Pythagoras was a Greek philosopher who was born in Samos in the sixth century B.C. he was a great mathematician who explained everything with the help of numbers. He gave the Pythagorean Theorem.
The Pythagorean Theorem states that the sum of the squares of the lengths of legs of any right angled triangle is equal to the square of the length of its hypotenuse. The hypotenuse is known to be the longest side and is always equal opposite to the right angle.
The theorem can be written as an equation where lengths of the sides can be a, b and c. The Pythagorean equation is a2 + b2 = c2 where c is the length of the hypotenuse and a, b are lengths of the two sides of the triangle.
The Pythagorean equation simplifies the relation of the sides of the right triangle to each other in such a way that if the length of any of the two sides of the right triangle is known, then the third side can be easily found.
To generalise this theorem, there is the law of cosines which helps in calculation of the length of any of the sides of the triangle when the other two lengths for the two sides are given along with the angle between them. When the angle between the other side’s turns out to be a right angle, then the law of the cosines becomes the Pythagorean Theorem.
The converse of this theorem is also true. It is that for any triangle with sides a, b and c, if a2 + b2 = c2, then the angle between the two sides a and b would turn out to be 900
WHY IS THE PYTHAGOREAN THEOREM IMPORTANT?
– The Pythagorean Theorem can easily be used for finding out whether the triangle is acute, obtuse or right triangle. If the side lengths squared comes out to be equal to the hypotenuse squared, then the triangle is right triangle. If the hypotenuse squared is longer and the sides squared and added together is shorter, then the triangle is obtuse. If the hypotenuse squared is shorter and the two sides squared and added together is longer, then the triangle is acute.
– By using the Pythagoras Theorem, we can find out the missing side length of the triangle when one is known in a right triangle.
– Builders use this theorem for keeping the right angles for building houses, decks, windows, floors and doors etc.