Lesson video

Hi, I'm Miss Davies.

In today's lesson we are going to use Pythagoras' theorem to show if a triangle is right-angled.

Lets recap by Pythagoras' theorem first.

In this example we're calculating the hypotenuse which I've labelled as c.

Think about how we know this is the hypotenuse.

If it is it's opposite the right angle and is the longest side.

First thing we're going to do is write down Pythagoras' theorem.

Our two shorter sides a and b are 12 metres and nine metres.

If we substitute this into the formula we get nine squared add 12 squared equals c squared.

This gives us 81 add 144 equals c squared.

These add to make 225.

The square root of 225 is 15.

So the missing length of the triangle is 15 metres.

Here's some questions for you to try.

Pause video to complete your task resume once you finished.

Here are the answers.

In part b and c you were working out the hypotenuse of the right-angled triangle.

Whereas in parts a and d you were working out the shorter length.

If this is a right-angled triangle Pythagoras' theorem will work.

The hypotenuse is always the longest side in a right-angled triangle.

So if this is a right-angled triangle the hypotenuse will be 20 centimetres.

We'll substitute that into Pythagoras' theorem as c.

As both sides are equal to 400 this is a right-angled triangle.

If this is a right-angled triangle, Pythagoras' theorem will work.

The hypotenuse is always the longest side in a right-angled triangle.

So if this is a right-angled triangle then 17.

2 metres will be the hypotenuse.

So we will substitute that in as c.

121 add 88.

36, this is 209.

36.

This is not equal to 295.

84 therefore this is not a right-angled triangle.

Here are some questions for you to try.

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

Here are the answers.

Part a and d are right-angled triangles as Pythagoras' theorem can be applied.

Whereas in part b and c they aren't right-angled triangles.

Pythagorean triples are three positive integers in which Pythagoras' theorem can be applied.

The most common example is three, four, five.

Six, eight, ten is also a Pythagorean triple as all the numbers have been doubled.

The next most common Pythagorean triple is five, 12, 13.

Can you think of another Pythagorean triple? Here are some questions for you to try.

Pause the video to complete your task and resume once you've finished.

Here are the answers.

The Pythagorean triple is a set of three positive integers in which Pythagoras' theorem can be applied.

The two different ways that seven centimetres and 12 centimetres could be in a triangle are showed.

Why can't the hypotenuse be seven centimetres? Well done if you said that the hypotenuse has to be the longest side and 12 centimetres is bigger than seven centimetres.

If we apply Pythagoras' theorem to the first triangle we get a solution of 13.

9 on the missing side.

Pause the video and find the missing side of the second triangle.

The two possible lengths of the triangle are 13.

9 and 9.

7, both to one decimal place.

Here are some questions for you to try.

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

Here are the answers.

In part a, we could have said that the two shorter lengths of the right-angled triangle were five centimetres and eight centimetres which would give us a hypotenuse of 9.

43 centimetres.

We could have said that the hypotenuse with eight centimetres in which the shorter length would have been five centimetres, which was given and 6.

24 centimetres.

That's all for this lesson, thanks for watching.