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.

In this lesson, we're going to be finding lines of symmetry in 2D shapes, and explaining the link between lines of symmetry and the number of sides in regular polygons.

Ooh, lots going on in today's lesson.

Let's have a look at what we're going to be talking about.

So we've got some keywords and phrases here, line of symmetry, symmetrical, and regular polygon.

So let's just rehearse those.

I'll take my turn, then it'll be your turn.

So my turn line of symmetry.

Your turn.

My turn symmetrical.

Your turn.

My turn, regular polygon.

Your turn.

Fantastic.

Let's have a look at those words in a bit more detail.

They're gonna be really useful to us in our lesson.

So if you were to fold a shape on its line of symmetry, both halves would match exactly.

So have a look at that picture of a heart and that dotted line.

If you folded the heart on the dotted line, one half of the heart would exactly match the other half.

When a shape, pattern or image has two halves that match exactly when folded, it can be described as symmetrical so that butterfly has a line of symmetry, and therefore we can say that it is symmetrical.

And a regular polygon has sides that are all equal and interior or inside angles that are all equal as well.

So all those shapes, there are regular shapes.

They each have sides that are the same length, and the angles inside the shape are all the same as well.

So there are two parts to our lesson today.

We're going to be finding lines of symmetry using a mirror in part one, and in the second part we're going to be finding lines of symmetry in regular polygons.

So let's make a start.

And we've got Laura and Jun helping us in our lesson today.

Have you ever noticed symmetrical patterns and shapes in the environment around you? Have you ever looked for them? I wonder what you can see.

Maybe have a look round your room now where you are.

I can see a door.

You can't see my door, but it is symmetrical.

I think it's only got one line of symmetry though.

Down the middle.

Laura says, "My dad is a graphic designer.

He creates symmetrical designs on tiles and wallpapers".

What a lovely job to have.

I wonder if that's something you'd like to be.

And Jun says, "I've noticed that some buildings are symmetrical and there is even symmetry in nature.

Look at a butterfly." That's a really lovely thing to do.

Next time you're out for a walk, see if you can see a butterfly.

And when their wings are open, you notice that they are beautifully symmetrical, but just look at them, they're very fragile.

Laura says, look at this tile.

It has a line of symmetry.

Where would you draw the line of symmetry on this tile? Jun says ,"I usually check if it has a line of symmetry by folding, but I can't fold a tile." He can't, can he? How else could he check? Ah, you can use a mirror to find a line of symmetry.

So we've put the mirror down the middle of the tile.

Can you see? Did it change? Didn't, did it? Laura says, "What I see in the mirror and what I see on the tile are the same." So let's do that again.

It didn't change, did it? What she saw in the mirror is the same as what she sees on the tile as a whole.

"The line, the mirror was on, must be a line of symmetry", says Jun.

"And the same thing happens when I place the mirror on these lines as well", says Laura.

Jun says, "That means this tile must have four lines of symmetry." It's a lovely tile, isn't it? Laura and Jun continue using a mirror to find lines of symmetry.

Where would you put the mirror on this shape? Ah, did it change? It didn't did it.

Laura says, "The reflection in the mirror matches the shape I see when I take the mirror away".

Jun says, "Then you found a line of symmetry".

What about this shape? Where would you place the mirror here? Ah, that's right.

Not a horizontal or vertical one this time.

And Laura says, "The reflection in the mirror matches the shape I see when I take the mirror away".

So you found a line of symmetry and you could also call it the mirror line.

What about this shape? It's a parallelogram, isn't it? Do you know something about parallelograms and lines of symmetry? Oh, was that the same? Let's check.

No, it changed, didn't it? The reflection in the mirror is not the same as the shape I see when I take the mirror away.

So Jun says, "You have not found a line of symmetry." He says, "Maybe try a horizontal line." Do you think that's going to work? Let's look.

Was it the same or did it change? It changed, didn't it? The reflection in the mirror is not the same as the shape I see when I take the mirror away.

So you have not found a line of symmetry.

"Maybe you should try the diagonal", says Jun.

So joining the opposite vertices.

Should we try? Do you think it's gonna work? Oh, goodness me.

No, that didn't work, did it? Nope.

"The reflection in the mirror is not the same as the shape I can see when I take the mirror away", says Laura.

So this parallelogram has no lines of symmetry.

Time to check your understanding.

We've got a shape there.

Where would you place the mirror on that shape to show a line of symmetry? Would it be position A, B, or C? Pause the video, have a think.

And when you're ready for some feedback, press play.

How did you get on? It's A, isn't it? Because A is the only one where the shape looks the same.

So that is the line of symmetry and the mirror line.

B and C do not show a line of symmetry on the original shape because the image in the mirror does not match the shape you can see when you take the mirror away.

I think we've got some more tiles here.

Laura says, "Let's look at some more of my dad's tile designs.

I wonder if they are all symmetrical".

What do you think? Jun says, "We can use a mirror again to help us look again for lines of symmetry." So let's look at this tile.

Oh, what happened there? Was that the same? Jun says, "What I see in the mirror does not match what I see on the tile when I take the mirror away".

So that means there is no line of symmetry here.

That purple dotted line is not a line of symmetry.

Where else could we put the mirror? Ah, what do you notice there? Jun says, "What I can see in the mirror matches what I can see on the tile when I take the mirror away".

So that means that there is a line of symmetry here.

So this tile has one line of symmetry.

What about this tile? Jun says, "I can already see that there will not be a horizontal or a vertical line of symmetry on this tile." If you imagine putting the mirrors there, it wouldn't work, would it? We are not making two parts that are identical.

Laura says, "We don't need to use a mirror to check these lines.

Maybe we should check the diagonals," she says.

Oh, I don't think that one worked, did it? Let's have a look again.

Jun says, "What I can see in the mirror does not match what I can see when I take the mirror away." So that means there's no line of symmetry there on that purple dotted line.

What about the other diagonal? Ah, nothing changed there, did it? Let's check again.

Jun says, "What I can see in the mirror matches what I can see on the tile when I take the mirror away." So that means that there is a line of symmetry here.

There's one diagonal line of symmetry for this tile.

Time to check your understanding.

Which tile has a line of symmetry drawn correctly? Pause the video, have a look, and when you're ready for some feedback, press play.

How did you get on? It was B, wasn't it? You can imagine if we put the mirror there, then what we saw in the mirror would look exactly the same as what we saw on the tile when we took the mirror away.

So it was a diagonal line that gave us our line of symmetry.

The other diagonal didn't work and there wasn't a horizontal or a vertical line of symmetry.

So just B.

Time for you to do some practise.

How many lines of symmetry can you find in these shapes? If you've got one, you can use a mirror to help you to find them.

If not, you might want to cut them out and fold them.

And in question two, these tiles are symmetrical.

Draw the line of symmetry on each tile.

Can you use a mirror to help you again? And for question three, shade in squares to create your own symmetrical tile design.

Can you create a tile design that has more than one line of symmetry? Pause the video, have a go at your task.

And when you're ready for some feedback, press play.

How did you get on? So these are the lines of symmetry on each shape.

Did you get them all right? Did you use a mirror to help you? And for question two, this is where each tile has a line of symmetry.

So three of them had diagonal lines of symmetry.

And we can talk about horizontals and verticals and diagonals because of the way we've positioned these tiles.

If we positioned them differently, we could create horizontal and vertical lines of symmetry.

And question three, you are creating your own designs.

So here are some that we came up with.

So you could have designed your own symmetrical tiles like this.

Did you find all the lines of symmetry? And did you create any designs with more than one line of symmetry? The one we created with two lines of symmetry was actually very simple, wasn't it? The more complicated ones just had one line of symmetry.

I hope you enjoyed investigating that and creating your own tile designs.

And on into the second part of our lesson, we're looking at finding lines of symmetry in regular polygons.

So Jun has noticed something about the lines of symmetry on a square.

He says A square has four equal sides, and it has four lines of symmetry.

So a square is an example of a regular polygon.

Any shape that has all equal sides and all equal angles is a regular polygon.

Laura says, "Let's explore lines of symmetry and other regular polygons.

Maybe we'll find a pattern." So Laura and Jun start with an equilateral triangle, which is a regular polygon with three sides.

Jun says, "I can see the line of symmetry that goes from a vertex to the middle of the opposite side." Laura says, "Let's draw some more lines of symmetry starting at the other vertices." We know that all the sides equal in length and all the angles at the vertices are the same.

So we can draw another line of symmetry here.

And another line of symmetry here.

This regular polygon has three sides and three lines of symmetry.

Now Jun and Laura will explore this regular pentagon.

Jun says, "I can see a line of symmetry that goes from the vertex to the middle of the opposite side." Well, that was sort of the same with the triangle, wasn't it as well.

But this time we've got a pentagon.

So how many lines of symmetry will we find? Laura says, "Let's draw some more lines starting at the other vertices." So we've got one, two, three, four, five.

This regular polygon has five sides and five lines of symmetry.

Are you spotting something here? So far we've investigated an equilateral triangle, a square, and a regular pentagon.

So can you think about the pattern that we found? And think about this true or false question.

A regular heptagon will have seven lines of symmetry.

A heptagon has seven sides.

So do you think that's true or false? And why do you think it is? Pause the video, have a go.

And when you're ready for some feedback, press play.

What did you think? It's true, isn't it? Here is a regular heptagon.

Again, all seven sides the same length, all the angles the same.

So there will be one line of symmetry for each side of the shape or for each vertex, One, two, three, four, five, six, seven.

So yes, it's true.

Laura and Jun continue to explore lines of symmetry in different shapes.

Jun says, "Do you think a circle has only one line of symmetry because it has one curved line?" And Laura says, "A circle is not a regular polygon, so it won't follow the same rule.

She says, I think it might be a special case." Any line that passes through the centre of a circle is a line of symmetry.

There's one, another one, another one.

And we could just keep going if we have a sharp enough pencil.

A circle has infinite lines of symmetry.

This means that the number of lines of symmetry in a circle could go on forever.

You just end up needing a sharper and sharper pencil to draw the lines in between the ones you've drawn already.

So time to check your understanding again, true or false, this rectangle has four sides so it will have four lines of symmetry.

Do you think that's true or false and why? Pause the video, have a go.

And when you're ready for some feedback, press play.

What do you think? Oh, it's false in this time, isn't it? This rectangle is not a regular polygon.

So the number of sides will not tell us the number of lines of symmetry.

This rectangle has two lines of symmetry.

And the way we've drawn it, it would be one horizontal and one vertical.

But because the sides are not the same length, it won't have any more lines of symmetry.

Regular polygons, remember, have all sides the same length and all angles equal.

The rectangle does have all angles equal, but it's got two pairs of equal sides, but they're not equal to each other.

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

In question one, you're going to draw all the lines of symmetry on these regular polygons.

Remember to use the number of sides to help you to find all the lines of symmetry.

And for question two, you're going to decide if each sentence is always, sometimes, or never true.

And can you sketch some shapes to support your answer? Pause the video, have a go at the two questions.

And when you're ready for the answers and some feedback, press play.

How did you get on? Wow, what a lot of lines of symmetry.

So we had our equilateral triangle, which is a regular triangle, all three sides and all angles the same.

So it has three lines of symmetry.

A square has four lines of symmetry.

A regular pentagon has five lines of symmetry.

A regular hexagon has six lines of symmetry, a regular heptagon has seven lines of symmetry.

And a regular octagon has eight lines of symmetry.

Did you notice the number of lines of symmetry was the same as the number of sides of each shape when the shapes are regular? And let's then consider these sentences.

So A said, a shape with four sides has four lines of symmetry.

Well, that's sometimes true.

For example, it's true for a square, but not for a kite.

It's true for a regular shape with four sides and that's a square.

B says an isosceles triangle has two lines of symmetry.

Is that true? No, that's never true.

An isosceles triangle only has one line of symmetry.

From the angle which is different to the side which is different.

And C.

C says irregular pentagon's have no lines of symmetry.

Well, that's sometimes true.

An irregular pentagon can have a line of symmetry.

As we can see there.

It's the pentagon that you can sort of make look like a house, can't you? It's not a regular pentagon, but it does have a line of symmetry.

So D said, all regular polygons have at least one line of symmetry.

Well, this is always true.

The regular polygon with the least number of lines of symmetry is an equilateral triangle.

And that has three lines of symmetry and E said the number of lines of symmetry in a regular polygon is equal to the number of sides.

Yes, that is always true.

In regular polygons, the number of sides is always equal to the number of lines of symmetry.

And in this part of the lesson, we've gone through and looked at quite a lot of regular polygons, haven't we? And we found that that is always true.

I hope you enjoyed exploring and investigating and proving whether those sentences were always, sometimes or never true.

And we come to the end of our lesson.

We've been finding lines of symmetry in 2D shapes.

So what have we discovered today? Well, you can use a mirror to find a line of symmetry.

When the image in the mirror is the same as what you see when you take the mirror away, you know that the mirror was placed on a line of symmetry, and that shape is symmetrical on that line.

In regular polygons, the number of lines of symmetry is always equal to the number of sides that the shape has.

That's a really useful one to remember.

Thank you for all your hard work.

I hope you've enjoyed exploring some more symmetrical ideas, and I hope I get to work with you again soon, bye-bye.