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.

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Presentation transcript:

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

Proof of Pythagoras’ Theorem Consider this square It has side length c It’s area is thus c 2 c c

Rotate the Square Surround it with another square Label Triangles’ sides a & b Now calculate area of large and small squares SHADED is c 2 c c a a a a b b b b

Area Larger Square = (a + b) 2 = a 2 + 2ab + b 2 Area of EACH small Triangle = ½ab Area of 4 small triangles = 2ab c c a a a a b b b b

Shaded Square’s area is…… = a 2 + 2ab + b 2 – 2ab = a 2 + b 2 BUT Shaded Area is c 2 SO c 2 =a 2 + b 2 c c a a a a b b b b