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Exercise for The converse of Pythagoras

Decide whether a triangle is right-angled

A triangle has sides 6, 8 and 9. Is it right-angled?

Your answerNo: 6² + 8² = 100, not 9² = 81, and no other pairing of the three sides works eitherYes, right-angled at the angle opposite the side of length 9Yes, right-angled at the angle opposite the side of length 8Cannot be decided without measuring an angle directly

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Square all three sides. If two of them add up to the third, it's right-angled at the angle opposite the longest side. Close is not the same as equal.

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Algebra and geometry you can move.