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# The Pythagorean Theorem

The Pythagorean Theorem can only be applied on a Right Triangle; this theorem tells the relation between the sides of the triangle. As we know that if we are having a triangle it consist of three sides and  Pythagorean theorem tells the relation between the sides of the triangle, with the help of this theorem we can find one side if two sides are given.

As we know a Right Angle triangle is having three sides as base, perpendicular and hypotenuse. Hypotenuse is the bigger side among all. According to Pythagorean Theorem, the Square of hypotenuse is equal to sum of square of base and perpendicular. This statement looks very simple but it is having a wide application in Geometry. Very few people know that we can also use Pythagorean Theorem in finding the angles of triangle. As we well know that the sum of angles of a triangle is 180 degree and as Pythagorean Theorem is only applied on right angle so one angle will be 90 degree. As the right angle is always opposite to biggest side, that’s why it will the biggest angle in the triangle and if other two side are equal then the angle of both the side will be equal so there is only possibility that is both the angles are of 45 degree.

The use of Pythagorean Theorem is mainly in finding the sides of triangle, if we are having base of the triangle as 6 and perpendicular as 8 and we are asked to find the hypotenuse then we can use Pythagorean Theorem, we just need to square the base and perpendicular and then find the square root of result. The sum of square will be 64 + 36 = 100 and square root of 100 will be 10, so our hypotenuse will be 10.

## Extension to the Pythagorean Theorem

Pythagorean Theorem is given for three sides of Right Triangle. Now we will see the extension to Pythagorean Theorem.  According to Pythagorean Theorem, hypotenuse Square id equal to the sum of square of other two sides i.e. base and perpendicular. Suppose we have a right triangle having three sides ‘P’ , ‘Q’ and ‘R’ then according to the Pythagorean...Read More