Lesson video

Hello and welcome to this lesson on Diagonals in quadrilaterals with me and Ms. Oreyomi.

We're going to need a paper, a pen, pencil, and a ruler in today's lessons.

You probably get a rubber as well in case you make a mistake.

So, if you need to pause the video now to go get these equipments before you start also minimise the distractions by putting your phone on silent just to get ready for this lesson and to concentrate the duration of the lesson then please do so.

So pause the video now if you need to get anything and then resume when you're ready to start.

In this lesson, you'll be able to compare the properties of diagonals in quadrilaterals.

If you're thinking, I don't know what diagonals are, don't worry, we're going to find out what they are very soon.

In this lesson, you'll be able to compare the properties of diagonals in quadrilateral.

If you're thinking I do not know what quadrilaterals are don't worry, we're going to find out in a few seconds.

Okay, your try this task is using this dotted grid can you draw different quadrilaterals that have one line of symmetry? So can you draw say four quadrilaterals that have one line of symmetry? How many quadrilaterals can you draw that have rotational symmetry of order two? And how many quadrilaterals can you draw that have exactly two lines of symmetry? So pause the screen and attempt this task and then once you're done press play to resume with the lesson.

Okay, an important question here is what are diagonals of a shape? I've got a shape and I want to know the diagonals, how can I tell where the diagonals are of a shape? Well, diagonals can be found by connecting two vertices that are opposite to each other.

If I've got this shape here, my kite, I can find my diagonals by connecting, 'cause this is a vertex here, and this is the opposite vertex, so by connecting these two vertices together I know that this is a diagonal.

And then by connecting this vertex here with this vertex here that is also a diagonal.

And I can see that my diagonals are at right angle to each other.

So the vertices of a quadrilateral can be found by connecting opposite vertices together.

So say for example, I've got sticks in pile A and all of the sticks in pile A are the same length.

All of the sticks in my pile B are of the same length However, the length in pile A and the length I pile B are different.

What quadrilaterals can I form or can you form using two of the sticks as diagonals.

Either two sticks from pile A or two sticks from pile B.

What quadrilaterals can you form using two sticks as diagonals? I am going to give you two examples and then you're going to have a turn yourself Okay, the two or three examples I'm going to show you before you get a chance to work through this yourself.

So I've taken two sticks from pile A and I want to see the quadrilateral that I can make If I connect my sticks up.

What shape is this? This is a rectangle.

So I have made a rectangle by connecting two parts of stick from pile A.

Let's move on to our second one.

What shape can I make if I connect the tips of my diagonals? Yeah, I have made a square.

What can you tell me about where my diagonals intersect? Can you tell me anything about where they intersect? Well, they at right angle to each other aren't they? This diagonal and this line, this line here and that line here are at right angle to each other.

So I could say the diagonals of my square are at right angle to each other.

What of this one? If I connect it from here to here, from here to here, what shape am I making? Yeah, I hope you've said a kite.

'Cause that would be correct, so I have made a kite here and again my diagonals are right angled to each other.

Later on in the lesson, we're going to learn a way that the mathematical word of seeing two lines are right angle to each other.

So pause your screen now and I want you to attempt making quadrilaterals from diagonals.

So going back here what quadrilaterals can you form using two of the sticks as diagonal.

Pause your the screen now have a go, when you're ready press play to resume the lesson.

Okay, these are some of the ones that I came up with.

So previously we did saw the rectangle, we saw a square, we saw a kite, we saw delta too.

So this is taking one stick from pile A and another from pile B and then connecting up like so.

You could also get an isosceles trapezium, a parallelogram or rhombus and a trapezium.

Okay, If I create attention to diagonals of a rhombus and a diagonal of a square, we can see that the diagonal of a square are of equal length, whereas the diagonals of a rhombus are of different lengths.

Also the similarities here is that they both bisect at right angle.

To bisect is to cut something into two equal parts.

So I cut this here, this side is the same as that side.

So this side is equal to that side and is always equal to the below.

And the same with my square, this side is equal to that side and my up is the same as the bottom of my square.

So the diagonal bisect each other at right angle.

And also perpendicular, which of these would you say the diagonals are perpendicular? Right, perpendicular means lines that cross each other at right angle.

So I could see the diagonals of my square perpendicular, diagonals of my kite perpendicular, diagonals of my rhombus are perpendicular.

Okay, so we've learned two key words now, bisect to cut something into two equal parts and perpendicular lines that cross each other at right angles.

So now, I want you to sort the shapes into two groups by using the features of the shapes that are drawn.

So for example, I've given you some keywords here to use so you can you can either cause put into group of diagonals of perpendicular, diagonals bisect each other, or degree of how they intersect.

So your choice, sort this shapes into two groups by using only using the features of the shape's diagonals and then I want you to write how you grouped them.

So again, pause you screen now.

And once you're done press play to carry on with the lesson.

Okay, let's look at some of the ways we could have grouped our shapes based on the diagonals features.

So the first group could be the diagonals that bisect each other.

So remember, we said to bisect means to cut something into equal halves.

So these four bisect each other whereas these do not.

Our kite diagonal for example, they do not cut the kite into two equal halves nor do the diagonals of a trapezium.

Other ways you could have grouped are, some are perpendicular and some are not.

Some diagonals have the same length like our square and our rectangle and some don't like our kite and our parallelogram, Some diagonals do or do not intersect.

So for or example our delta diagonals they do not intersect okay? Okay, lets take these a little bit further.

In your book when I tell you to, I want you to draw this table in your book, it doesn't have to be perfect.

Just a rough sketch of this table in your book.

And then I want you to sketch and name a quadrilateral for each of the sections in the table.

For example, I want a shape or quadrilateral with two lines of symmetry and the diagonals are perpendicular.

What shape have i drawn here? Yes, it is a rhombus So I'm going to write rhombus here after I have sketched my quadrilateral.

So now pause your screen, try to each one, try to fill the table for each one and then when you're done press play to resume with the lesson.

Okay, some of the examples you could have come up with a quadrilateral that's got zero lines of symmetry and the diagonals are perpendicular.

Well I could have brought any type of quadrilateral as long as they don't have one line of symmetry, as long as they don't have any lines of symmetry.

So this quadrilateral that I brought is scalene, because all the lengths are different.

it doesn't have a line of symmetry.

However, the diagonals are perpendicular to each other.

One line of symmetry and the diagonals are perpendicular, well, that's a kite I hope you see that.

Perpendicular and one line of symmetry going across here.

Two lines of symmetry and diagonals are perpendicular is a rhombus.

Diagonals are not perpendicular, they do not meet up at right angle.

Well a parallelogram's got zero line of symmetry and the diagonals don't meet at right angle so it is a parallelogram.

One line of symmetry on the diagonals are not perpendicular is an isosceles trapezium.

And two lines of symmetry and again, the diagonals are not perpendicular is a rectangle.

So pause the screen out If you have to just to get this information and to into digest this information and understand it more and then carry on watching the video, when you're ready to.

You now have your independent tasks.

So I want you to pause the video, attempt every question on your independent task and then when you're ready, come back and we will go through for the answers together.

Okay, let's think about the answers together.

We want to draw on the diagonals on this quadrilaterals.

Remember earlier, we said diagonals of quadrilaterals are formed by connecting the opposite vertices together.

So if I connect the vertex from here to here, I get my burgundy straight line and then the opposite vertices from this line here.

So that is my diagonal for my kite.

These are diagonal for my parallelogram, diagonal for my rectangle and diagonal for my rhombus as well.

Lets take a look at the answers to question two.

Copy and compare the following sentences that refer to the four shapes in question one.

So the four shapes in question one were kite, rhombus, parallelogram and a rectangle.

So the first sentence is, diagonals and the kite and the rhombus are are perpendicular.

The diagonals in the kite, the parallelogram and the rhombus have different length.

The diagonals in the kite are the only diagonals that do not bisect each other.

Remember bisect means to cut something in half okay? Right, question three, would you want to draw quadrilateral that is different to the shapes in question one? So a different quadrilateral where the diagonals are perpendicular is a square, A different diagnosis where So for question three, we want to draw quadrilaterals that are different to the ones given us in question one.

So we want a quadrilateral where the diagonals are perpendicular and that quadrilateral is a square like the example shown on your screen right here.

We want a quadrilateral where the diagonals bisect each other.

And again, the answer for a and b can be a square.

And then we want quadrilaterals where the diagonals do not intersect and that is of course a delta.

Right, let's look at question four then, we want to draw sketch, I haven't gone drawn a sketch, I have just written the answer down.

But check in the book, the right answer and you've gotten the correct sketch as well.

So we want to draw a sketch of a quadrilateral for each of the numbered sections in the Venn diagram.

So the first one, we want diagonals perpendicular, so quadrilateral where the diagonals are perpendicular and we've got a kite or rhombus.

We want a quadrilateral where the diagonals are perpendicular and the diagonals have same length and that is a square.

We want a quadrilateral where the diagonals have the same length and that must be a rectangle or an isosceles trapezium.

And Number four is asking us for a quadrilateral that doesn't fit into either of this, the diagonals are not perpendicular and the diagonals are not same length and that's a parallelogram.

Next, we want diagonals that intersect and are rectangle intersect.

It's an example of the quadrilaterals where the diagonals intersect.

What do you want for number two, that the quadrilaterals where the diagonals intersect and the diagonals are perpendicular and that is a kite.

Number three, we want a quadrilateral where the diagonals are perpendicular, remembering that perpendicular means lines that cut each other at right angle and that is a square.

And number four we want a quadrilateral where the diagonals do not intersect and the diagonals are not perpendicular and that is a delta.

Let's look at the last one then we want diagonals that bisect each other.

If we look at our rhombus the diagonals do bisect each other, they do cut each other in half.

Number two, diagonals that bisect each other and have the same length.

The diagonals are a square have the same length and they cut each other in half as well.

We want diagonals with the same length for a quadrilateral and that is an isosceles trapezium.

Now again, it's very important to remember the diagonal in a parallelogram do not have the same length nor do they bisect each other okay? Okay, Moving on to explore task.

I am going to read the sentence out for you.

The diagonals of four quadrilaterals have been drawn on the eight dots circles.

What quadrilaterals are they? Describe their symmetry? So when I say describe their symmetry, I want you to describe the order of rotation of symmetry and also their lines of symmetry.

So pause your screen now If you know exactly what to do and get on with it.

If you need some more support then carry on watching the video.

Okay, let's think about it.

This diagonal, I want to connect the points.

I've connected one here, connected, assuming I can draw a straight line connected the other one, connect to the bottom and the top.

What shape have I formed? Right, I have drawn a rectangle.

So I'm going to do the first one, rectangle, And it's going to write rect for short.

If I want to describe the lines of symmetry, how many lines of symmetry can I see here? Well, it's a rectangle, so my lines of symmetry would be here and horizontally along as well.

So I am going to write two lines of symmetry.

Okay, two lines of symmetry.

Now, if I want to describe the order of rotation and symmetry that means, If I'm starting here, how many times can I rotate the shape and it would still have the shape I started with by the time I get to the end.

How many times can I rotate the shape and it will keep same shape I started with by the time I get to the end.

Well for a rectangle, it would be two.

So the first one has been done for you.

The quadrilateral is a rectangle, its got two lines of symmetry and the order of rotation of symmetry is two.

So pause your screen now, so order of rotational symmetry.

Pause your screen now and attempt the rest and once you're done, come back to see how you got on.

Good job all, you have now reached the end of today's lesson.

A very big well done for sticking all the way through and completing your work as well.

I will see you at the next lesson.