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* Task 1 * What is Pythagoras' Theorem? "The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides." According to the Pythagorean Theorem, the sum of the areas of the two red squares, squares A and B, is equal to the area of the blue square, square C. Thus, the Pythagorean theorem stated algebraically is: for a right triangle with sides of lengths a, b, and c, where c is the length of the hypotenuse. As the sum of the areas of a square and the four triangles: Now, setting the two right hand side expressions in these equations equal, gives Therefore, the square on c is equal to the sum of the squares on a and b. (Burton 1991) * Explanation of the Pythagorean theorem Begin with a rectangle divided up into three triangles, each of which contains a right angle....

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