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Proving the Pythagorean Theorem

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					Activity 1: Proving the Pythagorean Theorem Solutions

1. b b A c b C b
90°

a a a B c

a

c

c Proof: Consider the shaded regions as being moved from the small squares into the large square. b b A c b C b
90°

a a a B c

a

c

c Moving all four such regions shows that : a2 + b2 = c2

2. 1/2c2 + 1/2ab + 1/2ab = 1/2(a + b) + (a + b)

1/2(c2 + ab + ab) = 1/2(a2 + 2ab + b2) c2 + ab + ab = a2 + 2ab + b c2 + 2ab = a2 + 2ab + b2 c2 = a2 + b2

3. The length of the side of the small square is (b – a). (b – a)2 + 4 (1/2ab) = c2 b2 – 2ab + a2 + 2ab = c2 b2 + a2 = c2


				
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posted:12/14/2008
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