Lesson video

Hello, my name's Mrs. Hopper, and I'm really looking forward to working with you in this lesson from our unit on properties of 2D shapes and symmetry.

I'm sure you've met lots of 2D shapes in the past, but we're going to remind ourselves about their names, the properties they have, and maybe introduce a few new ones.

And we're also going to be thinking about symmetry and how we know when a shape or a pattern is symmetrical.

So if you're ready to make a start, let's get going.

So in this lesson, we're going to be identifying the different types of triangles and describing their properties.

I'm sure you've come across triangles before, but have you ever thought about how they can look sort of different in some ways? Well, let's learn a bit more about them in this lesson.

Our keywords are the names of the triangles.

We've got equilateral triangle, isosceles triangle, and scalene triangle.

So I'll take my turn, and then it'll be your turn to say them.

Are you ready? My turn, equilateral triangle.

Your turn.

My turn, isosceles triangle.

Your turn.

My turn, scalene triangle.

Your turn.

Well done.

They might be new words to you.

We're going to learn a lot more about them as we go through the lesson, but let's just look at what they mean and then we'll be able to spot them as we go through our learning today.

So an equilateral triangle has three equal sides and three equal angles.

We've got that equi bit at the beginning, equilateral, equilateral.

So we can see that equal idea.

That's a good way of remembering that that's a triangle where all the sides and all the angles are the same.

An isosceles triangle, that's a tricky one to read and a tricky one to spell as well.

It's one I have to work hard to remember how to spell it.

Worth learning, though.

An isosceles triangle has two equal sides and two equal angles, so that means one of its sides and one of its angles is different from the others.

And you can see there that we've used those little lines to mark equal sides.

We'll learn more about those in the lesson.

And the final name of triangle is a scalene triangle.

And this has no sides or no equal angles, so all the sides are different lengths and all the angles are different sizes.

So, we're going to be looking out and thinking of ways that we can recognise these triangles and name them and think about their properties as we go through this lesson.

There are two parts to the lesson.

In the first part, we're going to be exploring the properties of triangles, and in the second part, we're going to be naming types of triangles.

So our keywords will really come into play in the second part of our lesson.

So let's make a start on part one.

And we've got Jun and Aisha helping us with our learning today.

Jun has been cutting out some different shapes from paper.

So they're all flat shapes.

Some of them look as though they might have curved a bit, but think about the curves in a different way.

They're all flat shapes cut from a piece of paper.

He says, "Some of the shapes are definitely triangles, but there are some I'm not sure about.

I wonder how I could check which shapes are triangles and which are not?" How do you think he could check? Which ones do you think are triangles? Aisha says, "I have learnt about this before!" I wonder if you have too.

She says, "I know that a triangle always has three sides." So that can't be a triangle, and that can't be a triangle.

Can you see they've got different numbers of sides? One's got four sides, and the other one has actually got six sides.

It looks a bit like a triangle.

But by cutting that little nick out of one side, we've divided that side into two pieces and we've added two more pieces, so it's got six sides.

So if a shape has more than three sides, it's not a triangle.

She says, "I also know that the sides of a triangle must be straight." So that's got a curved side.

That's got a curved side.

That one's got three curved sides.

And that one's got a curved side as well.

So if a shape has a curved line, it's not a triangle.

Aisha says, "I remember that a triangle also has three vertices." Those are the points of the corners.

Jun says, "A vertex," which is one of the vertices, "is where two straight sides meet.

If it's curved, it's not a vertex!" Ah, so that's not a triangle either.

It looks as though it's got three straight sides, but those sides don't meet at a point.

They've got a curve around them, so that is not a true triangle.

So if the corners look curved, it's not a triangle.

So we're left with three shapes that are triangles.

They all look quite different, don't they? Let's check your understanding.

Which shapes are triangles, and how do you know? Pause the video, have a look, and when you're ready for the answer and some feedback, press play.

What did you think? Which of these are triangles? Well, A is a triangle.

It has three straight sides and three vertices.

There are no curves, no curvy corners, and no curved lines.

And D is a triangle, three straight sides and three vertices.

B is not a triangle 'cause it has four sides.

And C is not a triangle because it has a curved line.

So let's look at those three triangles that we identified from Jun's set of shapes.

So they know that these shapes are triangles.

Jun says, "These are all triangles because they have three straight sides and three vertices, but they do not all look the same.

I wonder how I could describe the ways they look different?" So how are these shapes different? Aisha says, "You could look at the orientation or the way the triangle has been positioned." Orientation just means the way it's been positioned on the page.

So we could turn it round and put it in a different orientation.

Jun says, "The middle triangle has been positioned so that it has one side which is horizontal." Horizontal means it's a flat side.

My arm isn't completely flat there.

And you can think about that thinking about looking at the horizon when you're looking away into the distance and you can see that straight horizontal line, that straight, flat line at the edge of what you can see.

Aisha says, "The other triangles are positioned so that they have no horizontal or vertical sides." So those were her horizontal sides, and her vertical sides, they go straight up and down.

Jun says, "You could rotate them until one of the sides is horizontal." So let's turn those other two triangles until we've got a horizontal side.

There we go.

"You could look at the length of the sides," says Aisha.

Jun says, "The first triangle has three equal sides, and I can mark them like this to show that they are equal." So to show that two sides are equal, we use a little dash across the side, and that shows us that all of the three sides of the triangle are the same length.

They are equal in length.

Aisha says, "The middle triangle has two equal sides," and she can mark them.

So we can see that those two sides of that triangle are equal, but the other side is different.

Does that remind you of one of our keywords in the definitions? And Jun says, "The last triangle has no equal sides." So he says, "I don't need to mark the sides at all." Because they've got no marks on, we know that they are all different lengths.

Aisha says, "You could look at the angles inside each triangle too." Jun says, "I will use angle strips to explore the angles inside each triangle." You might have used angle strips like this before, two strips of paper joined with a pin so that you can move them and make the angle change in size.

So one, two, three.

So she's marked the angles of that first triangle.

Remember, all its sides are the same length.

And Aisha says, "You could orient the angles the same way so that they are easier to compare." So she means turn them round so that they look more similar.

"Good idea," says Jun, "thanks Aisha." So there we go, he's turned them all round so that each one now has a horizontal side to it.

And what do you notice? All the angles are the same.

So the first triangle has three equal angles as well.

And we could pile the angle measurers up on top of each other just to double check that they are the same.

So we can say that all these angles are the same size.

I wonder if the middle triangle will have any equal angles? What do you think? Ah, Jun's got his angle measurers out again.

So there's one, two, and the third angle.

So again, let's orient them so we've got a horizontal or roughly a horizontal in each place.

What do you notice? Well, Aisha says, "One of the angles looks much smaller than the other two." Jun says, "You're right.

We could say that two of the angles are equal and the other is different." So in that triangle, two of the sides were the same and one was different, and two of the angles are the same and one is different.

And there we are, we've marked the two angles that are the same.

Aisha says, "I don't think the last triangle has any equal angles.

Let's check with the angle strips again." One, two, three angles.

Well, they all look very different, don't they? And we can orient them again so that we've got roughly horizontal lines at the top.

But Jun's right, "This triangle has no equal angles.

They are all different." So all its sides are different, and all its angles are different.

And Aisha says, "I've noticed that only one of the triangles has an obtuse angle." Do you remember, an obtuse angle is one that's bigger than 90 degrees, bigger than a right angle.

And there it is, the one obtuse angle in all of our triangles.

"Yes!" says Jun.

"The other angles are all acute because they're all smaller than a right angle." So that's the only angle in all of the triangles that's bigger than a right angle.

Time to check your understanding.

Can you match the descriptions to the correct triangles? So you've got three triangles and three descriptions.

Have a go at matching them.

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

How did you get on? So let's look at the first triangle.

Well, we can say that this triangle has no equal sides and no equal angles.

What about the middle triangle? What do you notice? What do those little dashes on the sides tell us? That's right, it tells us that those two sides are equal.

So this triangle has two equal sides, and we can look at it and see that it also has two equal angles.

What about the last triangle then? Well, those dashes tell us that the three sides are equal.

And you can also see, and you might have checked with angle strips, that the three angles are the same as well.

So it has three equal sides and three equal angles.

And it's time for you to do some practise.

So in question one, can you draw a peculiar triangle? So one that maybe nobody else might draw.

An ordinary triangle, the sort of triangle that you'd maybe picture straight away if somebody said triangle, the first shape that came into your head.

So you're going to draw a peculiar one in the first box, an ordinary one in the second box, or you might draw more than one of each.

And then you're going to write a generalisation, a rule to explain what a triangle always needs to have.

And then in question two, we've given you some pictures of some nine-pin pegboards.

So you can imagine that this was a piece of wood and there were pins sticking out, and you might be able to use an elastic band.

But you're going to draw on them, on these nine-pin boards.

How many different triangles can you draw by connecting the points around each of the nine-pin pegboards? And how could you describe each triangle? Look carefully at the sides and the angles.

So have a go at your two questions, and when you're ready for some feedback, press play.

How did you get on? Now, triangles are limited because they have to have three sides, don't they? But sometimes we might not think of triangles as being very long and thin or very short and wide, as we've got in here.

So some slightly unusual triangles.

But then the kind of ordinary triangle that lots of people might draw.

They look a bit like those two in the middle, don't they? Yours may be slightly different, though.

And what about this generalisation or rule to explain what a triangle always needs to have? Well, you might have written something like this, a triangle always needs to have three straight sides and three vertices.

It can be drawn in different orientations or positions.

So it's the three straight sides and the three vertices, three corners, which are really important to say what a triangle has to have.

But I hope you drew yours in different orientations so that they looked a little unusual, not just the sort of ordinary-looking triangle where it sits on a side.

And in question two, you were going to see how many different triangles you could draw by connecting the points around the pegboard.

So here are some that we had to go at.

There's a very small triangle there.

Slightly bigger one.

Ooh, that's got a property we might be able to recognise.

Another one.

Another one.

So, some different triangles there.

Did you recognise when you'd made a triangle that was the same but in a different orientation? Can you see that these two triangles are the same? Their short side is just one dot apart.

And then we're going to the one dot that's sort of opposite the gap between those two dots.

So we've made the same triangle, and you could imagine spinning one of those nine pegboards around and we would have exactly the same triangle that we'd drawn in the other orientation.

All the other triangles, though, are slightly different.

I wonder how many different ones you found.

Something else here.

The first triangle has two equal sides and two equal angles, but the second triangle has no equal sides and no equal angles.

How can we be sure about that first one? Well, we can see that two of the sides are the same length because they both go from one dot to the next dot, don't they? I wonder if there are any others where we can see that as well.

Well, in fact, in the two that we've highlighted as being the same, the distances are the same, and we can tell because there's the same number of dots in between.

We've drawn a line from one dot to another dot that's not quite opposite because there are nine.

But there are three missing dots on either side, so we know that those two sides must be the same length.

And on into the second part of our lesson where we're going to name types of triangles.

So Jun and Aisha have another look at the triangles that they drew, so these are some of the ones that they drew in that first task we did.

Aisha says, "I know that the first triangle has two equal sides and two equal angles." And she can tell that by looking at where she's placed her lines.

And she says, "The last triangle has no equal sides and no equal angles." And again, we can tell that by where she's drawn her lines, that they're not sort of in the same place at any point, they're all different.

Jun says, "I wonder how we could name these types of different triangles?" Well, a triangle with three equal sides and three equal angles is called an equilateral triangle.

And do you remember we drew one before and we marked those sides with the three little dashes? And if it has three sides the same, it will have three angles the same.

So there's another one.

This time, the sides are marked as five centimetres long each time.

And these are not to scale, obviously, but this one is 75 millimetres for each side.

And a smaller one, but it still has all three sides the same length.

Jun says, "I know these are all equilateral triangles, they're just in different orientations and are different sizes." But if all three sides are the same length, they are an equilateral triangle.

So which triangle in this set is an equilateral triangle? Time to check your understanding.

Pause the video, have a look, and when you're ready for some feedback, press play.

How did you get on? It was C, wasn't it? A and B only have two equal sides, six centimetres and six centimetres marked on the first one, and the dashes to show that those two sides are the same length for B.

But C has all three sides marked as 62 centimetres.

All three sides are the same length, so C is an equilateral triangle.

A triangle with two equal sides and two equal angles is called an isosceles triangle.

And we can see two there, one marked with the little dashes to show that the two sides are the same length.

And in the one in the pegboard, we can see that two of those sides are the same length because they join dots that are one dot apart and the dots are equally spaced around the circle.

There's another one.

Another one, this time we've got the lengths of the sides on so we can see that two of the sides are five centimetres long.

And again, not to scale, but this one again shows us that two of the sides are the same, 60 millimetres, not much bigger than the five centimetres.

And Aisha says, "Did you know that the word isosceles comes from the Greek language, and it roughly translates as equal legs?" So there we go, two equal legs.

We only have two legs, so the legs are equal.

So time to check your understanding.

Which triangle is an isosceles triangle? Think about what we've just learned about.

Pause the video, have a go, and when you're ready for some feedback, press play.

Which one was isosceles? That's right, it was B.

A and C are both equilateral triangles because they have three equal sides.

B is an isosceles triangle because two sides are equal in length and the third side is a different length.

And we can see the two equal sides marked with the two little dashes.

And our final type of triangle for now, a triangle with no equal sides and no equal angles is called a scalene triangle.

And we can see one there in our nine-pin board and then a sort of version of it in a different orientation.

There's another one, and another one, and another one, and another one.

And Aisha says, "The word scalene also comes from the Greek language and roughly translates as unequal." So there we go, scalene means sort of unequal in Greek.

And that's what this triangle is, it has no equal sides and no equal angles.

All three sides are different lengths.

All three angles are different sizes.

Right, time for a check.

We've learned three new ways of naming triangles, so can you match each triangle to its correct name? We can see we've got six triangles, so we're gonna have more than one matching to each name.

Pause the video, have a go, and when you're ready for some feedback, press play.

How did you get on? So starting with the top triangle on the left side in the nine-pin board, what can you see? Any angles the same? Any sides the same length? No, they're all different, aren't they? This is a scalene triangle.

What about the one with 60 millimetres, 60 millimetres, and 95? Ah, well that's got two sides the same length and one different, so that must be isosceles.

What about the next one? Well, we can see from the little dashes that all the sides are the same length.

So do you remember that when all three sides were equal, it's an equilateral triangle? What about the one on the top right? We can see the dashes there saying that we've got two sides the same length and one side different, so that's isosceles.

The next one has all three sides marked as 62 millimetres, so that must be an equilateral triangle.

And what about the bottom right? Well, it doesn't look as though any of the sides are the same length, and I don't think the angles are the same size either, so that must be a scalene triangle.

Well done if you matched those correctly.

And it's time for another practise.

In question one, you're going to complete the sentences to describe each type of triangle, and you've got an example there to help you.

What does it mean about the sides and the angles for those different triangles? For question two, you're going to label each triangle with the correct name, and we've given you the names of those triangles on the right-hand side.

And finally, you're going to draw and label your own triangle.

And for question three, a little problem to solve.

Here is a square.

Inside the square is an equilateral triangle.

The perimeter of the square is 44 centimetres.

What is the perimeter of the triangle? Pause the video, have a go at the three questions, and when you're ready for some feedback, press play.

How did you get on? So question one, you were completing the sentences.

So a scalene triangle has no equal sides and no equal angles.

What about an equilateral triangle? Well, that's kind of the opposite, isn't it? It has three equal sides and three equal angles.

And do you remember about an isosceles triangle, that equal legs, how many legs have you got? Two legs, usually.

An isosceles triangle has two equal sides and two equal angles.

Those are really useful definitions to remember.

So can we label these triangles? So the first one, we've got those dashes to say that those sides are the same length, so that is an equilateral triangle.

There are no dashes on the next one.

So all the sides are different, all the angles are different.

It's a scalene triangle.

The next one, the dashes show that two sides are the same length, so that must be an isosceles triangle.

Now, we could use the dots to help us here.

So in this next one, you can see that all those dots are different distances apart around the edge of the circle, so that is a scalene triangle.

So for the next one, we can see we've got one short side, but the other two sides are the same length 'cause we can see the three dots left out.

So that's an isosceles triangle, two sides the same and one different.

And for the last one, we can see that there are two dots sort of left out between each of the vertices.

So that must mean that our sides are the same length, so it's an equilateral triangle.

What about your own triangle? This was the one that we drew, and that is another scalene triangle, but different from the other scalene triangle on the left-hand side.

Ooh, or you might have drawn another equilateral triangle, and that is the same as the last one, but just oriented, turned around slightly.

Or you might have drawn another isosceles triangle.

Again, the same as our other isosceles triangle, but rotated.

And finally, question three, we had a problem to solve here.

We had a square, and the perimeter of the square was 44 centimetres, and inside the square was an equilateral triangle.

What's the perimeter of the triangle? We've got no measurements on there.

How are we going to work this out? But we do know the perimeter of the square, so that's the distance around all four sides of the square.

So the perimeter of the square is 44 centimetres, so each side must be 11 centimetres long.

44 divided by 4 is equal to 11.

Or you might have realised that 4 lots of 11 were equal to 44 and thought of it as a multiplication fact.

So we know that that top side of the square is 11 centimetres long.

And we can see that one side of the equilateral triangle is equal to one side of the square.

So that means that each side of the triangle must be 11 centimetres long because it's an equilateral triangle.

It's got equal length sides.

So we can see that the perimeter of the triangle must be 33 centimetres because all the sides are equal and we know that 3 times 11 is equal to 33.

Well done if you got that right.

Some really good reasoning going on there.

And we've come to the end of our lesson.

We've been identifying different types of triangles.

So what have we learned about? Well, we've learned that all triangles have three straight sides and three vertices.

An equilateral triangle has three equal sides and three equal angles.

An isosceles triangle has two equal sides and two equal angles.

And a scalene triangle has no equal sides and no equal angles.

All the sides are different, all the angles are different.

I hope you've enjoyed exploring triangles today.

I've really enjoyed working with you, and I hope I get to work with you again soon, bye-bye!.