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Algebraic Proof for the Pythagorean theorem

Algebraic Proof for the Pythagorean theorem. 2009-2010 5 th Hr. T he area of each of these four triangles is given by an angle corresponding with the side of length C. ½ AB.

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Algebraic Proof for the Pythagorean theorem

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  1. Algebraic Proof for the Pythagorean theorem 2009-2010 5th Hr

  2. The area of each of these four triangles is given by an angle corresponding with the side of length C. ½AB

  3. Because both the A-side angle and B-side angle of each triangle are complementary angles, therefore each of the angles of the blue area in the middle is a right angle, making this area a square with side length C. The area of this square is C2 . 4(1/2 AB)+C2

  4. The large square has sides of length A + B, we can also calculate its area as (A + B)2, which expands to A2 + 2AB + B2. A2 + 2AB + B2 =4(1/2 AB)+C2

  5. (After the distribution of the 4) A2 + 2AB + B2 =2AB)+C2

  6. (after subtraction of the 2AB) A2 +B2 = C2

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