Lesson video

Hello there.

How are you today? My name is Ms. Coe.

I'm really, really excited to be working with you on this lesson as part of your geometry unit.

Now, you may not know the word geometry, but geometry is all about shapes and lines.

And so we're going to be doing lots of exploring with shapes and lines and the properties of shapes.

I'm really excited about this lesson and I hope that you are too.

By the end of this lesson today, you will be able to say that you can draw quadrilaterals and other polygons with given properties.

We have a few keywords in our lesson today.

I'm going to say them and I'd like you to say them back to me.

My turn, quadrilateral.

Your turn.

My turn, vertex.

Your turn.

My turn, vertices.

Your turn.

Excellent work.

Let's see what those words mean.

A quadrilateral is a polygon with four straight sides and four vertices.

And you might know the names of some special quadrilaterals as well.

A vertex is the point where two lines meet.

And the plural is vertices.

So you can see that we've indicated one vertex on the triangle.

And we know that a triangle has three vertices.

In this lesson today, we're going to be drawing shapes with given properties.

We have two cycles for our learning.

In the first cycle, we're going to be focusing on drawing quadrilaterals, four-sided shapes.

And then in the second cycle, we're going to be drawing different polygons with given properties.

If you're ready, let's get started with the first cycle.

Let's start here.

What quadrilaterals do you know? What are their properties? What's special about those different types of quadrilaterals? Which quadrilaterals can you draw on this isometric paper? Now, you may have seen isometric paper before.

Isometric paper has points that are equally spaced.

You might be able to see triangles in this particular isometric paper.

This is a trapezium.

It has exactly one pair of parallel sides.

Remember, we can show the parallel sides by drawing arrows pointing in the same direction.

A trapezium is a special type of quadrilateral.

It has four sides and four vertices, and exactly one pair of parallel sides.

If those parallel sides are extended, we can form a pair of parallel lines.

Let's take a look.

We have extended the parallel sides and we now have a pair of parallel lines.

You can see that they are parallel because they stay the same distance apart.

I wonder, can other trapeziums be drawn using these lines? Hmm.

Well, this one is also a trapezium.

It has exactly one pair of parallel sides and we can mark those with arrows.

Although they're both trapeziums, it is different to the first one.

It takes up more space.

You can also see that it has different side lengths to the first trapezium.

It is a different trapezium, but uses the same pair of parallel sides.

This one is a trapezium too.

And it also has one pair of parallel sides, but it also has two pairs of perpendicular sides.

Remember, perpendicular sides are sides that meet at right angles.

I can see two right angles in this trapezium, so it has two pairs of perpendicular sides, as well as having a pair of parallel sides.

It is different again from the first two trapeziums because it has perpendicular sides.

They're all still trapeziums, but they can look different.

Time to check your understanding.

I would like you to use the parallel lines to draw a different trapezium.

If you've got isometric paper, you might want to sketch these lines and have a go.

Pause the video here.

Welcome back.

There are a few different possibilities, but you may have drawn something that looked like this, which is a longer trapezium than the first one, or you may have drawn something like this.

Did you spot the perpendicular sides in this second example? Well done if you drew a different trapezium to the first one.

Remember, a trapezium is a quadrilateral with exactly one pair of parallel sides, so however your trapezium looked as long as it had exactly one pair of parallel sides, then it was correct.

I wonder then, can other quadrilaterals be drawn using this pair of parallel lines? We do some trapeziums, but can we draw other quadrilaterals? This is a rectangle.

Now, you may know that this is a special type of parallelogram.

A parallelogram has two pairs of parallel sides.

And remember, we can show that using the arrows.

A rectangle is a special type of parallelogram because it has four right angles, which means it also has four pairs of perpendicular sides.

Other parallelograms can also be drawn, and these also have two pairs of parallel sides.

Here's one.

It's different from the rectangle.

It is not a rectangle because it doesn't have any pairs of perpendicular sides.

But it is still a parallelogram because it has two pairs of parallel sides.

Here's another one.

Now this looks very similar to the rectangle, but look really closely at those angles.

There aren't any right angles.

So this is a parallelogram with two pairs of parallel sides.

Let's move on then to thinking about perpendicular lines.

Remember, perpendicular lines meets as a right angle.

We can show the right angle by drawing a square.

That's the symbol for a right angle.

This is a pair of perpendicular lines.

What quadrilaterals can we draw using these lines? So remember, we already have two sides of the quadrilateral here, and we only need four sides to make a quadrilateral.

I wonder, can you visualise some quadrilaterals that we could draw using these lines? Lots of rectangles can be made using these lines.

All rectangles have four right angles.

We could draw a rectangle like this one.

Or we could draw one like this.

Or we could draw one like this.

They are all rectangles because they have two pairs of parallel sides and four right angles.

And we've drawn them using the pair of perpendicular lines that we started with.

We could also draw a smaller rectangle.

Take a look at this shape.

I don't think this is a rectangle, do you? What shape has been drawn here? How do you know? Hmm.

Well, this shape is a trapezium.

It has exactly one pair of parallel sides, but it also uses that pair of perpendicular sides.

So we can say that this trapezium has a pair of parallel sides and it also has a pair of perpendicular sides.

Remember not all trapeziums need that pair of perpendicular sides.

It's just an additional property for this trapezium.

Can we create another trapezium? What about this one? Is this a trapezium? No, this is not a trapezium because it doesn't have any pairs of parallel sides.

This one is a quadrilateral.

It has a pair of perpendicular sides, but no other special properties.

So remember, if a shape has four sides and four vertices and we're not sure what type it is, we can always say it's a quadrilateral.

Time for your first practise task.

For question one, I would like you to draw a pair of parallel lines onto isometric paper.

Remember to use a ruler.

Remember to use the dots to help you, but they can be anywhere as long as they are parallel, they stay at the same distance apart.

I would like you to use those lines to draw some different quadrilaterals.

How many different quadrilaterals can you draw using those parallel lines? Then I would like you to label those quadrilaterals that you've drawn.

And talk about or write about what is the same about those quadrilaterals and what is different? For question three, I would like you to draw a pair of perpendicular lines onto the isometric paper.

Remember to use a ruler.

And you can use an angle checker to make sure that you have a right angle if you need to.

I would like you to again draw some different quadrilaterals using that pair of perpendicular sides.

Then I'd like you to label those quadrilaterals and think about what is the same and what is different.

Good luck with those tasks.

Pause the video here.

Welcome back.

How did you get on? I hope you had lots of fun drawing lots of different quadrilaterals.

Here are some examples.

Remember, you may have drawn your parallel sides in different positions to us.

We have polygons a, b, c, and d.

And again, there were other polygons that you could have drawn.

But let's take a look at these.

Can we label any of the quadrilaterals? What's the same about them? What's different? Shapes a and d are parallelograms because they have two pairs of parallel sides.

B and c are trapeziums because they have exactly one pair of parallel sides.

Did you draw different parallelograms and different trapeziums? All of the shapes have at least one pair of parallel sides using the same lines to make them, so that's something that they all have in common.

Shapes c and d also have at least one pair of perpendicular sides, so they have at least one right angle.

Shapes a and b do not.

And you may have also noticed that shape d is a parallelogram, but it is also a rectangle because it has four pairs of perpendicular sides.

For question three, we ask you to draw a pair of perpendicular sides.

Now remember, your perpendicular sides may have been in a different position to mine.

But you may have drawn some rectangles and you may have drawn some squares like these ones.

Remember that a square is a regular rectangle, so all the side lengths are the same.

You may have also drawn different trapeziums. So here is an example here.

Remember, a trapezium has exactly one pair of parallel sides.

You may have drawn different trapeziums. These will always have exactly one pair of parallel sides.

And these ones happen to have a pair of perpendicular sides too.

You may have also drawn some unusual quadrilaterals.

Look at this one.

It has a pair of perpendicular sides, but it doesn't have any parallel sides or any other special properties.

This one as well is a quadrilateral.

It has four sides and four vertices.

A pair of those sides are perpendicular.

It has one right angle, but no other special properties.

Well done if you do lots of different types of quadrilaterals using parallel and perpendicular sides.

Let's move on to the second part of our learning where we're thinking about drawing polygons with given properties.

So here's the challenge.

Draw a pentagon with at least one pair of parallel sides and at least one pair of perpendicular sides.

Oh, there's a lot to think about there.

Draw a pentagon, hmm, what do I know about pentagons? Pentagons have five sides and five vertices, so my shape at the end needs to have five sides and five vertices, but I have some specific properties I need to get in there as well.

I need at least one pair of parallel sides, so sides that stay the same distance apart, and at least one pair of perpendicular sides, sides that meet a right angle.

That's a lot to think about.

I wonder what strategy I can use to help me draw it.

To help us draw it, we're going to start by thinking about the properties.

We're going to start by drawing a pair of parallel lines and then we're going to draw a line which is perpendicular to one or more of the parallel lines.

So here's our pair of parallel lines.

They stay the same distance apart.

Remember, if we're going to draw a pair of perpendicular sides, there needs to be a right angle.

I can draw a line like this.

I now have two right angles that I can think about.

A pentagon has five vertices.

We have four vertices here, and if we place them like this, we can guarantee that our pentagon will have a pair of parallel sides and at least one pair of perpendicular sides.

It doesn't matter where the fifth vertex goes.

I'm gonna put it there, that's fine.

We now need to connect the vertices with straight lines using a ruler.

Let's take a look at our shape.

Is this a pentagon with at least one pair of parallel sides and at least one pair of perpendicular sides? Hmm.

Absolutely is yes.

We can see that we have the horizontal sides are parallel, and we have actually two pairs of perpendicular sides because we have two right angles.

Andeep draws a new pentagon.

Does this have at least one pair of parallel sides and at least one pair of perpendicular sides? Hmm, what do you think? Look closely.

Think about what we mean by parallel and perpendicular.

This new line is parallel to the first two lines.

They stay the same distance apart, so that means Andeep's polygon does have a pair of parallel sides.

And this pair of sides is perpendicular because they meet at a right angle.

So that means that Andeep's polygon has five vertices, it is a pentagon, and therefore it meets the criteria of a pentagon with at least one pair of parallel sides and at least one pair of perpendicular sides.

Well done, Andeep.

Time to check your understanding.

Laura draws a new polygon.

Is this a pentagon with at least one pair of parallel sides and at least one pair of perpendicular sides? Take a really close look, see what you think.

Pause the video here.

Welcome back.

What do you think? No, unfortunately, Laura has not met all of the criteria.

Laura does have a pair of parallel sides, but there are no right angles in her shape, so that means there are no pairs of perpendicular sides.

She has drawn a pentagon though, so she's most of the way there.

Well done if you spotted that.

Time for your second practise task.

We're going to be using this isometric paper and these parallel lines.

For question one, I'd like you to use the parallel lines that are drawn on the isometric paper to make the following.

A, a pentagon with at least one pair of parallel sides and no perpendicular sides.

B, a hexagon with two or more pairs of parallel sides.

And C, a hexagon with at least one pair of parallel sides and at least one pair of perpendicular sides.

For question two, I'd like you to draw your own pair of parallel lines.

You can draw them anywhere on the isometric paper, but make sure they are parallel.

Draw an octagon with at least one pair of parallel sides.

Can you draw an unusual example that no one else will have thought of? Good luck with those two tasks.

Pause the video here.

Welcome back.

How did you get on? I hope you enjoyed drawing different polygons and really carefully thinking about their properties.

There are lots of different ways you could have tackled question one.

Let's take a look at some examples.

This is a pentagon with at least one pair of parallel sides and no perpendicular sides.

You can see on both examples we've marked the parallel sides, but there are no right angles, which means there are no pairs of perpendicular sides.

Take a good look at your polygons.

Have you met that criteria? For B, there are lots of different things you could have drawn.

But it's worth checking that you have a hexagon, so you need six sides and six vertices.

Here are a couple of examples.

You can see for A, there are actually three lines that are parallel to one another.

Shape B has lots of parallel lines and we haven't marked all of them, but you can see lots of different examples there.

For C, shape B would've worked as well, so we needed a hexagon, a six-sided shape with at least one pair of parallel sides and at least one pair of perpendicular sides.

You can see here that we've got lots of pairs of parallel sides, and we've got lots of right angles too, so lots of pairs of perpendicular sides.

For question two, you had to draw your own pair of parallel lines.

Now, you could have drawn these anywhere, so your answers might look different to mine.

You did have to draw an octagon though, so make sure that your polygons had eight sides and eight vertices because that is what an octagon needs, and it also needed at least one pair of parallel sides.

We asked you to draw an unusual example, so I think these two shapes are quite unusual.

They have parallel sides, which we've marked with the arrows.

And they have eight sides and eight vertices, so they are octagons, but they're very strange looking octagons.

Hopefully you had fun drawing strange examples of octagons too.

We've come to the end of the lesson and I hope you've really enjoyed drawing shapes with given properties.

Let's summarise our learning.

Quadrilaterals are four-sided polygons.

They have special names depending on their properties, and we've learned about some of those today.

If you know the properties of a polygon, you can draw that polygon.

And different polygons can be drawn with similar properties such as parallel sides.

Thank you so much for all of your hard work today.

And I look forward to seeing you in another maths lesson soon.