GCSE Maths: Pythagoras' theorem

Right-angled triangles, the hypotenuse, and a² + b² = c².

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What is the longest side of a right-angled triangle called?
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The hypotenuse.
Where is the hypotenuse located in a right-angled triangle?
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Opposite the right angle.
What is the algebraic form of Pythagoras' theorem?
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a² + b² = c², where a and b are the shorter sides and c is the hypotenuse.
For what type of triangle does Pythagoras' theorem work?
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Right-angled triangles only (triangles with exactly one 90-degree angle).
How do you find the hypotenuse when the two shorter sides are known?
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Square both shorter sides, add them together, and take the square root of the result.
In a right-angled triangle with sides 3 and 4, what is the hypotenuse?
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5. (Because 3² + 4² = 9 + 16 = 25, so c = √25 = 5)
How do you rearrange Pythagoras' theorem to find a shorter side?
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a² = c² − b² (subtract the square of the known short side from the square of the hypotenuse).
What is a Pythagorean triple?
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A set of whole numbers that satisfy Pythagoras' theorem.
How is Pythagoras' theorem used to find the distance between two points on a coordinate grid?
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By treating the horizontal and vertical gaps as the two shorter sides of a right-angled triangle.

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