Lesson video

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Hello, and welcome to this lesson on constructing triangles with me Miss Oreyomi.

You will be needing for today's lesson, a ruler, a pair of compass, your pencil, and possibly your rubber.

As usual, you'll also be needing your book.

This lesson requires a lot of skills and attention.

So I would encourage you to minimise distractions.

And also if you need to pause the video to go grab what you need for this lesson, then please do so.

So pause the video now and go and grab your equipment.

And then when you're ready, press play to resume the lesson.

Okay, in today's lesson, you will be able to construct triangles using a pair of compasses and a ruler given the length of the sides.

So once you're given the length of sides, you should be able, you will learn how to construct the triangles using your compasses and your ruler.

So just a reminder that you will need your ruler, you will need a pencil and you do need your compass as well.

Our first task is to write a sentence describing the following.

So write a sentence in your book describing what diameter is, what a radius is, what the circumference is, and what construct is.

If you haven't heard what construct is, or if you don't know what it means, just have a guess.

If someone says to you, construct, what does that mean? And then once you finish number one, move on to number two, Mary has written the following, d, meaning diameter is equals to 2r.

Write a sentence to describe the relationship between the diameter and the radius.

So pause the video, attempt the questions.

Once you're done, come back and we'll go over it together.

Okay, the sentence I wrote for a diameter is that a diameter is a straight line that goes from one end of the circumference to the other through the centre.

The diameter line must always go through the centre, and it touches one end of the circumference to the other end of the circumference.

And a radius is a straight line, again, from the centre of the circle to one end of the circumference.

So it's from the centre to one end of this circumference.

And the circumference is the distance around the circle.

Now construct means to build or to make something which is what we'll be doing in today's lesson.

Now let's look at question two, diameter is 2r.

That means diameter is two lots of r.

So if we want to write a sentence to describe the relationship between the diameter and the radius, we can say the diameter is twice the radius.

Okay, for our Connect task, I would stop talking.

And you're going to watch the video on your screen in a second.

So pay close attention to what's happening on your screen.

And I'm going to come back and talk over it as well.

Our instruction was to construct a triangle with seven centimetre, six centimetre and four centimetre.

We were not told which length is the base, so we've just chosen seven centimetres here as the base.

We can count that's one, two, three, four, five, six, seven.

This green compass here will draw a circle with a radius of four centimetres.

So if I drag a slider across, it should draw a circle with a radius of four centimetres.

Remember, we said the radius going from the centre of the circle to any point of the circumference.

So if I come here I've got one, two, three, four.

I come up I've got one, two, three, four.

So this circle here is a radius of four centimetre.

If I drag my slider across the six centimetre compass, it should draw a circle of six centimetre.

What do you notice about this then? What do you notice about our circles? At what point are they intersecting? They're intersecting at this point and at that point.

So if I click draw triangle one, so we have seven centimetre, four centimetre, and our six centimetre circle.

If I click triangle two, it should draw the triangle on the other way.

So we can draw our triangles either at the first point where they intersect, where the circles intersect are the exact points where the circles intersect.

And this is how we construct triangles, where we're given three sides.

Okay, I thought it was all well and good to see a simulation.

But I thought if I did, if I show you a demonstration of me creating my own triangle, then perhaps you could understand it more, you can understand it better.

So I am going to then talk over this video.

And if there's any point you do not quite understand what's going on, do pause it, do rewind and watch again.

So go at your own pace essentially.

So, quick point.

Quick point to make is we are drawing a triangle with sides four centimetre, six centimetre, five centimetre.

Again, they haven't given us what the base triangle should be.

So, I have chosen five centimetres just because I can.

So I am starting by measuring my base of five centimetre, and I am labelling my line five centimetre so I do not get confused later on.

And then I am measuring four centimetre for my second side length using my compass and my ruler.

I am then going to draw a circle with a radius of four centimetre, that four centimetre that I just measured.

Then I am measuring six centimetre using my compass and my ruler.

I am then going to draw a circle with a radius of six centimetres going from the other point this time.

So I started on this point then I'm going to that point to draw my six centimetre radius circle.

Now, I am going to connect all my points to the intersection where the circles intersect.

So just connecting all my points, then I am going to measure it, just to make sure that I've accurately done this.

If I pause the video here, see that it's not exactly four centimetres, it's about 3.

8.

But because it's not so much off, I am just going to round it and write four centimetres.

So I am going to carry on playing the video.

So that's four centimetres.

And then that is six centimetres.

If again, I just pause the video there, I've measured with my ruler, although I do not have to.

I could count.

So that will be one, two, three, four, five, six.

The circle has a radius of six.

So whether I'm drawing my radius from this point to the end, or going from here to there, because it's still from the centre to the circumference of the circle, I know that this line is six centimetres.

So even if I go from here, to that point there, it's still going to be six centimetres, okay? Okay, to connect it to the bottom, all I do is just do the same thing.

So I'm just going to draw a line from here to the intersection point.

I'm going to put it on camera shine, it's a bit off the page.

And you would see that it should look exactly the same as my first triangle.

So I have a right angle scaling triangle.

And I'm just going to measure my lengths again.

And I know that they're both the same.

So that is how you construct your triangles.

When you're given the length, you start by drawing a base, and then you measure your sides and draw the radiuses and connect the lines up to the intersecting part of your circle.

Here are four constructions of four triangles.

What are the lengths of their sides? What is the same and what is different? So if you want to pause the video now to think about these questions before we go through it, and then resume when you think you have an idea, and we're going to go through it together.

Okay, let's go over it together.

I've got a first triangle, I know that the length from here to here is two, because each square is a centimetre, I'm just going to write two here.

If the length of this is two, what is going to be the length of this line? Well, I know that it is also two, the radius is two because it's going from the centre to the end of the circumference.

So therefore, this line will be two centimetre.

Because remember, as long as it's touching any point of our circle, the radius stays the same.

Again, this point is one, two centimetre.

So although it's going from here to this point over here, it's still touching my circle.

So the radius is two centimetre.

So what type of triangle is the first one? An equilateral triangle? Exactly.

I'm just going to write e there.

Let's look at this one, the base is one, two, three.

Okay, so we've got three centimetre over here.

What of the radius of this line? This radius is one, two.

So this is going to be two centimetres as well.

This is also going to be.

Well the radius is one, two.

So this length is also going to be two centimetre.

So we have drawn ourselves an isosceles triangle right here, I'm going to write i, for isosceles triangle.

What of this one over here? Well, my radius is one centimetre.

So that means this line will also be one centimetre.

And this is two centimetres, so this is going to be a two centimetre line.

And I've got again, one, two.

So this is also, just check in that.

this is also going to be a two centimetre line.

And the last one, I've got one, two, three, four, this is four centimetre.

This radius here is one, two, three.

So this is a three centimetre line.

And the last length the radius is two.

So this is a two centimetre line.

So I've got one equivalent triangle, one isosceles triangle, another isosceles triangle, and a scalene triangle.

So this is a neater version of what I've just explained to you.

So we can use the properties of circles to determine and to draw triangles when we're given the lengths.

And even though we don't have the length, we can use the radius of the circle to determine the lengths of our triangle.

You're now going to get a chance to work for your independent task.

So I want you to pause the video now and attempt every question.

When you come back, you will see the answers on your screen.

So just mark through your work when you resume the video.

So if I select that length for example, and then I select this length and then say I want eight centimetre over here.

These are my three lengths that I'm starting with.

And then once you've constructed that, you choose another three lengths and then another three lengths.

How many different triangles can you construct with these as your side lengths? And perhaps, would you come across one that you can't construct? So pause the video now and attempt to construct as many different triangles as you can pick in three different lengths each time.

Okay, hopefully you had a go at constructing lots of different triangles.

The ones with the ticks are the ones that you could construct with the three different lengths, and this one, five five, ten because the circles don't intersect, you can't construct them.