Pythagoras' theorem Revision Notes for Edexcel GCSE Maths

Pythagoras' theorem

What is Pythagoras' theorem?

Pythagoras' theorem is a mathematical rule that helps you find the length of a missing side in a right-angled triangle. This theorem is extremely useful and will not be given to you in the exam, so you must learn it.

The theorem states that in any right-angled triangle, the square of the longest side (called the hypotenuse) equals the sum of the squares of the two shorter sides.

chatImportant

This formula will not be given to you in the exam, so you must memorise it completely.

The formula

There are two ways to remember Pythagoras' theorem:

$a^2 + b^2 = c^2$ (where c is the longest side)
$\text{short}^2 + \text{short}^2 = \text{long}^2$ (easier to remember)

The mathematical relationship can be expressed as:

$a^2 + b^2 = c^2$

where $c$ represents the hypotenuse (longest side) and $a$ and $b$ represent the two shorter sides.

When can you use Pythagoras' theorem?

Before using Pythagoras' theorem, you need to verify that your problem meets these essential requirements:

A right-angled triangle (look for the square symbol in the corner)
Two side lengths that you know
One missing side length that you need to find

infoNote

Remember that this formula will not be given in the exam, so thorough memorisation and practice are essential for success.

Step-by-step method

When solving Pythagoras problems, follow these systematic steps:

Label the longest side as $c$ (the hypotenuse)
Label the other two sides as $a$ and $b$
Write out Pythagoras' theorem: $a^2 + b^2 = c^2$
Substitute the values you know into the formula
Rearrange the formula to solve for the unknown side

Worked example

A right-angled triangle has sides of 8 cm and 17 cm. Find the missing side x.

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Worked Example: Finding the Missing Side

Step 1: Identify the hypotenuse The longest side is 17 cm, so this is the hypotenuse ( $c = 17$ cm)

Step 2: Identify the known and unknown sides
One shorter side is 8 cm, and $x$ is the other shorter side

Step 3: Apply Pythagoras' theorem Using the formula: $x^2 + 8^2 = 17^2$

Step 4: Rearrange to solve for x $x^2 = 17^2 - 8^2$

Step 5: Calculate $x^2 = 289 - 64 = 225$

Step 6: Find the square root $x = \sqrt{225} = 15$ cm

chatImportant

Be careful when the missing length is one of the shorter sides. Always identify which side is the hypotenuse first.

Different forms of Pythagoras questions

Pythagoras' theorem appears in many real-world contexts. You should learn to recognise right-angled triangles in these common scenarios:

Ramps and slopes
Flagpoles and their shadows
Ladders leaning against walls
Building structures

The key skill is to identify the right-angled triangle within the problem and extract the relevant measurements.

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Many exam questions will present Pythagoras problems in disguised forms. Practice identifying right-angled triangles in various contexts to build your problem-solving confidence.

Calculator skills

For Pythagoras calculations, you need to master these essential calculator functions:

$x^2$ button to find squares
$\sqrt{x}$ button to find square roots
S⇔D key to convert between decimal and fraction form

Make sure you're comfortable with these calculator functions before your exam, as efficient calculation will save valuable time.

Exam tips

Here are proven strategies to maximise your marks in Pythagoras questions:

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Exam Success Tips:

Show every step of your working clearly
Label your diagram with the given measurements
Check your answer makes sense (is it reasonable?)
Remember that examiners often test this topic, so practice different question types

Remember!

bookmarkSummary

Key Points to Remember:

Pythagoras' theorem only works with right-angled triangles
The formula is $a^2 + b^2 = c^2$ where $c$ is the longest side
You need to know two sides to find the third side
This formula will not be given in the exam - you must memorise it
Always show your working step-by-step for full marks

Pythagoras' theorem (Edexcel GCSE Maths): Revision Notes