Lesson video

Hello and welcome to today's lesson on Classifying Triangles with me, Miss.

Oreyomi you'll be needing a paper and a pen as usual.

You will also be needing a pencil and a ruler.

So if you want to pause the video now to go get your equipment and also get into the correct headspace for today's lesson, please do so.

And when you're ready, press resume to continue with the lesson.

Okay, in today's lesson you will learn how to describe the properties of scalene, isosceles and equilateral triangles.

And you will also learn to identify and classify angles inscribed in circles.

Inscribed means inside a circle.

Today's keyword is conjectures.

what do I mean when I say conjectures? Conjectures means pattern or segments that haven't been proven yet.

So if I notice something and I'm like, "Oh, I'm starting to see this pattern here, "but I haven't yet proven it.

"And I don't know if it works in every given situation." Then I can say, "I've made a conjecture that this is happening.

"However, I do not know if it works every given time." Your try this task is to draw a triangle for each section of the table.

Looking at this one for example, you are to draw a scalene right angled triangle.

A scalene that has a right angle triangle.

I want you to pause the video now and complete the table.

Once you're done, come back and we'll carry on with the lesson.

Okay, I have some examples on the screen that I want us to go through very, very quickly.

So the first one, a scalene right angle triangle, right? What do we know about scalene triangles? We know that all the sides are different and all the angles are different.

So this one here is a right angle triangle and all our sides are not the same.

An Isosceles triangle that has a right angle.

Question, If this angle here is 90 degree.

What would this angle be? And what would that angle be? They would both be 45 degrees exactly.

Because it's an isosceles triangle.

An isosceles triangle mean we have two equal sides and two equal angles.

Do we get an equilateral triangle that has a right angle? The answer is no.

It's impossible because each angle in an equilateral triangle, each angle is the same so we can't have 90 degrees, 45 and 45 'cause that wouldn't make it an equilateral triangle.

So it's impossible to have an equilateral triangle that has 90 degrees.

Now again a scalene with no right angle.

Which is there.

An isosceles with no right angle.

That means the two angles at the bottom would be the same.

And this would not be 90 degrees.

And then an equilateral triangle where we know that each angle is 60 degrees, right.

Let's think about this task.

We are told to draw triangles by joining three dots on the different circles.

So I want to start with an isosceles triangle.

What do I know? What are some of the properties of isosceles triangle? Right.

This task is asking us to draw triangles by joining three dots on different circles.

I want to draw either an isosceles or a scalene or an equilateral triangle on three dots on this circles.

I want to start with an isosceles triangle.

What do I know about.

What are some of the properties of isosceles triangles? Well, so you may have said it's got one line of symmetry.

That would be correct.

You may have said its got two equal angles.

That may be correct, that is correct rather.

you may have said its got two equal sides lengths And again, that is correct.

So assuming I want to draw an isosceles triangle on one of this circles over here using three dots.

How could I go about that? Well, I know that I want two sides to be the same.

So if I go from here to here and then I connect it to this point over here and then I connect it to the top again.

I can see that the distance from my top dot to this dot is the same as the distance from my top dot to this dot over here.

What of the line of symmetry? Well, it would be going through the first dot 'cause if you remember, my line of symmetry is the way I cut my shape so that if I reflect the other half of my shape over my reflected line it fits exactly under the other half.

So this would be one way of drawing an isosceles triangle on three dots.

What of an the equilateral triangle? Let me count the number of dots in this circle I've got one, two, three, four, five, six, seven, eight.

Can I draw an equilateral triangle on a eight dotted circle? I want there to be equal space between my dots.

So I got, One, I've got two dots here.

So I want two dots again.

Mm-hmm Have I been able to draw an equilateral triangle? Well, no, because equilateral triangle all have equal length but here I can see that they're not equal length.

I've got two dots here.

Two dots here but one dot here.

So what triangle have I drawn? Yes, exactly.

I have drawn an isosceles triangle where this line, this side length is equal to this side length And again, if I want to draw my line of symmetry, it would be going through this dot over here.

That is interesting.

I couldn't draw an equilateral triangle on an eight dotted circle.

Let's see if we could draw it on this one.

I've got one, two, three, four, five, six, seven, eight, nine.

If you can draw it in here.

So I'm starting here again I want two dots in between.

I've got two dots here.

Got two dots here and I've got two dots here.

Wonderful.

I'm able to draw an equilateral triangle on a nine dotted circle.

What if I want to draw an equilateral triangle on a six dotted circle? Would I be able to do it? What do you think? so, there's one dot in between Yes, I was able or I am able to draw an equilateral triangle joining three dots on a six dotted circle.

What conjecture can you come up with? What pattern do you think you're seeing? And the number of circles I need to be able to draw an equilateral triangle? I'm thinking something along the multiple of three, I'm thinking it has to do with a multiple of three.

'Cause this is six and this is nine.

I could probably draw an equilateral triangle joining three dots on a 12 dotted circle.

Why don't you try it? Get a round object at home.

Trace it onto a paper, draw 12 dots around and see if you can draw an equilateral triangle.

For an equilateral triangle, we know that it's got how many lines of symmetry? Again, assuming this is straight drawn with a ruler three lines of symmetry.

Now I want you to pause your screen and I want you to attempt to draw different triangles.

Scalene, isosceles or equilateral using dotted circles.

So as I said earlier, just get a shape that is round and trace a circle around it.

Put your number of dots and see which triangle you can draw.

Can you draw a scalene, an isosceles, an equilateral triangle and how would you know that you have drawn a scalene? For example.

Pause the video now I want you ready, come back I'll resume with the lesson.

Okay, these are some examples of triangles being drawn on dotted circles joining three dots.

If we look at the scalene one, there are no lines of symmetry and the sides are not equal.

And we can tell they're not equal because the spaces the number of dots between each connected dots is different.

Okay.

I want you to read each of these statement.

I'm going to read each one out for you and I want you to decide whether it's true or false.

So we're making conjectures about these statements.

Are they true? Or are they false? The first one, isosceles triangles have at least two equal angles.

What do you think? Do you think that is true? Or do you think that is false? It is true as we saw from our try this task and also from my previous slide isosceles triangle have at least two equal angles.

Isosceles triangles have at least one line of symmetry.

Do you think that is false or true? It's true as again we saw that in the previous task that we just did.

Isosceles triangles have rotational symmetry order two.

You have to think back a bit now, if you want to pause the video and draw your isosceles triangle out and try to see if it's got a rotational order symmetry two.

What do you think? Does it have a rotational symmetry order two? No, it doesn't.

Isosceles triangles have rotational symmetry order one.

Next one, scalene triangles have two equal angles.

What do you think? Is that true or is that force? It's false, they don't.

None of the angles in a scalene triangle are equal.

Only scalene triangles have a right angle.

Think back to your try out task.

Only scalene triangles have a right angle.

Is that a true statement or is that a false statement? It is very false.

You can have an isosceles triangle with a right angle.

Equivalent triangles have three lines of symmetry.

Think back to the previous slide.

Equivalent triangles have three lines of symmetry.

Is that true? Or is that false? It is very true.

We're now moving to our independent tasks.

So I want you to pause your screen now attempt all the questions on the task.

Once you're finished that, come back, press play and we'll carry on the lesson.

Okay, welcome back, I hope the independent task was challenging and engaging enough.

Now question number one, state with reason if the following triangles are equilateral, isosceles or scalene.

Why is the first one equilateral? Well, the sides, the space between the connected dots are the same.

This is scalene, why is it scalene? All the sides have different lengths.

Third one is an isosceles triangle because the space between two of the dots are the same.

So we've got two dots here, two dots here.

Shows us that these two lines are the same.

These two sides rather have equal length.

And also if I draw my line of symmetry I would get one line of symmetry showing that it's an isosceles triangle.

Again, it's an isosceles triangle.

Again, these is scalene.

Equilateral for the same reason.

Isosceles for the same reason, the space between this point and that point is the same as the space between here and here.

Scalene and isosceles triangle as well.

Okay, number two, decide if the following statements are always true, sometimes true or never true.

And I don't have a sketch here, but you are meant to sketch a triangle to justify your responses.

So let's look at the first one, equilateral triangles have three lines of symmetry.

That is always true.

Now we established that in today's task as well.

Where we drew our triangles, we're able to draw three lines of symmetry that intersected at a point remember lines of symmetry intersect at a point.

An isosceles triangle has order of rotational symmetry order two.

No, they don't.

They have how many order of rotational symmetry? Just one, exactly.

A triangle has same number of lines of symmetry as its order of rotational symmetry, sometimes.

Take an isosceles triangle for example, it has how many lines of symmetry? One.

What's the order of rotational symmetry for an isosceles triangle? one.

So that sometimes will be true for an isosceles triangle.

A scalene triangle has no symmetries yes.

It does not have symmetries.

The equal sides of an isosceles triangle are longer than the third side.

Sometimes they are and sometimes they are not.

Can you draw a triangle? Can you sketch a triangle for when they are, and when they're not? Right-angle triangles are also scalene.

So this in our try this task, yes.

Some right-angled triangles are also scaling triangles.

And looking at this one, you are told to copy and complete the table of types of triangle below.

Where the triangle is possible, draw an example.

So where the ticks are on the screen, you should have drawn an example otherwise write impossible.

So the black ones are the ones that are not possible.

And remember to label angles and sides that are equal.

So can I have a scaling with no right angle? Yes I can.

Can I have an isosceles with no right angle? Of course I can.

Can I have an equilateral triangle with no right angle? I definitely can, I should have an equilateral triangle with no right angle.

Can I have an equilateral triangle with exactly one right angle? That is impossible.

Can I have an equilateral triangle with exactly one obtuse angle? Well I can't because obtuse angle are greater than 90.

So if I have one angle that is greater than 90, then it's not going to be an equilateral triangle.

Can I have an isosceles triangle with more than one obtuse angle? Say for example, I have a 100 degrees on one side and then I have 95 degree on another side, well, that is going to be more than 180 and I can't have that, it's impossible for there to be a more than 180 degrees in a triangle.

Okay, our explore task we've got three students here and they've come up with their own conjectures and now I'm wanting you to prove them right or wrong.

The first students saying, "You can draw a scalene "triangle with any number of dots." That means if my circle's got five dots or 10 dots or 15,000 dots, you can draw a scalene triangle with any number of dots.

Second student is saying, " You can only draw "an isosceles triangle on six or eight dots circles." Can you? can you not? And our last student is saying, "you can draw an "equilateral triangle on circles with any number of dots." So your task is to prove or test their conjectures and say whether it's true or false.

And then take that further by writing other conjectures that you've come up with as well based on today's lesson.

So pause the video now and attempt this explore task.

If you're really struggling then carry on watching the video where I'll provide you with some more help.

Okay, let's take the third student's conjecture.

"You can draw an equilateral triangle on circles "with any number of dots." I am going to choose this middle circle over here.

Our middle circle has eight number of dots.

So we want to prove whether what he's saying is true or false.

I am going to start from here and I want to have two spaces in between my connected dots.

About to move here and I'm connecting to this dot over here.

So I've got two spaces here.

Because it's an equilateral triangle, all my sides should have two dots between them.

So that it is an equilateral triangle.

So from this dot to my other connected dot I should also have two dots.

Okay, I'm doing well two dots here, two dots here if I connect to my starting dot I only have one up here.

So, what does that tell us about this student's conjecture? That it is not true.

I can't draw an equilateral triangle on any number of dots.

What if I've got one, two, three, four, five, six.

Yes I can.

Got one dot separating.

There's an equilateral triangle I can draw.

This is not an.

So pause the screen now and attempt this task where you are trying to prove the conjectures of these students.

Once you're finished, come back we'll carry on with the lesson.

Okay, your answers are here.

Checking your work.

Seeing if you came up with the same answer if you agree or disagree with the conjectures also it would be very interesting to learn about your own conjectures and make sure you send those to your teachers and they can check it for you as well.

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

I am looking forward to seeing you at the next lesson.