Lesson video

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Hi everybody my name is Mr Castle and welcome to today's lesson on angles within a shape.

We're looking at parallel lines and composite shapes.

Now before we start, we're going to need a pen and a piece of graph paper or square paper.

Also please try and find yourself a quiet place, somewhere that you're not going to be disturbed, and don't forget to remove any sort of distractions, for example put your mobile phones on silent or move away completely.

Pause the video, and then when you're ready let's begin.

Today's Lesson is all about calculating angles within a shape.

We're looking at composite shapes, which is one or more shapes put together to make another shape.

We'll also be looking at parallel lines.

We're going to start with angles in a quadrilateral and look at angles in parallel sides, and then look how we can use this to solve problems. At the end its quiz time.

I mentioned already that you need a pencil and graph paper.

Now star words for today are vertically opposite angles, within triangles we'll talk about Scalene, Isosceles and Equilateral.

And within quadrilaterals, we'll talk about parallelogram, trapezium, rhombus, square and rectangle.

In order to access this lesson you'll need to understand some basic angle facts.

You'll need to understand that angles at a right angle add up to 90 degrees, you'll need to understand angles on a straight line add up to 180 degrees, and angles around a point add up to 360 degrees.

You'll need to understand that vertically opposite angles are equal, and you need to understand that angles in a triangle add up to 180 degrees.

So my example here, if I have the top angle as 40 degrees, I need to understand what are my base angles.

180 take away 40 leaves me an angle of 140 degrees, and I need to split that equally between these two angles here, so my base angles will be 70 degrees each.

Similar with an equilateral triangle, I need to divide 180 by 3, so each angle is 60 degrees.

And finally we need to understand that angles in a quadrilateral add up to 360 degrees.

And that's because I can find two triangles within any quadrilateral.

You also need to understand some properties of quadrilaterals, we have five main quadrilaterals, we've got square, rectangle, rhombus, parallelogram and trapezium.

And you need to understand the angle properties and information about the sides.

When we talk about the sides, we're thinking about whether the sides are equal length and also whether the sides are parallel.

Pause the video, take a moment to read through these.

Okay, so let's start with our new learning, can you draw one line in each of the quadrilateral from one vertex to another vertex to create two triangles.

Once you've done that can you create your own examples of quadrilaterals and then draw a triangle within a quadrilateral.

Pause the video, when you're ready press play to continue.

There's lots of ways to do it, I'm just going to draw, one line on each to show you that each quadrilateral has two triangles inside it.

The reason I say that is because angles in a triangle add up to 180 degrees.

So angles inside two triangles will add up to 360 degrees.

Okay so now to our new learning for today, we'll look at parallel lines.

What do you notice about the angles in these shapes and can you explain your thoughts.

So the first thing I'm thinking is I'm going to use facts that I know to work out facts that I don't know.

I know that vertically opposite angles are equal.

So if I was to say that this angle here is 50 degrees I know this angle is 50 degrees too.

How do I explain that? How do I prove that? Well I have got a straight line there, so 50 degrees which means this angle must be 130 degrees.

I can follow that logic through and I know another straight line there, so I've got my 130 degrees add on 50 degrees takes you to 180 degrees, I could do the same here 50 degrees add on 130 degrees.

But can I use the information there to help me with this line here? Well yeah I can actually because I got a line there and another line which is parallel there, and then when this line dissects it, my 50 degrees here is going to be 50 degrees here.

My 50 degrees here will also be 50 degrees here.

And therefore that's 130 and that's 130.

if you look at this, I know that these angles are equal, therefore these angles are equal.

If I draw another parallel line here, these angles would be the same size too.

So let's take this line in, and let's start applying it.

I have a pair of parallel lines on the screen, and I'm going to give you a clue here, we're thinking about half of a right angle, we're thinking 45 degrees, you should be able to find all of the angles on my page.

Pause the video, have a go, and then I'll show you.

Okay, so I'm going to start with the bottom right hand corner.

And I know I've got half a right angle which is 45 degrees.

If this angle is 45 degrees, I know that this one must add up to 180 to give me 135 degrees.

This ones 45, and this one is 135.

I'm going to use my properties of parallel lines to work out these angles, 45, 45, 135, 135.

The angle here I can see is 90 degrees, therefore that's 90, 90, 90.

This angle here, two ways to work it out, first it is half of a right angle, the second way is to identify that within this shape there is a triangle.

I'm just going to draw on the side of the screen here so it's a bit easier to see.

I know that's 90 degrees, I know this is 45 degrees.

Angles in a triangle add up to 180 degrees, so 180 take away 90, take away 45, leaves me 45 degrees.

Do you remember what type of triangle this is called? It's an isosceles triangle because I got 2 equal base angles and therefore 2 equal sides.

So I know this angle is 45, this angle is 45, which means that angle and that angle must be 135 degrees each.

I can use my properties of parallel lines to understand that those two are 45 degrees, and that one and that one are 135 degrees.

So we've managed to work out every single angle on the page, without there being any angle there at all, well done.

Now to our develop learning for today.

This shape can you find quadrilaterals? Can you explain their properties? And can you think of their angle sizes? Pause the video, and when you're ready press play to continue.

I'm sure you got lot's of different quadrilaterals, and I'm sure you got lot's of different properties of those quadrilaterals, and you've lots of different angle sizes, I'm just going to choose a few.

I'm going to draw a, do you remember what shape this is? It's got one pair of parallel sides, so it's trapezium.

Now I know that these angles are 90 degrees here, I know that I have got half a right angle there which is 45 degrees.

I can either look at a right angle and half a right angle, to give me 135 degrees, or I can say angles inside a quadrilateral add up to 360 degrees.

So 360, take 90, take 90, take 45, gives me 135 degrees.

I'm also going to use my own knowledge of the shapes of the quadrilaterals so far to draw my own quadrilateral.

I'm going to draw a line , one here, another one here.

What shape have I drawn? Let's think I've got one pair of parallel lines which are equal length, and I have another pair of parallel lines which are also equal length, I can check the lengths because I got, 1,2,3,4, 1,2,3,4 jumps.

So I have created a parallelogram.

Now can I find the angles within this parallelogram? Well I can see this angle here is 45 degrees, therefore this angle must be 45 degrees.

Now that adds up to 90 degrees, so if I do 360 take away 90 degrees, 270 degrees.

And if I divide that by two, I will get the size of this angle and this angle.

So 270 divided by 2 is 135 degrees.

So I know I got 135, 135, 45, 45.

I might want to create myself another parallelogram, or is it a parallelogram.

What shape have I just drawn? Well spotted is not a parallelogram, it does have one pair of parallel sides, but the other sides are not parallel, so it can't be a parallelogram.

So a shape with one parallel side is a trapezium, so now I have got a trapezium here.

But can I work out these sides of the angles? Well I know that this is 45 degrees because it is half of a right angle, and this angle is 45 degrees, half of a right angle.

Now, what about these angles? Two ways to work it out, the first one is, I've got a right angle and half a right angle, so it's 135 degrees.

Second way is I can say well I consider these two angles are equal size, so I could do 360, take way 45, 45 is 270 degrees, split that into 2, which means that each of these angles here is 135 degrees.

That brings us to our independent task for today.

Using your new learning, find the missing angles in these shapes.

I say new learnings cause you can find these just by using angle properties.

Pause the video, when you're ready, let's play to continue.

You might have solved these different way than me, but I'm just going to show you my thinking with parallel lines.

My first shape is a trapezium because it has one pair of parallel sides.

I know I have got 90 degrees and 90 degrees that means I got half a right angle here, which is 45 degrees, therefore, 90 and 90 is 180, add 45 is 225 degrees, which means that my missing angle must be 360, take away 225 degrees, which gives me 135 degrees.

My second shape is a parallelogram, I can see my parallel lines here.

I know I've my equal lines 40 and 40, and I have got equal angles here, so my missing angles must be 140 degrees.

You'll notice that I used my properties of a parallelogram to find out the missing angles rather than doing 360 take away 40, take away 40, take away 140.

Think which way might be quicker, For me, opposite angles in a parallelogram are equal, is much quicker.

The next shape, I have spotted a pair of parallel sides again, I know that this is a trapezium cause I got one pair of parallel sides, I've got 30 degrees, 30 degrees, 150 degrees, let's see what those add up to, 30, 30 is 60, add 150 is 210 which means that this angle must be 150 degrees.

And finally my last shape, again I have spotted a pair of parallel sides that's useful to know, and now I have got a 90 degree angle, a 90 degree angle and 60 degree angle.

Got to find my missing side here, sorry my missing angle here.

90, 90 is 180, add 60 is 240, so this angle here must be 120, because 240 add 120 is 360.

However what's this missing angle here? Well I have got angles on straight line, so I know this is 60 degrees, or I could go back and use my properties of parallel lines and I can say that I got 2 parallel lines here.

Let me just clear the screen for you so you can see this.

From there is one pair of parallel line, that parallel line I can see that is 60, therefore that angle must be 60.

Now I find that way a little bit quicker.

Let's see what you think.