Pythagorean Theorem.

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Presentation transcript:

Pythagorean Theorem

a = altitude b = base c = hypotenuse c a b

a = altitude b = base c = hypotenuse

a = altitude b = base c = hypotenuse

a = altitude b = base c = hypotenuse

a = altitude b = base c = hypotenuse Area of each rectangle is ab

a = altitude b = base c = hypotenuse Sum of areas = 2ab

a = altitude b = base c = hypotenuse

a = altitude b = base c = hypotenuse Sum of areas = 2ab

a = altitude b = base c = hypotenuse Sum of areas = 2ab

a = altitude b = base c = hypotenuse Sum of areas = 2ab

a = altitude b = base c = hypotenuse Sum of areas = 2ab

a = altitude b = base c = hypotenuse Sum of areas = 2ab

a = altitude b = base c = hypotenuse Sum of areas = 2ab

a = altitude b = base c = hypotenuse Sum of areas = 2ab

a = altitude b = base c = hypotenuse a - b Sum of areas = 2ab

a = altitude b = base c = hypotenuse a - b Sum of areas = 2ab Area = (a - b)2

a = altitude b = base c = hypotenuse a - b Sum of areas = 2ab Area = (a - b)2 Total area = c2

c2 = (a - b)2 + 2ab a = altitude b = base c = hypotenuse Sum of areas = 2ab Area = (a - b)2 Total area = c2 c2 = (a - b)2 + 2ab

c2 = (a - b)2 + 2ab c2 = a2 - 2ab + b2 + 2ab c2 = a2 + b2 a = altitude b = base c = hypotenuse Area = (a - b)2 Total area = c2 Sum of areas = 2ab c2 = (a - b)2 + 2ab c2 = a2 - 2ab + b2 + 2ab c2 = a2 + b2