Lesson video

Hi.

I'm Mr. Chan.

And in this lesson, we're going to learn how to identify similar shapes and also show shapes are similar.

So in maths, you're going to come across the word similar.

What does it mean for shapes to be similar? Well, it means that they have the same size angles and proportions.

And one is an enlargement of the other.

So, let's have a look at an example.

Here are two squares.

These two squares are similar because one square measures side lengths to centimetres, and the other square measures side lengths to six centimetres so all the sides have been enlarged from the two centimetres by a multiple, a scale factor of three.

So, two times three gets me six and all the side lengths would be six centimetres.

So I know that the six centimetres square has been enlarged.

Now, what's happened to the angles? The angles were 90 degrees each inside the square, but in the enlarged shape they have remained 90 degrees.

And that's a very important concept with similar shapes.

The angles remain the same size.

Here's another example.

Which of the two shapes are similar? Now, they all look like plus symbols, and similar shapes are all enlarged in set proportion for the side lengths.

And the angles must remain the same.

So let's have a look at which two shapes are similar.

It would be these two.

We can see in the middle diagram that the middle part of the diagram is out of proportion with the others.

Here's some questions for you to try.

Decide which two shapes are similar.

Pause the video to complete the task and resume when you're finished.

Here are the answers.

So remember, for the shapes to be similar, one is just an enlargement of the other.

So, with these questions here, there's no trick questions, so hopefully you got these correct.

So, this example, we're asked the question are these two triangles similar? Well, they're missing angles so let's work those out.

So that must be 65, 'cause angles in a triangle sum up to 180 degrees.

And the second diagram, we also have 83 degrees as the missing angle.

So what we see in both triangles, we have 32 degrees, then 83 degrees, then 65 degrees.

Now, because all the angles have remained the same in both diagrams, in both of those triangles, we can then say yes they are, because the three pairs of angles are equal.

Let's look at these two triangles now.

Are these two triangles similar? Again, let's work out the missing angles.

32 degrees, 81 degrees, they've got to sum up to 180, so that must be 67 degrees.

And in the second triangle, 32, 83, and 65, they add up to 180 degrees.

So, the angles don't actually match up.

We have 32 degrees, and then 81 degrees, and then 67 degrees in the first triangle.

In the second triangle we have 32 degrees, then 83 degrees, and 65 degrees.

The angles don't actually equal each other in both triangles.

Now, for similar shapes to be similar, they must have the same angles.

So we can say no, these angles are not equally in both triangles, so these two shapes are not similar.

Here's some questions for you to try.

Pause the video to complete the task, resume the video once you're finished.

For question 2, a really important concept for similar shapes is that the shapes must have the same angles, so what we're looking for is all three angles in these similar triangles to be similar, if indeed the shapes are similar.

And as you can see in part a, all the angles remain the same, so they are similar, whereas in part b the angles don't quite match up to each other, so the shapes are not similar.

So we've looked at similar shapes where we look at the angles to see if they are similar, but what happens when we look at the side lengths and whether they're in the same proportion? So in this example, we're looking at whether these two shapes are similar, so how do we decide? Well, let's have a look at what happens with corresponding sides.

So, we're looking at the eight centimetres there has been multiplied by 1.

5 into the second diagram to get 12 centimetres for a corresponding length.

So, we can say that the second diagram has been enlarged by a scale factor of 1.

5.

Does that happen with all the other side lengths? The 10 centimetres corresponds with the 15 centimetre side length.

Again, that's being multiplied by 1.

5, brilliant.

The 12 multiplied by 1.

5 gives me 18 centimetres, and so it's looking good so far.

And the 3 centimetre side length corresponds with the 4.

5 centimetre side length by multiplying by 1.

5.

Yep, that works.

So what I can say about these two shapes is, yes, they are similar because the corresponding sides have a scale factor of 1.

5.

Here's a question for you to try.

Pause the video to complete the task, resume the video once you're finished.

Here's the answers.

So in these questions, we're really asking, for the shapes to be similar, are the two shapes simply an enlargement of each other? So to decide that, we look at corresponding side lengths and see if they are actually enlarged in the same proportion.

So, in part a, we can see that all side lengths have been enlarged with a scale factor of two, so for example side AB and side EF correspond to each other.

So 11 multiplied by two gives me 22 centimetres, and that happens with all the other sides apart from the two that are circled and, because they're not enlarged by a scale factor of two, those two shapes in part a are not similar.

In part b, every side length has been multiplied by a scale factor of 3, so those two shapes are indeed similar.

Here's another question for you to try.

Pause the video to complete the task, resume the video once you're finished.

Here are the answers for question 4.

We can see that Ben is correct because if two angles are the same in a pair of triangles, that means the third angle must also be the same because angles in a triangle add up to 180 degrees.

In part b, Amy's not quite correct because if we only have two side lengths that have been enlarged by a certain scale factor, we must also be given information about the third side length for it also to match up, otherwise we cannot say that the two shapes would be similar.

That's all for this lesson.

Thanks for watching.