Lesson video

Hi, I'm Ms. Davis, in today's lesson we're going to be starting to look at Pythagoras' theorem.

Pythagoras' theorem can be applied to right-angled triangles only, in a later lesson we'll look at how can we apply it to isosceles triangles.

All right-angled triangles are formed by a hypotenuse and two shorter sides.

The hypotenuse is the the longest side in a right-angled triangle; it's the side that's opposite the right angle.

In this first example, this is the hypotenuse, with the two shorter sides.

In this next example, this is the hypotenuse.

You can see from the examples that the hypotenuse is always opposite the right angle.

It is always diagonal side, depending on the orientation of the triangle.

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.

The easiest way to identify the hypotenuse is that it's the side opposite the right angle.

No point of that side touches the right angle.

The square of a number is found by multiplying it by itself.

For example, seven squared is the same as seven multiplied by seven, which is 49.

0.

4 squared can be written 0.

4 multiplied by 0.

4, which is 0.

16.

The square root of a number is the number that is multiplied by itself to give that initial number.

The symbol used to represent square root is shown.

For example, the square root of 49 is seven or negative seven.

The square root of 0.

16 is 0.

4 or negative 0.

4.

We will be focusing on the positive square roots.

As you cannot have a negative length.

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, you might have used a calculator for some of these and that's absolutely fine.

Pythagoras' theorem states that the area of two smaller squares sum to give the area of a larger square when the sides form a right-angled triangle.

Let's have a look at what that means.

In this example, six squared, at eight squared gives 100, which is 10 squared.

These numbers relate to the lengths of the sides of the right-angled triangle.

Pythagoras' theorem states a squared plus b squared equals c squared, in which a and b are the shorter sides and c is the hypotenuse.

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, the hypotenuse is the longest side of a right-angle triangle.

Pythagoras' theorem states that it should be labelled with the letter c.

The two shorter sides should be labelled with a and b.

It doesn't matter which way around those are labelled.

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.

The hypotenuse is always labelled with the letter c.

If you've labelled a and b the other way round, that's fine.

Here is a question for you to try.

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

Here's the answer.

Mia should have labelled the hypotenuse with the letter c.

Here's some questions for you to try, pause the video to complete your task and resume once you're finished.

Here are the answers.

To find the area of that larger square, we need to add together 16 and nine, this gives 25 centimetres squared.

To find the length of the hypotenuse, you square root the 25, to get five centimetres.

That's all for today's lesson.

Thanks for watching.