Lesson video

Hello there, my name is Mr. Goldie and welcome to today's math lesson.

And here is the outcome for today's lesson.

I can use different properties to identify and sort triangles.

Here are the keywords for today's lesson.

I'm going to say each keyword, can you repeat it back? So the first keyword is triangle.

The next keyword is vertex.

The next keyword is vertices and the last keyword is properties.

Let's take a look at what those words mean.

A triangle is a polygon with three straight sides.

A vertex is the point where two lines meet to form an angle.

Vertices are more than one vertex.

So when we talk about one corner, we call it a vertex.

When there is more than one corner, we call them vertices.

And finally, properties are a character or quality that something has.

And here is our lesson outline.

In the first part of the lesson, we're going to be finding out what is a triangle.

You might have some idea what a triangle is already.

And the second part of the lesson, we are going to be sorting triangles by their properties.

Let's get started.

In this lesson, you will meet Aisha and Laura who will be helping you with your maths today.

What does tri mean? I don't mean try as in when you're having a go at something and it sometimes goes right and sometimes doesn't go right.

This is spelled differently, T-R-I.

What does it mean? Laura says, "The prefix tri- means three." Let's look at some words.

Where do you think the tr- part is? Let's look at the first one, here is a trilogy.

A trilogy of books.

What do you think the tri- means? So a group of three books or films is called a trilogy.

Here we have a tricycle.

You might know this one already.

Where is the tri? Where is the three in tricycle? Well, a bicycle with three wheels is called a tricycle.

A tricycle, a trike has three wheels.

Here we have a trident, not so familiar, this one.

So trident, what do you think the three part is in trident? So a trident is a spear with three prongs.

And finally, triple.

What do you think triple means? It means to multiply a number by three.

So if you multiply a number by three, you are tripling that number.

Let's look at some properties of a triangle.

If a trilogy is a series of three books, what is a triangle? "A triangle is a 2D shape," says Laura.

"A triangle has exactly three sides." So this shape here is not a triangle.

It does not have exactly three sides.

In fact, that shape there has four sides.

So it's a different type of shape.

This is not a triangle.

One of the sides is curved instead of straight.

So triangle has to have three straight sides.

And finally, this is a triangle.

It has exactly three straight sides.

What are the other properties of a triangle? "A triangle has three sharp vertices." "A vertex is the point where two lines meet." So it's like a corner on the shape and a triangle has three sharp vertices.

Careful you don't cut your fingers on the corners.

This shape a triangle? This is not a triangle.

Two of the lines do not meet to form a vertex.

To be a triangle all three lines have to meet to form three vertices.

Is this a triangle? This is not a triangle.

The vertices are rounded instead of sharp.

This a triangle? What do you think? This is a triangle.

It's got three straight sides and it's also got exactly three vertices.

A triangle has three angles, tri- angle, three angles.

Which shapes are triangles? There are six shapes there.

Which of them are triangles? Which of them are not triangles? Pause the video and see if you can work out which shapes are triangles and which are not.

And welcome back.

How did you get on? Did you manage to work out which shapes are triangles and which ones aren't? Let's take a look.

So let's start with this first shape here.

This a triangle? No, it is not.

Why isn't it? It's got rounded vertices.

So remember to be a triangle that has to have sharp vertices, sharp corners.

This second shape, is it a triangle? Yes it is.

It's got three straight sides and three sharp vertices.

This next shape, is this a triangle? Yes it is.

This is also a triangle.

This is not a triangle because two of the lines do not meet to form a vertex.

So it's actually only got two vertices.

A triangle has to have three.

And finally, the last shape.

Is this a triangle? No, it is not because it does not have three sides.

So very well done if you correctly identified which shapes are triangles and which ones are not.

Aisha draws a triangle on this grid.

"I need to use three straight lines," says Aisha.

Laura says, "Aisha also needs to make sure the lines meet to make vertices.

And each vertex must meet at one of the points." So Aisha draws one line, two lines, three lines.

So she's used three straight lines and they join together to make three vertices.

She's drawn a triangle.

Laura draws a triangle next.

"Make sure it's a different triangle to mine," says Aisha.

"It needs to have three straight sides and three vertices," says Laura.

So Laura draws her triangle.

There's one side, two sides, three sides.

So she's used three lines altogether and it's got three vertices.

Aisha says, "Sorry, Laura.

I think they're the same shape." Look what happens if I rotate mine.

So Aisha rotates her triangle.

"Oh no!" says Laura, "It's exactly the same shape." Laura tries again.

"Which shape is correct and is also different to my triangle?" says Aisha.

So here's Aisha's triangle here.

So here's one of Laura's efforts.

Here's another one of Laura's efforts.

And here's the third one.

Which shape has Laura drawn correctly and which shape is also different to Aisha's triangle? Pause the video, see if you can work out the answer.

And welcome back.

How'd you get on? Did you work out which one it is? Let's take a look, see whether you got it right.

Let's take a look at this first triangle.

Aisha says, "Oops! Sorry Laura, but this is the same as mine again!" So same as Aisha's shape.

All she's done is rotated it round slightly.

Let's look at the second one.

Aisha says this isn't correct because one vertex does not meet at one point of the grid.

Now Laura has drawn a triangle.

It is a triangle.

It's got three sides and three sharp vertices.

But for this activity, Laura has to make sure that all of the vertices meet on one of the points on the grid.

And Laura has not done that.

So this one here is not correct.

And finally, the last shape.

"This triangle is correct! It has two longer sides and one shorter side," says Aisha.

So it's got three straight sides and it's got three vertices.

So very well done, Laura, for drawing a triangle correctly.

Excellent work.

And well done, if you spotted that, that was the correct answer, excellent.

Let's move on to task A.

So task A, you're going to draw some different triangles.

You need to remember that each vertex must meet at one of the points on the grid.

And there are eight possible different answers that are all different to each other.

So remember, a triangle has three straight sides.

It also has three sharp vertices.

Each of the lines must meet at a vertex.

So pause the video and see if you can work out the eight possible answers.

And welcome back.

How did you get on? So let's take a look at those answers.

So here are the eight different triangles you could have drawn.

So each shape has three sides and every vertex meets at one point on the grid.

So there are the eight possible answers.

Very well done if you've got some of those.

Excellent work if you've got all of them, that is absolutely brilliant 'cause they're quite tricky to find.

Very well done indeed.

And let's move on to the second part of the lesson.

So the second part of the lesson is sorting triangles by their properties.

All triangles share some of the same properties.

So every triangle has three straight sides and three vertices.

So to be a triangle, it must have those properties.

Here are the three vertices on this triangle.

There's one here, there's one here, there's one here.

Some triangles have other properties too.

Is there anything else you notice about this triangle? Here's a clue.

That's a very big clue.

What do you reckon? Well, it is, this triangle has a right angle.

So some triangles are right-angled triangles.

So every triangle has to have three vertices and three straight sides.

Some triangles are also right-angled triangles.

Not all of them, just some of them.

Laura identifies right-angled triangles.

"I'm going to check if these triangles have any right angles," she says.

Now sometimes you can tell if an angle is a right angle just by looking at it, but sometimes you have to measure and check really, really carefully.

So the Laura checks that first triangle.

Does it have any right angles? No, this triangle has no right angles.

She moves on to the second triangle.

Did that have any right angles? No, this triangle has no right angles either.

Let's try that third triangle.

What do you think, is it going to have a right angle? You might even be able to identify just by looking at it.

This triangle has one right angle.

Here's one for you to try on your own.

Does this triangle have a right angle? Can you see a right angle in this triangle? You should be able to look at that triangle and think, ah, some of those angles definitely are not right angles, but you might be looking at one angle in particular and thinking, hmm, that could be a right angle.

So how could you check whether it has got a right angle or not? You might have a right angle measurer with you, but you can also use a corner of a book or the corner of a piece of paper, or anything at all that's got a right angle on it to check another right angle.

So pause the video.

Has that triangle a right angle or has it not? And welcome back.

Did you manage to find a right angle in that triangle? Well, this triangle does have a right angle.

This is a right-angled triangle.

Very well done if you identified the right angle in that triangle.

Aisha has an interesting thought.

Aisha does have interesting thoughts every now and again.

"Can a triangle have two right angles?" she asks.

"Hmm, I'm not sure," says Laura, "let's start with a right angle." So Laura draws two lines that meet at a right angle.

"Let's add another right angle," says Laura.

So Laura draws another line to make another right angle.

There are now three lines, but it doesn't make a triangle.

So Laura can't add any more lines to that to make it into a triangle, otherwise it would no longer be a triangle.

Aisha says, "I don't think a triangle can have two right angles." Can you draw a triangle with two right angles? Is it possible? What do you think? No, it's impossible.

A triangle can ever only have one right angle and sometimes they don't have any right angles at all.

Some triangles have sides the same length.

So this is another property that some triangles have.

"Let's look at the triangles we made earlier," says Aisha.

There's Aisha's triangle that she drew earlier.

"The first triangle has two sides the same length." So these two sides here are the same length as each other.

Here's the triangle that Laura came up with.

"The second triangle also has two sides the same length." Can you spot them? These two sides here are the same length.

So some triangles have sides that are the same length.

That's a different property of some triangles.

Let's look at this third triangle.

Can you spot any two sides that are the same length? Well, two sides are definitely longer and one side's definitely shorter.

Are those two longer sides the same length? No, they are not.

This triangle has sides which are all different lengths.

Sometimes you have to measure the sides really carefully to work that out, double check that.

But this triangle does not have any sides which are the same length as each other.

Do these triangles have sides the same length? So have a good look at those two triangles.

Do they have sides that are the same length? Pause the video and see if you can work out whether those two triangles have sides the same length or whether they do not.

And welcome back.

Let's check to see whether you got the right answers.

So Aisha says, "This first triangle has two sides the same length." So we've got two slightly shorter sides and a longer side.

So those two slightly shorter sides are the same length as each other.

That second triangle, again, we've got two longer sides and a shorter side.

Are those two longer sides the same length as each other? No they are not.

"The second triangle has sides which are all different lengths." Some triangles have reflective symmetry.

"Reflective symmetry is where one half of the shape is a reflection of the other.

If I folded the shape, the two halves would match if the shape had reflective symmetry." "Let's look at the same three triangles," says Laura.

"The first triangle has a line of symmetry," says Aisha.

You might be even able to spot what that line of symmetry is.

Imagine folding that triangle into half.

Where would you fold it so the two halves fit together exactly? You'd fold it there.

Aisha says, "I can position a mirror on the shape and the reflection matches the other half." To have reflective symmetry, the two halves need to look exactly the same.

So Aisha places a mirror on the shape and she can still see the same shape.

Let's take a look at that second shape.

Does it have reflective symmetry? The second triangle has a line of symmetry.

And again, if you placed a mirror on that line, you would see exactly the same half reflected in the mirror to make that exact same complete shape.

Or if you folded that shape into half along that line, the two halves would fit together perfectly.

Let's take a look at that third shape.

Does it have reflective symmetry? This last triangle has no line of symmetry.

Now you could try and place the mirror in lots and lots of different places, you'd never see that same shape again.

One part of the shape does not match the other.

When Laura places the mirror on the shape, the part that she can see is not the same as the part that she's covering up.

It's not the same shape anymore.

So that shape there does not have reflective symmetry.

So some triangles have reflective symmetry, some do not.

Do these triangles have reflective symmetry? Now some people are really good at just looking at the shape and thinking, I know where the line of symmetry is.

Some people need to actually use a mirror.

So pause the video and see if you can work out whether those two triangles have reflective symmetry or not.

And welcome back.

How did you get on? Did you work out the answers for both of them? Let's take a look to see whether you got it right.

So Aisha says, "The first triangle has a line of symmetry." You can cut that shape exactly into half by placing a mirror there or by folding the shape at that point.

"The second triangle has no line of symmetry." Very well done if you correctly identified which of those triangles had a line of symmetry and which one did not.

Now Aisha goes back to those eight triangles we looked at earlier and she describes one of them to Laura.

"Can you work out which triangle I am describing?" says Aisha.

"I'm going to do my best!" says Laura.

That's all we can ask anybody to ever do Laura, their best.

So very well done for trying.

"My triangle has a right triangle," says Aisha.

Hmm, so Laura looks at those triangles and she knows the one that Aisha is thinking of has a right angle.

So I'm looking for triangles that have right angles.

So Laura is going to get rid of any triangles that do not have right angles.

So let's take a look.

This one here does not have a right angle, so it can't be that one that Aisha is thinking of.

This one does not have a right angle.

Neither does this one and neither does this one.

Ah, that's a good start Laura, you managed to get rid of four of the triangles already.

So the one that Aisha is thinking of must be one of those other four.

"My shape does not have two sides the same length," says Aisha.

"Hmm," says Laura, "I'm rejecting any triangles with two sides the same length." So this triangle here has two sides the same length, so it can't be that triangle.

Next triangle has two sides the same length, so it can't be that one either.

And there two triangles left.

Which one has two sides the same length? This one here does, so it can't be that one either.

Ah, so Laura is left with one triangle.

"Is this the triangle you were describing?" Says Laura.

"Spot on! Well done, Laura." So Laura did get the right answer.

Very well done Laura.

Now Laura is going to have a go trying to describe one of the shapes to you and you're going to see if you can work out which triangle Laura is describing.

So Laura says, "This triangle has one right-angle.

This triangle has one line of symmetry.

This triangle fills exactly half the grid." Pause the video and see if you can work out which triangle is in Laura's head.

And welcome back.

Did you manage to work out the answer? Let's check to see if you've got the right triangle.

So, Laura says these triangles do not have a right-angle.

So the one that Laura is thinking of does have a right-angle.

So these triangles cannot be the one she's thinking of.

So it can't be this one here, no right angle or this one, or this one, or this one.

This triangle does not have one line of symmetry.

So the one that Laura is thinking of does have a line of symmetry.

So this triangle cannot be the one she's thinking of because it does not have a line of symmetry.

And finally these triangles do not fill exactly half the grid.

The one that Laura is thinking of fill exactly half the grid.

These ones do not fill exactly half the grid.

There's only three triangles left, aren't there? So it can't be this one.

This one's quite a small triangle, does definitely not fill half the grid.

But this finally, this triangle down here does fill exactly half the grid.

If you had two of those triangles on the grid, they'd fit it exactly.

"This was the triangle I was describing," says Laura.

So very well done if you managed to work out the correct answer, excellent work.

Aisha is sorting shapes onto the Venn Diagram.

So on the Venn Diagram there are two circles.

In one of the circles it says triangles and the other circle it says has at least one right angle and all the shapes Aisha could be given in the whole world.

She could put somewhere on that Venn diagram.

Aisha says shape A is a triangle without a right angle.

So it's a triangle, but it does not have a right angle.

So it's good to go in the triangle circle because it is a triangle but it cannot go in the has at least one right angle circle.

So in fact that shape there, shape A would go here.

Shape B is a triangle with a right angle.

Shape B is inside both circles because it belongs in both groups.

And finally, shape C.

Shape C is not a triangle, but it does have at least one right angle.

So where would shape C go on the Venn Diagram? It would go in here.

So it's not a triangle, does not belong in the triangles group, but it has got at least one right angle.

In fact that shape there has got two right angles.

So it will go in this circle here.

Now here's a couple of shapes for you to sort yourself.

Shape D and shape E.

Whereabouts would those shapes go on the Venn Diagram? Pause the video, see if you can work out where they were going.

And welcome back.

Let's take a look to see whether you sorted those shapes correctly.

So Aisha says, "Shape D is not a triangle and it has no right angles." So it cannot go in the triangle circle and it cannot go in the has at least one right angle circle.

So shape D goes outside both circles.

Shape E is a triangle with a right angle.

So shape E would go in both circles.

So very well done if you sorted those two shapes correctly.

Excellent work.

And let's move on to task B.

So in task B, you're going to choose one of the shapes.

You're going to describe it to a partner and see if they can guess it.

Here are some ideas to help you.

So this shape has three vertices.

That could be one of the things you describe using your shape only if it does have three vertices.

This shape has at least one line of symmetry.

That could be one of the properties you use to describe your shape.

This shape has two sides the same length.

You could use that property to describe your shape.

This shape has at least one right angle.

So using different properties to describe your shape.

Can your partner work out which shape you are describing? So that part one, task B.

And part two of task B, you're going to sort the shapes onto the Venn Diagram.

And it's the same Venn Diagram we looked at a moment ago.

One of the groups is triangles and one of the groups is, has at least one right angle and all the shapes you've got will go somewhere on that Venn Diagram.

Remember they can go outside both circles if they do not have either of those properties.

And here are the shapes you're going to be sorting.

So its eight shapes to sort altogether.

So look at them carefully.

Make sure you get them in the right place on the Venn Diagram.

So pause the video and have a go at task B.

And welcome back.

How did you get on? Did you manage to sort out all the shapes? Did you manage to describe the shapes to a partner? Did they manage to work out the shape correctly? Let's take a look to see how you got on.

So for part one of task B, your learning may have looked like this.

Of course you may have chosen a completely different shape and described it in a different way.

But Laura choose the shape and says, "This shape has three vertices." So it can't be any of these.

She says, "This shape has two sides the same length." So it cannot be these two shapes here.

And this shape has one right angle, so it cannot be A or H.

So she's left with shape B.

So the answer was shape B.

So your learning may have looked something like that or you may have chosen compete different shape and described it in a different way.

But very well done if you described it in such a way as your partner worked out which shape you were describing.

And here are the answers for part two of task B.

So that is where you should have sorted the shapes onto the Venn Diagram.

So B and F were both triangles with at least one right angle.

C and G had at least one right angle, but were not triangles.

And A, D and H were triangles but did not have a right angle.

And finally, shape E was neither.

Doesn't fit into either group.

It's not a triangle and it doesn't have any right angles.

So very well done if you managed to sort those eight shapes correctly, and excellent work today, and hopefully you are feeling much more confident about what a triangle is and about the properties of different triangles and thinking about ways in which triangles may be similar to each other and may be different.

Excellent work today, very well done.

And finally, let's move on to our lesson summary.

So triangles always have three sides, three vertices and three angles.

Triangles always have straight sides and sharp vertices.

Triangles can have right angles.

And vertices are the corners of a shape.