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Proof of Pythagoras’s Theorem

Proof of Pythagoras’s Theorem. GCSE Higher. ‘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.

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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 c c

  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 a b a b b c a c b a

  5. a b a b b c a c b a Area Larger Square • = (a + b)2 • = a2 + 2ab + b2 • Area of EACH small Triangle = ½ab • Area of 4 small triangles • = 2ab

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

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