AQA · Mathematics · 8300
GCSE Maths: Pythagoras
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Pythagoras (Corbettmaths Video 257), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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Pythagoras' theorem applies only to ? triangles.
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right-angled
What is Pythagoras' theorem?
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a² + b² = c², where a and b are the two shorter sides and c is the hypotenuse (the longest side opposite the right angle).
In a right-angled triangle, which side is the hypotenuse?
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The longest side, opposite the right angle.
How can you test whether a triangle is right-angled using Pythagoras' theorem?
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Check if a² + b² = c², where c is the longest side. If the equation holds true, the triangle is right-angled.
How do you find the height of an isosceles triangle using Pythagoras' theorem?
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Drop a perpendicular from the apex to the base. This creates two right-angled triangles. Use Pythagoras with half the base and one equal side to find the height.
If a right-angled triangle has sides 14 cm and 18 cm, why are there two possible lengths for the third side?
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Because it's unclear which of the given sides is the hypotenuse. If 18 cm is the hypotenuse: third side = √(18² - 14²). If 14 cm is a leg: third side = √(18² + 14²).
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