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Proof of Pythagoras s Theorem

?Prove' means what exactly?. A proof in mathematics is a process of logical stepsEach step makes a statement using facts that are recognised

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Proof of Pythagoras s Theorem

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    1. Proof of Pythagoras’s Theorem GCSE Higher

    2. ‘Prove’ means what exactly? A proof in mathematics is a process of logical steps Each step makes a statement using facts that are recognised & known to be true In vast majority of cases, a proof involves some manipulation of algebra

    3. Proof of Pythagoras’ Theorem Consider this square It has side length c It’s area is thus c2

    4. Rotate the Square Surround it with another square Label Triangles’ sides a & b Now calculate area of large and small squares SHADED is c2

    5. Area Larger Square = (a + b)2 = a2 + 2ab + b2 Area of EACH small Triangle = ˝ab Area of 4 small triangles = 2ab

    6. Shaded Square’s area is…… = a2 + 2ab + b2 – 2ab = a2 + b2 BUT Shaded Area is c2 SO c2 =a2 + b2

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