'm just about to draw probably one of the worst lines you're about to see. So here we go, we've got a is going to be greater than b. So if I set out and draw a line that looks like this, so really really obtuse angle here. Very very obtrusive angle. So looks something like this. And then I also draw another one. This maybe perhaps not as much of a turn. So I've got b looking like this and we can very clearly see that they cross over. Right? So when b is less than a, we can clearly see they cross. But what about another case whereby actually they're equal? Well, if they're equal, they're going to start off looking something like this. Now, if Mr. Thomas can stabilise his hand a moment, we'll say very good, that of course they don't ever meet. Now, if I mark that b, then I mark this is a, we can very clearly see they have give or take about the same angle, but you can clearly see they don't actually meet. So these lines are parallel. They never meet. So we can conclude that when the angles are equal, they are parallel. Even I have a little smiley face just to be here, yes, we've discovered that, excellent. We can move on now. So what I'd like you to consider is the independent tasks. So as a result of me doing that, I'd really like you to now have a go at proving how much you've learned just now at that independent task. So pause that video, look back, if you need to, if you don't go for it. Awesome, let's go through it then. I'm going to assume you've had a go, or if you're already stuck here, just looking for a little bit of a hint for first few. So let's fill that in. If we have straight lines continue blank, even if we only see a part of them drawn or straight lines continue forever, always go on. So these straight lines here will keep going forever and ever and ever. And then if a pair of lines blank intersect, they're described as being blank, so we can get rid of that forever one. But if a pair of lines never intersect, they're described as being parallel, that makes sense. If they never intersect, they're described as being parallel. Let's delete parallel, let's delete never. And then parallel lines will form the same angle when crossed by an intersecting line. Therefore we can say this angle of course would be 65 degrees. Lo and behold, we know it's going to be 65 degrees. So let's keep going we've got that now. You've got to explore task now for you to complete. So what I'd like you to do is I'd like you to decide whether each of the pairs of lines would intersect or not. If they do intersect, I'd like you to describe that point of intersection. If you'd like some help with the video by all means continue to listen. If you'd like have go at that task though, please pause that video now. Okay, great. I'm going to assume you want to go on with the answer or you want to get a little bit of a hint. So let's go through it. If I've got an angle of 130 and 130.1, do we remember that if we've got parallel lines, the angles are always the same or they're equal. So they're very, very close to each other, but they will continue for a very long time before they intersect. So we can say these will intersect, but they will need to be continued for a much longer distance. Awesome, what about these ones though? Well, they're both 70, aren't they? So if they're equal angles, then they'll never intersect. So these ones will never intersect. They will never intersect. And what does that mean they are? They will never intersect, they are parallel aren't they? So they are parallel, we can use that, I'm so happy to use that word, let's just make it really really big, say parallel. Let's even make it three exclamation marks. We discovered those parallel lines. Fantastic, yes. So that brings us to the end of the lesson unfortunately, it's been a really really quick lesson, isn't it? I just want to say if you've done a really good job with that, if you've managed to keep up. Parallel lines are really really important part of maths and you'll keep on discovering them as time goes on. This is just the beginning of it all. So remember do that extra quiz you could show me and the rest of the Oak team and indeed the rest of the country and your teacher, how well you're doing. So just prove how much you've learned, smash out the park and keep going. Remember, take care and stay safe and I'll see you in the next episode. Bye bye.

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

In this lesson, we will learn how to understand the properties of parallel lines.

Maths

Y7 Maths

Key Stage 3

Year 7

Angles

Geometry

THEME

UNIT

Describing and comparing angles

Measuring and drawing angles

Partitioning angles

Transversal angles

Alternate angles

Corresponding and allied angles

The space BETWEEN two lines is called the...

The space OUTSIDE two lines 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...

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

Lesson overview:Exploring intersections

Core Content

Angles: