Lesson video

Hello, and welcome to this lesson on constructing quadrilaterals with me Ms. Oreyomi.

For today's lesson, you will be needing your pair of compasses, you'll be needing your protractor, your pencil, your book, and a ruler as well.

So if you need to pause the video to go get this equipment, then please do so.

Also try to minimise distraction by getting into a space with less noise, and also putting your phone in silence to avoid distraction.

So pause the video now if you need to do any of those things and then resume when you are ready.

For your try this task, I am going to read the statement on the board for you.

A student has drawn a triangle using the dotted circles that you can see on your screen right now.

What quadrilaterals could he form by adding another triangle to the triangle we currently have on our screen? So by connecting another triangle to the triangle we already have on our screen, what other quadrilaterals could he form? So, pause your screen now, attempt this, once you're done, proceed with the video, and we'll carry on with the lesson.

Okay.

Here are some of the quadrilaterals that he could have formed.

For the first one, he could have formed a kite.

For the second one, he could have formed a scalene quadrilateral.

For the third one, he could have formed an isosceles trapezium.

And for our last one here, he could have formed a parallelogram.

Did you manage to get some of this or were yours different? So these are some of the quadrilaterals our student could have formed by joining another triangle to our dotted circles.

So, moving on to our connect task, Ciara drew this construction for a triangle.

What side lengths will her triangle have? Take a moment to think about this.

What would be Ciara's triangle's side lengths? Let's start with our base over here.

We've got one, two, three, four, five, six.

So our base here would be six centimetre.

What of the length from here to here and from here to here? Well, we know that our radius is always the same regardless of where we are on our circumference.

So our radius is three centimetre.

So this level will also be three centimetre.

Over here, our radius is one, two, three, four, five.

So this length here is going to be five centimetre.

Okay? She then decides to draw, to use this construction that we have on our screen, to draw a kite instead.

What are you thinking? If I want to change or rather add a kite to this triangle, if I want to form a kite from this triangle, what should I do? You're probably thinking back to your try this task now.

If I just change the pen so that we can see this clearly.

So I hope you're thinking that she should connect her, from the centre of the circle to this point on her circumference, and also to this level here.

Because we know that a kite has one line of symmetry.

So whatever value she's got for her first triangle, that same value will be reflected on her second triangle.

So this will be five centimetre.

So starting with a triangle, she has been able to use that same construction for her triangle to draw a kite instead.

Okay.

We are now moving on to construction using our compass, a protractor, and our pencil.

First thing we want to construct is a kite and a parallelogram.

We have our skeletal starting point, our skeletal foundation.

So, if I have this three centimetre, five centimetre, and then an angle of 127 degrees between them, what would I do if I want to construct a kite? Think about the features of a kite.

What would this length be, if I just draw a rough construction of a kite, what would this length be? Yes.

It should be three centimetre.

What would this length be? Yeah, five centimetre.

What do we know about opposite angles then? Well, what do we know about this angle over here? Well, it would be the same, wouldn't it? So this would be 127 degrees too.

Okay.

And it would have one line of symmetry.

What of, if I want to construct a parallelogram? So assuming, I'm just going to do a rough sketch here, I'm starting with three centimetre and then five centimetre and then I want 127 degrees here.

If I want to construct a parallelogram, what would this length be? If you said three centimetre, then you're correct.

Because we know that for a parallelogram, opposite sides have equal length.

So if this is five centimetre, this would be, sorry, if this is three centimetre, this would be five centimetre.

Okay, what would this angle, what rather should this angle be? It should be 127 as well.

And these two angles should be the same.

So I'm just going to label this b and b.

If, going back to our kite, if I want to get this line of five centimetre using a compass, what am I going to do? I'm going to show you a video of me constructing a kite.

Pay close attention because you are going to get a chance to construct a parallelogram.

So, on the next slide, I'm going to be talking over how to construct a kite, and then feel free to pause the video should you wish and to rewind and to go through at your pace.

Because you're then going to get a chance to construct a parallelogram.

So, first thing I'm doing is I am drawing that skeletal figure we had on the previous slide.

So I'm starting with three centimetre.

And then I am going to measure my angle of 127 degrees.

So remembering how we use our protractor, I am reading from the outer scale because that's where my baseline is on.

I want 127, which is right there.

Then I am going to measure five centimetre, right there.

But I'm not quite done because I haven't actually constructed my kite yet.

So, I know that adjacent sides are equal.

So I measuring five centimetre now, and I'm going to draw my circle with a radius of five centimetre.

The compass is a fiddly tool.

So do feel free to take as many takes as you can to get that perfect circle of five centimetre radius.

I'm measuring three centimetre again.

And from the top point, I am drawing a circle with a radius of three centimetre.

Now I am going to connect all my points to that point of intersection right there.

So connecting that point and connecting that point to the intersection.

Measuring my length.

It should be five centimetre.

And my top length should be three centimetre.

And that is how I go about constructing my kite.

Now, your turn.

Draw two copies in your book of the line segment shown.

So you need your protractor for this.

First thing, draw two copies of this line segment shown, accurately.

And then using the base, using the skeletal drawing that you've just drawn, can you construct a kite and a parallelogram? Feel free to go back and rewatch what I've just showed you and pause the video now and complete this task.

Once you come back, we would see if you've drawn the correct.

If you've constructed the correct shape.

Okay.

I wonder how you got on with this task.

And I hope you were able to use your compass and your protractor to accurately construct a kite and a parallelogram.

So let's quickly go over it.

So for a kite, just to recap, we measured a point.

We measured five centimetre and we drew a circle with a radius of five centimetre from this point over here.

And then we did the same but with three centimetre on that point over there.

For our parallelogram, you started with the skeletal figure of five centimetre here, three centimetre here, and our included angle of 127 degrees.

From this point here, you should have draw a circle, putting the tip of your compass here, you should have drawn a circle with a radius of three centimetre.

Okay? And then putting your tip of your compass on this point here, you should have drawn a circle with a radius of five centimetre and then connected your lines up to this point of intersection over here.

So I hope you were able to do that.

If you're still not done, please do go back and try again as is a very important skill to master.

In the last activity, we learned how to, or rather we practised, how to construct a parallelogram and a kite.

Now we want to move that further and construct a rhombus and a kite.

So if I want to construct the first one right here, my A, and I want to construct a kite with sides five centimetre, five centimetre, well, that's already been given to us, hasn't it? So how would I go about constructing four centimetre and four centimetre? That's for you to think about.

And you're going to get a chance to practise very soon.

I am going to show you, using a video, how I went about constructing my rhombus and how I marked on my lines of symmetry and measured any other internal angles.

So again, watch very closely how I do this.

And because you're going to get a chance to draw your own, to construct your own rhombus and your own kite with the given sides on your screen.

Okay, so this video, I'll be talking over it as usual.

Do feel free to pause the video to understand what I've just said, and go watch it at your pace essentially.

What do I know about a rhombus? Well, I know that all the sides of the same, don't I? So my rhombus should have all sides of five centimetre.

So this should be five centimetre, and this should be five centimetre as well.

So this should be five centimetre and this should be five centimetre as well.

What do I know about the angles? Well, I know that opposite angles are equal, so this should be 37 degrees, and I believe this should be 143 degrees.

So therefore this should also be 143 degrees.

What do I know about the lines of symmetry? I've got two lines of symmetry, don't I? So it you should be from here to there, and then from there to there.

Let's see how we do that using our compass and our protractor.

So first thing I'm doing is I am measuring five centimetre for my base.

I'm going to label that.

Then I am measuring 37 degrees using my protractor and I'm reading the inside scale.

I'm going to try and do it as accurately as I possibly can.

So 37 degrees.

And now I want a line of five centimetre.

Okay.

As I've said, because it is a rhombus, all our sides would be the same.

So five centimetres, I am now measuring five centimetre on my compass so that I could draw a circle with a radius of five centimetre.

So I've done it for one side.

I am now going to do the same on the other side as well.

Okay, I'm trying to get that perfect circle.

Right.

Now, I've seen that point of intersection there.

So that's where I am going to connect all my lines to.

So, connecting it to that point of intersection, it should be five centimetre right there.

And then I'm going to do the same for the other end, connecting it to the point of intersection.

Okay.

I'm going to label my lines.

No, I'm not.

I'm going to measure my angle.

So that is 143 degrees.

I'm going to measure the other side.

Like I said, it should be equal, roughly equal.

Sometimes we go about two or three degrees below or above.

So I think I measured 40 degrees.

And then the other side I measured about 143 degrees.

Now I am going to draw on my lines of symmetry.

And that is how we construct a rhombus.

Your turn.

Your turn.

Can you construct a kite using what you have, using the image you have on your screen as your starting point, can you accurately construct a kite with sides of five centimetre, five centimetre, four centimetre, four centimetre? And then can you proceed to construct a rhombus with, well, we've just spoken about how to construct a rhombus.

And then I want you to mark on your construction all the lines of symmetry and measure any internal angles.

So pause your screen now, complete this, once you're done, come back and we would see if you got the right image.

Okay.

I wonder how you got on.

I hope you were able to use your compass and your protractor to have constructed the image that you can now see on your screen.

Let's talk about the kite then.

So we were given five centimetres, five centimetres, and 37 degrees.

So hopefully you were able to have connected your point here to construct four centimetre for the adjacent side.

So four centimetre here and four centimetre here.

Hopefully, your angle here is the same as this one over here.

So if your angle for this is anything between 136 to 140 degrees, then you are fine.

If it's anything too much above 140 degrees, then you've probably done something wrong.

Or if it's anything a lot higher than 138 degrees, then you probably should measure that again.

For this one, if you get any angle between 45 to 49 degrees, again, you are within the range.

And obviously, your line of symmetry is going from that vertex through that vertex over here.

Let's move on to our rhombus then.

Hopefully this is a bit more straight forward due to the video tutorial.

But like I said, this angle and that angle are the same, and this angle and this angle are the same.

We have two lines of symmetry cutting through the vertices, and all our sides are five centimetre.

It is now time for your independent task.

Please do get your compass ready and do get your protractor ready and your pencil as you'll been needing it for this task.

Pause the video, attempt every single question.

Once you're done, resume, and the answers will be on your screen.

Okay, your explore task.

Three circles intersect at their circumferences and centres.

They intersect at the circumferences and at the centre there.

Connect four dots in this image to find a kite, to find a rhombus, and to find a delta.

Once you've connected your dots, the four dots, what are their side lengths and lines of symmetry? So for example, would you connect, to form a kite, would you connect the blue dot to the red dot and the dark red to the purple? What would you do? So you can just write the colour of the four dots you would connect.

And then once you've done that, write down the side lengths and their lines of symmetry.

Pause the video now and attempt this.

Once you resume, you would see the answers on your screen.

We've now reached the end of today's lesson, and a very big well done for sticking all the way through and completing your task.

It takes great skill and great practise to understand and to be able to construct quadrilaterals using tools, mathematical tools, such as a compass and a protractor.

So if you feel really confident in doing this, well done, keep on practising.

And if you don't feel too confident, keep practising as well.

Literally, it takes practise to become better.

Before you go, make sure you complete the quiz as that shows you what you've gained from today's lesson.

And I will see you at the next lesson.