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Hello, and welcome to today's lesson on further constructions with me Miss Oreyomi.

For today's lesson, as the title suggests, you'll be needing your pair of compasses, you'll be needing your ruler, your protractor, and your pencil.

And of course you'll be needing your book.

It would also help if you can minimise distraction.

So if you need to go to a space with less noise then please do so.

Pause the screen now if you need to get your equipment and when you're ready, press play to carry on with the lesson.

Okay, your try this task.

Draw two copies of the line segments shown.

This is the line segment, draw two copies of this.

And then construct two more sides to form a kite with five centimetre, five centimetre and three centimetre, three centimetre.

So those are the sides for your kite.

And then secondly, construct another kite with sides of five centimetre, five centimetre and seven centimetre and seven centimetre.

So pause the video, construct your two kites.

Once you're done, press resume to carry on with the lesson.

Hopefully you were able to get something like this.

So we have five centimetre, five centimetre, three centimetre and three centimetre.

Five centimetre, five centimetre, and seven centimetre and seven centimetre.

Let's move on to our connect task.

Using your construction from the try this.

So it's very important that you've actually done the task from the previous slide.

We want to take this further and use our construction of a kite to then construct a delta with sides of five centimetre, five centimetre and three centimetre and three centimetre.

And then to construct a delta with sides of five centimetre, five centimetre, seven centimetre and seven centimetre.

I am going to talk through a video of me constructing a delta from my kite with sides of five centimetre, five centimetre and three centimetre and three centimetre.

So as usual, you can always pause the video and go at your own pace, just so that you understand everything that is happening, happening in this lesson, okay? So first thing I'm doing is I am measuring my five centimetre.

And I always label it so I do not get confused about which line I've just drawn, so five centimetre right there.

And because I do not have an included angle, I'm just drawing another line of five centimetre.

Right now, I am not really bothered about the angle.

So another line of five centimetre.

Then I'm taking my compass and making sure that the point and the pencil aligns.

Then I am measuring three centimetre using my ruler.

I am then going to go to one point.

So you already know this, this is constructing a kite essentially.

So I'm going to draw a circle with a radius of three centimetre.

And then I'm going to check again, just so that, 'cause sometimes the compass move, making sure that I'm still on three centimetre and I'm going to do the same for my other point.

So now, I have.

This.

Then I am going to draw my kite.

Three centimetre, three centimetre, but I don't want a kite, I want a delta.

Do you see how on my screen there are two points of intersection? So I have one intersect, one point of intersection on my circle here.

And then I have another point where I've just put my X.

To get my kite, I have connected my three centimetre line to this end to get a kite.

To get my delta, I am going to connect, I'm going to draw lines to this second point of intersection as the video is going to show in a second.

So.

Connecting to the second point of intersection on my circle, that is how.

I get my kite.

So using my shape of a kite, I can get my delta by connecting to the second point of intersection.

And again, my line should still be the same, three centimetre, three centimetre.

I am now drawing my line of symmetry.

Again, delta and kite both have one line of symmetry.

So, you're now going to have a go at drawing your own delta shape.

So using your construction from your try this task, if you did not do that, please ensure that you do it.

Using your construction from your try this task.

Can you construct a delta from that? So I have just shown you how to construct a delta using five centimetre, five centimetre, three centimetre, three centimetre, do feel free to have a go at that again.

And then also construct a delta with sides of five centimetre, five centimetre, seven centimetre, seven centimetre.

Pause your screen now, complete that, resume the video and we'll carry on with the lesson.

Okay.

Hopefully your construction looks something like this.

So, these blue lines form the kite.

And the green lines form the delta.

So remember what I said, this further end of the, further end of our intersection on our circle forms the kite, the same as here.

Whereas this further end forms our delta.

Let's think about the discussion these two students are having, Ciara and Billy.

Ciara and Billy, they want to construct a rhombus with a six centimetre diagonal.

So this diagonal here is six centimetre.

Ciara is saying, I think the rhombus could have any side length.

That is with a diagonal of six centimetre, our rhombus can have any side length.

Billy's saying, no, I don't think they can.

Can you drawing your diagonal of six centimetre, can you construct your own rhombus, starting with this diagonal? And then decide who you agree with.

Do you agree with Ciara or do you agree with Billy? So if you're not sure how to construct a rhombus, just choose any side, okay? 'Cause we know that a rhombus will have the same length, every side is equal.

So just choose any side, and using your compass, draw a circle with a radius of your given length.

So for example, if I choose five, I'm going to draw a circle with a radius of five.

Draw another circle with a radius of five here and connect all my points to the intersection.

Once you've done that, who do you agree with? So pause the video now, construct your rhombus and let me know who you agree with.

Hopefully you were able to construct your rhombus and also decide who, also decided who you agreed with, whether it was Ciara or Billy.

So, reminder, that Ciara said, regardless of the length of the diagonal being six centimetre, she could have constructed, she's saying that she could have constructed a rhombus with any side lengths.

And Billy was saying not every length would work.

And in this diagram in front of you, we see that if the side length is less than the radius of our circle, the circles would not intersect.

And if the circles don't intersect, then we can't draw our rhombus.

We can only construct a rhombus if the side length is greater than the radius of our circles.

So in this case, if the side length is greater than three centimetre, that is when we can construct our rhombus.

You're now moving on to your independent task.

So pause the screen now and attempt every question on your screen.

Once you've completed those questions, come back and the answers will be in front of you, so you can mark your work.

Your explore task essentially tests your knowledge that you've gained in today's, your knowledge and skills you've gained in today's lesson.

So you are to firstly, construct a quadrilateral that has two sides of eight centimetre and one line of symmetry, and practising with drawing diagonals, practising with constructing with diagonals.

You are then to construct a quadrilateral that has a diagonal of five centimetre and two lines of symmetry.

So pause your your video now, and have a go at doing this, and then press play when you're ready to start.

Okay, here are possible solutions.

So for the first one, you could have formed a kite or a delta.

And the second one is definitely a rhombus because we have two lines of symmetry.

A very big well done for sticking right to the end and completing today's lesson.

Practise with your compass, practise constructing with your protractor, and you would get better in no time.

Before you go, make sure you complete the quiz, just so that you know what you've learnt in today's lesson.

And I will see you at the next lesson.