## Pythagoras' theorem (1): introduction

## Starter

### Key question

What is Pythagoras' theorem and how can it be used?

### Learning Objective

- To review how Pythagoras' theorem relates to right-angled triangles

### What to do?

Watch the clip *Pythagoras' theorem (1): introduction.*

Use the clip to answer these questions:

- How many degrees are there in a right angle?
- What is the longest side of a triangle called?
- What is the formula for Pythagoras' theorem given by Katie?
- What is meant by the square of a number?

Complete the worksheet Introducing Pythagoras' theorem to review the ideas introduced in this clip. You can watch the clip again to help you.

If you know the lengths of two sides of a right-angled triangle, the theorem of Pythagoras' can be used to calculate the length of the third side. What information would you need to use Pythagoras' theorem to calculate the length of the hypotenuse?

## Main activity

### Learning Objective

- To understand how to apply Pythagoras' theorem to calculate the length of the hypotenuse

### What to do?

First, watch the clip *Pythagoras' theorem (2): find the hypotenuse* up to 02:13 and use it to answer these questions:

- What is the height of the tower to which the rope slide is fixed?
- What is the distance from the anchor point to the base of the tower?
- Which side of Ben's right-angled triangle represents the rope?
- What is the value of c²?

Review Ben's calculation so far and consider how to calculate the value of c.

Next, watch the rest of the clip from 02:13 and use it to answer these questions:

- What is the symbol used to represent the square root function?
- What is the length of the rope according to Ben's calculation?

Practise your understanding of squares, square roots and how to use Pythagoras' theorem to find the hypotenuse by completing the six questions on the worksheet Pythagoras' theorem: Practice questions.

## Plenary

### Learning Objective

- To review how to apply Pythagoras' theorem to calculate the length of the hypotenuse

### What to do?

In 'tick or trash' Ben and Katie both tackle a typical exam question. Your task is to look carefully at their working out and decide who has the correct answer.

First, watch the clip **Tick or trash: Pythagoras' theorem** up to **00:48** to find out the 'tick or trash' question on calculating a percentage increase. Make a note of the question and then have a go at answering it.

Next, watch the clip *Tick or trash: Pythagoras' theorem* from **00:48** to **02:12** to see how Ben and Katie answered the question.

- Whose working should you tick (correct) and whose should you trash (incorrect)?
- What is the reason for your answer?

Finally, watch the rest of the clip *Tick or trash: Pythagoras' theorem* from **02:12 **to find out whose working was correct and what was wrong with the incorrect answer.

- What is the exam tip that Katie gives for questions involving simple and compound interest?

Complete the worksheet Pythagoras' theorem: Tick or trash. There are three questions on using Pythagoras' theorem to calculate the hypotenuse, each one with answers from Ben and Katie. For each set of answers, decide which working to tick and which working to trash giving reasons for your choice.

## Extension

### What to do?

1. Watch the clip *Pythagoras' theorem (3): find a shorter side* in which Ben explains another use of Pythagoras' theorem:

Use the clip to answer these questions:

**1a.** What is height of the wind speed mast?

**1b.** How long are the metal guy ropes attached to the mast?

**1c.** What is the answer to Ben's question at the end of the clip?

**1d.** How far from the mast would these guy ropes be if the wind speed mast was 8 metres tall?

2. Design an inventive and innovative poster about Pythagoras' theorem to illustrate and explain the demonstrations shown in the clip Pythagoras' theorem (1): introduction. Use the supporting text with this clip and/or other research to help you.

3. Find out more about Pythagoras' life and theorem from these two useful sites, which include many facts and anecdotes about one of the most famous ancient Greek mathematicians: