Lesson video

Welcome to our second lesson in the missing angle, in this unit.

Today we'll be comparing and classifying triangles.

You will need a pencil and a piece of paper.

As always, you will also need a piece of paper cut into the shape of a triangle today.

Pause the video and get your equipment together.

In today's lesson, we're comparing and classifying triangles.

We'll start with a knowledge quiz to test your knowledge from yesterday's lesson, then we will classify triangles.

We'll look at the angles in a triangle, and then you'll do some independent work and a final quiz.

So let's start with the knowledge quiz.

Pause the video and complete the quiz.

Great work.

Now here's your Do Now.

Match the picture of the triangle to its name and description.

Pause the video while you work on this task.

So your first triangle which had size of equal length was an equilateral triangle.

All of the sides are equal, and all of the angles are equal Your second triangle, which you could see had a right angle is a right angle.

And the right angle triangle can also be Isosceles or Scalene.

We'll come on to this in more detail later.

The third triangle which has these two lines here, that show you that the sides are equal length is called an Isosceles triangle.

And an isosceles triangle is named from the Greek word of Iso which means same, and skelos which means legs, so the two equal sides are called the legs and the third is the base.

So it has the same length legs.

The last triangle is a scalene triangle.

All of the sides are different lengths, and all of the angles are different.

Now let's work on classifying some triangles.

We want to know which type of triangles are scalene, which of these triangles are scalene and which are not.

And we need to be able to look at the information given and determine the type of triangle from it, because they're not always drawn to scale.

Now, I know that in a scalene triangle, none of the sides are equal.

So let's do one together.

For triangle a, all of the sides of equal length, they're all five centimetres therefore, it's not a scalene triangle.

It is, in fact, an equilateral triangle.

So I'll put a in that column.

Now pause the video and classify the rest of the triangles.

So we did a together.

We worked out that a was an equilateral triangle.

b, each of the sides are different lengths, therefore it must be scalene.

c, again, they were different lengths.

So c is scalene.

In d, we have two of the sides are equal.

Remember that the legs and the base is different.

So that is an Isosceles triangle.

So that goes into a not scalene column.

e, we have three sides of different lengths.

So it's scalene.

And f, all sides are equal.

So it is equilateral.

Let's look at a different type of triangle.

So which of these triangles are Isosceles? Pause the video and sort the triangles.

So, you will have looked at a and seen that the legs were equal length fair.

So this a is an isosceles triangle, b, all three sides are different lengths, so it's not isosceles.

You're right, it's scalene.

c, all sides equal, therefore equilateral, not isosceles.

d, this is a right type of triangle.

But these lines here tell us that these two sides are the same length.

Therefore, it is an isosceles, that was meant to be a comma.

It is an isosceles triangle, and it's also a right angle triangle.

In a, two legs of the same length, isosceles an f, all sides, different lengths, not isosceles but scalene.

Now, let's look at the Angles in a triangle.

Take your triangular piece of paper, and rip off the corners, as shown here.

If you put your corners together so that vertices touch, so these parts of them.

What do you notice? I'm going to draw a line along here to help you think.

Well, when we put the vertices together, they create a straight line.

And we know that angles on a straight line add up to 180 degrees.

Therefore, we can infer that the angles in a triangle always add up to 180 degrees.

Let's look at this in the context of a triangle.

So here we have an equilateral triangle, we know that in an equilateral triangle, all sides are equal lengths, and all angles are equal.

We know the three interior angles that inside the triangle are equal.

So we represent it pictorially.

We know the whole is 180 degrees.

And this is split into three equal parts, and we've labelled these a.

So if we think about it algebraically, we know that a plus a plus a is equal to 180 degrees.

And we also know that we can, instead of using repeated addition, because these are the same number, we can use multiplication, so a times three is equal to 180 degrees.

Now we need to use the inverse to find the value of a, 180 divided by three, gives us a.

And we can use all related facts.

If we know that 18 divided by three is six, we know 180 divided by three is 60.

Therefore, a is equal to 60 degrees, an equilateral triangle, the interior angles are always 60 degrees.

And we know that 60 plus 60 plus 60 is equal to 180 degrees.

Now we're going to look at finding missing angles, in triangles in lesson four.

So what you need to remember from this, is that the angles inside a triangle add up to 180 degrees.

Let's have a look at some reasoning around triangles, I want to know is this statement, always sometimes or never true? A triangle only has acute angles.

So I know that an acute angle, is larger than zero degrees, and less than 90 degrees.

But I do know that some triangles are right angle triangles.

And that angle is equal to 90 degrees.

So that's not an acute angle.

I also know that there are some triangles that have obtuse angles like this one.

This one has an obtuse angle which is greater than 90 degrees, and less than 180 degrees.

So I think that this statement is sometimes true.

And if I use my acute angle up here, and join it up to make a triangle, I've got three acute angles there.

And in fact, I can prove that even further.

If I have an equilateral triangle, like we learnt on the previous slide, each of the angles in an equilateral triangle was 60 degrees.

And now they are all acute angles.

So I have one that has acute angles, one that has a right angle, and one that has an obtuse angle.

Therefore it must sometimes be true.

So when you're asked to reason about an answer, it's really important to give multiple examples to show that you can prove what you're saying.

Now it's your turn.

Is this statement always, sometimes or never true? A triangle has a reflex angle.

Pause the video, and make some notes to explain your answer.

So we know that angles in a triangle add up to 180 degrees.

Now what do we know about the reflex angle? Well, we know that a reflex angle is greater than 180 degrees.

So if a triangle is made up of three angles, then none of them can be a reflex angle, because we can't have a triangle with one angle of 180 and two of zero that will just be a straight line.

Therefore, this statement is never true.

Now its time to do some independent learning.

Pause the video and complete the task.

Restart it once you're finished.

In question one you were asked to match the triangle to the correct name.

The first triangle has a right angle, therefore it must be a right angle triangle.

It also has sides of different lengths, so it's scalene as well.

So it's a scalene right angle triangle.

The second one has got the lines to indicate that these two sides or legs are the same length, therefore it is isosceles.

The third one has got sides which are all different lengths, so it's scalene.

And the final one has the three lines to indicate that those sides are equal length, therefore, it is equilateral.

So in question two, you were asked to identify the two isosceles triangles, which had two sides of equal length, and you could see that this was an d, and you could use the grid lines to help you out with that one.

Question three, what type of triangle is shown? We looked at this earlier.

And although this one doesn't have those on to help you, you know that this is definitely equilateral because an equilateral triangle has equal sides and equal angles and we know that the angles in an equilateral triangle are always 60 degrees each.

In question four, what type of triangle is shown here? Well, you could have given this two different names.

So first of all, although it wasn't drawn in the usual square way, this is a 90 degree angle.

So this is a right angle triangle, but it also has two equal angles, and we know that an isosceles triangle has two equal sides, but also two equal angles, so it's a right angle isosceles triangle.

In question five, this triangle was not drawn to scale.

So the reason that I drew it in this way, was to try and trick you into thinking that it was a different type of triangle.

The most important thing is that you looked at the values of the angle sizes.

So you could see that these are three different angles.

Therefore it is a scalene triangle.

Scalene triangle has sides of different lengths, and angles of different sizes.

Finally, Fatma says I have drawn a triangle with one acute angle, one right angle, and one obtuse angle.

Why is she incorrect? Well, we know that the angles within a triangle add up to 180 degrees, and an obtuse angle is at least 90 degrees.

A right angle is 90 degrees.

So already that would add up to 180 degrees, so she cannot be correct.

Great work, but it's time for your final quiz.

Pause the video, and then click Restart once you're finished.

Great work today.

In tomorrow's lesson, we'll be comparing and classifying quadrilaterals.

See you then!.