Pythagorean theorem which states the special relationship between the sides of a right triangle is perhaps the most popular and most applied theorem in Geometry. The algebraic statement of the Pythagorean theorem is used to derive the distance formula in coordinate Geometry and to prove the Pythagorean identities in Trigonometry. In fact, the fundamentals of Trigonometry are taught using the ratios of the sides of a right triangle.

Right triangles and Pythagorean theorem are not only used to solve real life problems, but often used in solving many advanced problems in Mathematics and Physical Sciences.

The theorem was named after the Greek Mathematician Pythagoras who lived in 500 B.C in the year 1909. It is now known that Babylonians, Egyptians , Chinese and Indians knew the theorem earlier than the time of Pythagoras. Even though ancient sources agree that Pythagoras gave a proof for the theorem no original documents exist.
The statement of the theorem in proposition 47 of Euclid's Elements is as follows:
"In right angled triangles, the square on the side subtending the right angle is equal to the sum of the squares on the sides containing the right angle."
Euclid used squares drawn on the sides of the right angles and showed the area of the square drawn on the hypotenuse is equal to the sum of the areas of the squares drawn on the legs of a right triangle.

Pythagorean History

The algebraic form of the statement of Pythagoras theorem c2 = a2 + b2 is used in solving right triangles.