# Lesson video

In progress...

Hello everybody.

My name is Mr. Kelsall and welcome to today's lesson about angle within shapes.

Now, before we start, you will need a pen and a piece of paper or something to write on.

You'll also need some graph paper or square paper, and you can print this off from the slides.

Please try to find a quiet place around the house somewhere, somewhere you won't be disturbed, and don't forget to remove any sort of distractions, perhaps sounds from mobile phone or move it away completely.

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

So, today's lesson, we are looking at angles inside a shape.

And to do that, we need to think about how we recognise angles inside a shape.

We're then going to use that information to start comparing angle statements, deciding if the statements are true all the time, sometimes or never true.

We're then going to look at how we can draw those angles statements, and finally we're going to take a quiz.

As I mentioned, you'll pencil, a piece of paper and some graph paper.

And we're introducing more new words this time.

So, we're going to revisit right angle, acute and obtuse.

We're also looking at a triangle, which is a three-sided shape.

So, it's a four-sided shape.

A pentagon, which is a five-sided shape.

A hexagon, which is a six-sided shape.

The first one is a trapezium and that's a quadrilateral with at least one pair of parallel sides.

We have a parallelogram, which is a quadrilateral with two pairs of parallel sides.

And then we have a rhombus, which is a parallelogram, but it has four equal length sides.

So, let's start with some information that you will need to access this lesson.

First of all, you need to understand that an angle is the point where two lines meet.

And on the right hand side, you've got two angles.

One is formed where two lines meet and the other one is not an angle because the lines do not meet.

Secondly, you need to know that turn refers to rotating around the point.

You'll have heard people say a full turn, which means turning around 360 degrees.

A half turn means turning halfway around, which is 180 degrees.

A quarter turn is turning a quarter of the way around, which is 90 degrees.

90 degrees we call a right angle.

We also know that to mark on a right angle, we draw a small box, where the angle is.

We also need to know that an acute angle is an angle less than 90 degrees.

And we know that an obtuse angle is an angle between 90 and 180 degrees.

So, our new learning, we're going to start by looking at angles.

On your screen, you've got some shapes.

Pause the video, ask yourself these questions, how many right angles can you count? How many acute angles can you count? And how many obtuse angles can you count? Okay, there are 13 right angles, you can see both of the squares have four right angles, the rectangle has four right angles, and one of the triangles has a right angle.

There's one obtuse angle, which is the triangle on the far right side, and that leaves four other acute angles.

Have a read of this statement.

See what you think of it.

A triangle has a right angle.

A triangle has a right angle, is this statement true all of the time, is it true some of the time or is it true never? Pause the video.

Perhaps use your graph paper and see if you can draw some of these triangles to see if it's true all the time, sometimes or never.

Okay, I've drawn two triangles here.

The first one is a triangle and it has a right angle.

The second one is a triangle and it does not have a right angle, it has an obtuse angle and two acute angles.

That means that I've proved one example where the is a triangle with a right angle, and one example where the triangle does not have a right angle.

So, the statement, a triangle has a right angle is true some of the time.

So, it's sometimes true.

A square has four right angles.

Is this always true, sometimes true or never true? Pause the video, try and draw it out.

Okay, this statement is true all of the time.

A square will always have four right angles.

It doesn't matter which way you draw the square, if you draw it straight, if you turn it on an angle, it will still have the four right angles.

Task number three, the next statement is a triangle has three acute angles.

Pause the video and try and draw this.

The statement's quite interesting because I've managed to draw a triangle which has three acute angles, but I've also drawn a triangle which has two acute angles and one obtuse angle.

So, this statement is true some of the time, it's sometimes true.

Okay, let's take this learning a little bit further.

So, in this section of the lesson, we're looking at angle statements and we're looking at explaining our angle statements rather than drawing them out.

So, we will start with the first one, a quadrilateral has four right angles, is this true always, sometimes or never? Take five seconds to think about it.

Okay, a quadrilateral has four right angles.

Just imagine the first quadrilateral you're thinking of, I'm thinking of square, it's a four-sided shape and that four-sided shape has four right angles.

So, I then thought about a rectangle, and I imagined a rectangle and a rectangle has one, two, three, four, that also has four right angles.

So, I found two quadrilaterals, which all have four right angles.

So, this moment I'm thinking this statement is always true, but I need to think a little bit more, I need to try and find an example of something which does not have four right angles.

So, I'm thinking of a trapezium.

Now, I know that a trapezium has one pair of parallel sides, but I also know that the angles inside a trapezium are not right angles, sometimes one or two might be right angles, but the others not right angles.

This means that that quadrilateral does not have four right angles.

That means that the statement, a quadrilateral has four right angles, can be true some of the time.

Now, I have to explain my thinking and I've just talked through my thinking there.

Take a moment, pause the video and see if you can talk through your thinking out loud.

Okay.

Once you've done that, have a look at the other statements, see if you can find examples where these statements are true and where they're false and then decide what the answer is, are these statements true always, sometimes or never? I would suggest starting by imagining these quadrilaterals and then I would start drawing them if you need to.

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

Okay, I've just drawn out an example of my first one.

I'm looking at a quadrilateral which has four right angles, I know this statement is true some of the time.

My next statement, I was looking for a quadrilateral that has three acute angles.

So, I thought, could I draw this? So, my second shape is a four sided shape, and if I look carefully, it has one, two, three internal angles, three angles, which are acute angles, and the fourth angle is a reflex angle, it's bigger than 180 degrees.

So, I've drawn a quadrilateral which has three acute angles.

Now, I've got to think, "Can I think of a quadrilateral which it doesn't have three acute angles?" Well, the square next to it that doesn't have three acute angles, it has four right angles.

So, I know that my statement must be it's sometimes true.

Statement number three says, a quadrilateral that has two obtuse angles, can I draw it? On my third shape, is a parallelogram, and two of the angles are acute angles and two of the angles are obtuse angles.

So, I've proved that that statement can be true at least on one occasion, and I need to find an example where it is not true.

So, I look back to my square and I can see that a square does not have two obtuse angles.

So, that means that the quadrilateral has three obtuse angles is true some of the time.

And my final statement, a five-sided shape has no acute angles.

So, I have to really think about this and I've drawn a shape, and in that shape, I've got one, two, three, four, five sides, and I can see I've definitely got three acute angles.

So, I've proved that I can draw a shape which has an acute angle.

But can I draw a shape which has no acute angles? Well, I kept thinking about this and I couldn't do it.

Have you found one, which has no acute angles? So, let's explore this idea a little bit further.

Question number one, what are the names of these shapes? Question number two, what do you know about their angles? Pause the video now, make any notes, press play, when you're ready to go.

Okay.

A bit of general information, a four-sided shape is called a quadrilateral.

We have four quadrilaterals on this page, we've got a parallelogram, a trapezium, another trapezium, and a rhombus.

The first parallelogram has two pairs of parallel sides and also has two acute angles and two obtuse angles.

The second shape, the trapezium, I can see that's only got one pair of parallel sides.

However, it does have two right angles, it has one acute angle and one obtuse angle.

Compare that to shape number three.

Shape three is also a trapezium, it also has one pair of parallel sides, but it doesn't have any right angles.

This time it has two acute angles and two obtuse angles.

And my final quadrilateral is a rhombus or a square.

It's got two pairs of parallel sides, it's got four right angles and all the sides are equal length.

A five-sided shape is called a pentagon and a six-sided shape is called a hexagon.

Interestingly, all of the angles are obtuse angles, no acute angles.

Look at shape number two.

Doesn't seem like a pentagon to begin with, but if we check it's got one, two, three, four, five sides, that means it's a pentagon.

Well, what about these angles? How many angles does it have? It has one, two, three, four, five angles.

Three of those angles are right angles, and the other two angles are obtuse angles.

Compare that with the pentagon at the end, this is a regular pentagon.

So, five sides, all the sides are equal length and five internal angles, all of the angles are above 90 degrees or below 180 degrees.

So, all of the angles are obtuse angles.

Using the information that we've just learned about these shapes, I'd like you to create your own statements about these shapes and then decide whether they are true always, sometimes or never.

Keep referring to the angles, think about obtuse angles, acute angles and right angles.

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

Hopefully you've managed to successfully complete that task.