# Pythagoras Theoram

In a right angled triangle, the area of the square on hypotenuse is equal to the sum of the areas of squares on the remaining sides.

## Pythagorean Triplet.

If a, b, c are natural numbers and a>b, then [(a2+b2), (a2-b2), (2ab)] is Pythagorean triplet. (a2+b2)2 = (a2)2 + 2a2b2 + (b2)2 (a2+b2)2 = a4+ 2a2b2 + b4   ............................(I) (a2 - b2)2= (a2)2 - 2a2b2 + (b2)2   (a2- b2)2 = a4 - 2a2b2 + b4  ............................(II) Subtracting (II) from (I), we get (a2+b2)2 - (a2- b2)2 = 4a2b2 (a2+b2)2 - (a2- b2)2 = (2ab)2 (a2+b2)2 = (a2- b2)2+ (2ab)2 Therefore [(a2+b2) , (a2- b2) and (2ab)] is Pythagorean Triplet. Taking different values of a & b we can find more and more triplets.
Property of 300-600-900 Triangle If acute angles of a right angled triangle are 300,600 and 900, then the side opposite 300 angle is half of the hypotenuse and the side opposite to 600 angle is times the hypotenuse.

## Property of 30-60-90 type triangle.

Property of 450-450-90triangle If the acute angles of right angled triangles are 450 each, then each of the perpendicular side is times the hypotenuse.