Proof of Pythagorass Theorem

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Proof of Pythagorass Theorem

• GCSE Higher

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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 Theorem

• Consider this square
• It has side length c
• Its area is thus c2

c
c
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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
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Area Larger Square

• (a b)2
• a2 2ab b2
• Area of EACH small Triangle ½ab
• Area of 4 small triangles
• 2ab

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Shaded Squares area is

• a2 2ab b2 2ab
• a2 b2
• BUT Shaded Area is c2
• SO
• c2 a2 b2