. Pythagoras Theorem Among all existing theorems in mathematics, Pythagoras theorem is considered to be the most important because it has maximum number of proofs. There are more than ways of proving Pythagoras theorem through different methods. Each of these proofs was discovered by eminent mathematicians, scholars, engineers and math enthusiasts, including one by the th American president James Garfield.
The book titled “The Pythagorean Proposition” written by Elisha Scott Loomis, published by the National Council of Teaching of Mathematics (NCTM) in America contains proofs of Pythagoras Theorem. Three natural numbers ( , , ) a b c are said to form Pythagorean Triplet, if they form sides of a right triangle. Thus ( , , ) a b c is a Pythagorean Triplet if and only if c Now we are in a position to study this most famous and important theorem not only in Geometry but in whole of mathematics. Activity (i) (ii) (iii) (iv) Fig.
. Step : Take a chart paper, cut out a right angled triangle of measurement as given in triangle (i) . Step : Take three more different colour chart papers and cut out three triangles such that the sides of triangle (ii) is three times of the triangle (i), the sides of triangle (iii) is four times of the triangle (i), the sides of triangle (iv) is five times of triangle (i). Step : Now keeping the common side length place the triangle (ii) and (iii) over the triangle (iv) such that the sides of these two triangles [(ii) and (iii)] coincide with the triangle (iv).
Observe the hypotenuse side and write down the equation. What do you conclude?