Lesson video

- Hi, I'm Mr. Chan.

And in this lesson, we're going to learn how to find missing lengths in similar separate shapes.

So let's begin by explaining why two shapes may be similar.

So if we look at both of these diagrams here, we can see the both triangles have angles 32 degrees, 83 degrees and 65 degrees.

So the pairs of angles actually match up with each other.

So what we can say then is that one shape is an enlargement of the shape because the angles are equal, we can say that both of these triangles are similar.

Now that we've established that both of these triangles are similar, what that means is, one shape is simply an enlargement of the other and we can use that fact to work out missing side lengths.

So here, we're asked to work out the missing side marked x.

So work out the length of the side marked x.

So let's look at corresponding side lengths to start with.

So I can see that there's a 12 centimetre side between the 32 degrees and the 83 degrees in the first triangle there.

That corresponds with the same side length in the second triangle so the sidelines between the 32 degrees and the 83 degrees is 24 centimetres.

Now, those two sides, the 12 centimetres has been enlarged by a scale factor of 2, it's just been multiplied by 2 we call that having a scale factor of 2.

So 12 multiplied by two gives us 24.

So what that means is, the corresponding side lengths of the side marks x would be the sides between the 83 degrees and the 65 degrees in both triangles.

So we can say that x multiplied by 2 gives us 5 centimetres and I could just do a division.

So I could do 5 divided by 2 to calculate that x actually equals 2.

5 centimetres.

Here's some questions for you to try.

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

Here are the answers to the first question.

We can see in part A, that the two shapes are similar there, because all the angles are the same.

Now the shape has been slightly rotated in the second diagram.

However, it doesn't really matter for the orientation of the shapes whether they are similar or not as long as the angles are the same.

In Part B, those two triangles are the same, because in the first triangle, all the corresponding side lengths have a scale factor of 2.

So if the side lengths have a corresponding scale factor they all matchup, then they are also similar.

Here's another question please to try.

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

Here are the answers.

So to find missing side lengths, it's important that we do find the scale factor and you can see that we found scale factor for this two similar triangles to be a scale factor of 2.

So what we can say is shape B has been enlarged by a scale factor of 2 from shape A.

Now in terms of trying to find the missing side length x, what we can do is find the corresponding side which would be the 4 centimetres, multiplied by the scale factor which is 2, 4 multiplied by 2 gives us 8, so x must be 8 centimetres.

Here's another question for you to try.

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

Here's the answers.

The question tells us in each part, the two shapes are similar.

So what that means is one is an enlargement of the other.

So we start by finding the scale factor.

Once we find the scale factor, we can use that to find the missing side lengths.

Here's a question to try.

Pause the video to have a go at the task, resume the video once you're finished.

Here's the answer.

In this question, Mary is trying to use her shadow to work out the height of the tree.

And the shadows form a pair of similar triangles so what that tells us is that one triangle is an enlargement of the other triangle.

So we've used the base length to work out the scale factor of 12 and we can use that scale factor to apply it to Mary's height in order to find the height of the tree.

So 1.

4 metres, which is Mary's height, multiply that by 12 gives us the height of the tree.

That's all for this lesson.

Thanks for watching.