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Pythagoras’ Theorem (F)

Learn GCSE Pythagoras’ theorem: find missing sides in right-angled triangles and apply 3-4-5 facts to real problems.

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Fascinating Fact:

In tile cutting, square tiles 1 cm each, a 3 by 4 rectangle’s diagonal uses 3² + 4² = d², so d = 5. Same 3-4-5 triangle idea.

In GCSE Maths, Pythagoras’ theorem links the sides of a right-angled triangle. You’ll use a² + b² = c² to find unknown lengths, check if a triangle is right-angled, and solve real-life distance problems.

Key Terms

Right-angled triangle: A triangle with one angle equal to 90°.
Hypotenuse: The longest side of a right-angled triangle, opposite the right angle.
Pythagoras’ theorem: For a right-angled triangle, a² + b² = c², where c is the hypotenuse.

Frequently Asked Questions (Click to see answers)

How do I use Pythagoras’ theorem to find a side?

If you know two sides of a right-angled triangle, square them, add or subtract as needed, then take the square root. Use c = √(a² + b²) or a = √(c² − b²).

Which side is the hypotenuse?

The hypotenuse is always opposite the 90° angle and is the longest side. It is the side labelled c in a² + b² = c².

When should I not use Pythagoras’ theorem?

Do not use it in non-right-angled triangles. For those, use trigonometry or the cosine rule instead.