1. Pythagoras Theorem Proof of the Pythagorean Theorem using Algebra

2. We can prove that a 2 + b 2 = c 2 There are four ‘abc’ triangles in this figure The big square formed by these triangles has a side a+b

3. Total area of the big square is A=(a+b)(a+b) The area of the smaller square (inside the big one) is A= c 2

4. The area of a triangle is A =½ab

5. The area of four triangles together is A = 4(½ab) = 2ab

6. So the area of the four triangles and the small square is A = c²+2ab

7. The area of the big square is equal to the area of the small square and four triangles So we have (a+b)(a+b)= c²+2ab a 2 +2ab+ b 2 = c²+2ab Subtract ‘2ab’ in both sides and we have a 2 + b 2 = c 2

8. Pythagoras Theorem 2 nd Proof

9. β c - bb c c S OR Q P yx a α P P RS R Q P S Q α α β β x y a a c + b 2c x y