Lesson video

Hi, my name's Miss Kidd-Rossiter and I'm going to be taking you through this lesson on similar triangles.

It's going to build on all the work we've done so far on enlargements.

Before we get started, can you please make sure that you're free of all distractions and if you can be you're in a nice, quiet place so that you can concentrate.

If you need to, pause the video now to get yourself ready, if not, let's get going.

So we're starting today's lesson with a try this.

So I want you to pause the video now, read the slide and then have a go at answering these questions thinking about all the work we've done previously on enlargements.

Okay, so one way that I thought about this was writing the sides as ratios.

So I've written AB to BC is in the ratio three to four, AB to AC is in the ratio three to five and AC to BC is in the ratio five to four.

And now I'm going to think about what would those be if I enlarged by a scale factor of two? Well, AB enlarged by a scale factor of two would become six, BC enlarged by scale factor of two would become eight, and AC enlarged by a scale factor of two would become 10.

What about if my scale factor was 3.

5? What about if my scale factor was 0.

5? If you are struggling with this activity, pause it again now and have a go at this.

So hopefully that might have helped you a little bit.

So if we enlarged by scale factor of 3.

5, AB would become 10.

5, AC would become 17.

5 and BC would become 14.

If we enlarged by a scale factor of 0.

5, AB would become 1.

5, BC would become two and AC would become 2.

5.

Now, what you might have noticed here is that all the ratios that we've created are what we call equivalent ratios.

We're going to move on now to look at the connect task and how what we've done here relates to similar triangles.

So on your screen, you've got an orange triangle and the green triangle.

Pause the video now and tell me what's the same about these triangles and what's different.

So hopefully, one of the things that you should have realised was the same was the angles.

So in the orange triangle, this angle here is a right angle and the same angle, the corresponding angle in the green triangle is also a right angle.

If you had a protractor, you could have measured that this angle here would be the same as this angle here, that's the corresponding angle in the green triangle.

And also this angle here is the same as this angle here.

So the corresponding angles in the shapes are equal.

Now, clearly you can see that the side lengths are different, right? So that was something that you realised was different, did anyone notice anything about the green and orange shapes? Hopefully you noticed that they are enlargements of each other.

So the green shape is an enlargement of the orange shape.

What's the scale factor, tell the screen? Brilliant, two.

And the orange triangle is an enlargement of the green triangle.

What's a scale factor, tell the screen? Brilliant, a half or null.

5, well done.

So we can see that the green triangle is an enlargement of the orange triangle or the orange triangle is an enlargement of the green triangle and these shapes are similar, okay.

So similar shapes have corresponding angles that are equal and one shape is an enlargement of the other.

So these two triangles are similar triangles.

You might want to pause the video now and just note down that definition.

Two shapes are similar if one shape is an enlargement of the other and corresponding angles are equal.

So now you're going to apply this to an independent task.

So pause the video, navigate to an independent task and then resume the video when you're ready.

So here's the first question of the independent task, which triangles are similar to A? Did you find any? Hopefully you did.

I'm going to give you one of the answers, but there are more.

R is similar to A, because if we look at the ratio of the base to the height for A, it's five squares across and four squares high for A and R is two and a half squares across and two squares high so we can see that these two are equivalent ratios so therefore they must be similar.

What about here? Triangle BEF is an enlargement of triangle ABC, what is the scale factor of enlargement? So what have we multiplied all the lengths here by to get this shape here? So, six multiplied by something gives me nine.

And you know from your work on inverse operations, that the opposite of multiplication is division so to find our scale factor, we can do nine divided by six, which gives us three over two, if you like working in fractions, or if you prefer to work in decimals, it gives us 1.

5.

So our scale factor of enlargement is 1.

5.

Work out the length of the side EF, so that's this side here.

So we know our scale factor of enlargement is 1.

5.

So four multiplied by our scale factor gives us six centimetres.

And what is the length of side AC? So this time we're going backwards.

So AC multiplied by our scale factor of 1.

5 gives us 11.

So how would we work out what AC is here? AC would be 11 divided by 1.

5.

We can write our answer as a fraction, 22 over three, or if you really prefer working in decimals, you can write that as 7.

3 recurring.

Question three then, these triangles are similar, work out the value of w.

So let's look at two corresponding sides.

We've got this side here, which is v and we've got the corresponding side on the green triangle, which is two v.

So v multiplied by our scale factor gives us two v and we know from our work on inverse operations, that to work out our scale factor, we do two v divided by v to get our scale factor, which in this case is just two.

So we've worked out our scale factor is two for these triangles to go from the orange triangle, to the green triangle.

So now we need to work out what's the value of w? So we know that this length here is 12.

So we're going to multiply 12 by our scale factor of two to get 24 so w is 24.

Finally, we've got the explore task.

If you enlarge any shape by any scale factor, you end up with two similar shapes, is the student correct? How do you know? If you're struggling with this task, it might help you to think about some specialist examples.

So have a go by drawing your own example and enlarging it by lots of scale factors.

Are they all similar? I'm going to leave it there for today, 'cause I think you can keep going for ages with this task and I know it's really, really great, and hopefully you're having a good time with it.

So this is the end of today's lesson.

I hope you've learned loads and you can all tell me what a similar shape is, just tell me to the screen now.

Brilliant, I'm so pleased that you know that.

If not go back through the video, find my definition and make sure you write it down.

Hopefully I'll see you again soon.

Thank you for today's lesson and all your hard work, bye.