Introduction of the Pythagoras Theorem

Pythagoras theorem was introduced by Greek mathematician Pythagoras of Samos who was an ancient Greek philosopher. The Pythagoras theorem is also known as the Pythagorean theorem. 

Definition of the Pythagoras theorem

According to Pythagoras, the square of the hypotenuse is equal to the sum of squares of the other two stopicIdes of the triangle.

We can apply the Pythagoras theorem when the angle is a right angle triangle that is 90°. 

When there is a right-angle triangle, the longer stopicIde of the triangle is known as the hypotenuse. And the other two stopicIdes are adjacent and opposite stopicIdes of a triangle. 

A detailed explanation of Pythagoras theorem

As per the Pythagoras theorem if a triangle is a right-angle triangle, then the square of its hypotenuse will be equal to the sum of squares of its adjacent stopicIdes and opposite stopicIde.

As given in the figure, we can state the Pythagoras theorem as;

( ^ this symbol means square or raise to the power. In our case, the power is 2)

AC^2 = AB^2 + BC^2

Hypotenuse^2 = adjacent stopicIde^2 + opposite stopicIde^2

This formula justifies that the square of the hypotenuse will always be equal to the sum of its squares of the adjacent stopicIde and opposite stopicIde. This formula can also be used to find the length of an unknown stopicIde of the right-angle triangle.

Example 1: In a right angle triangle, the opposite stopicIde is 5 cm, adjacent stopicIde is  12 cm find hypotenuse? 

As per the Pythagoras theorem, the square of the hypotenuse is always equal to the square of the adjacent stopicIde and the opposite stopicIde

Hypotenuse^2 = adjacent stopicIde^2 + opposite stopicIde^2

                       = 12^2 + 5^2

                       = 144 + 25

                       = 169

Hypotenuse = under root 169 

( you need to find the square root of 169. So,13* 13 =169)

Hypotenuse = 13. 

Example 2: in a right angle triangle PQR, PR is equal to 20 cm, PQ is equal to 12 cm find the measure of QR?

Hypotenuse^2 = adjacent stopicIde^2 + opposite stopicIde^2

PR^2 =  PQ^2 + QR^ 2

20^2 = 12^2 + QR^2 

400 = 144+ QR^2

400 - 144 = QR^2

256= QR^2 

Under root 256= QR^2 

( 256 comes under the table of 16* 16) 

Therefore, QR= 16 

Features of Pythagoras theorem

⦁ First, you have to see if the triangle is right angle triangle or not next

⦁ Then you have to find out the hypotenuse, adjacent stopicIde, and the opposite stopicIde of a right-angle triangle.

⦁ Pythagoras theorem is used to find out alone are stopicIdes of a right-angle triangle.

⦁ If the stopicIdes of the triangle are given you can use the Pythagoras theorem and check whether the square of the hypotenuse is equal to the sum of squares of the adjacent stopicIde and opposite stopicIde. By using the Pythagoras theorem you can also find whether the triangle given is a right angle triangle or not.

⦁ If a square or rectangle is given And it is asked to find outstopicIdes, we first need to find the diagonals of a figure as it may divtopicIde the or it into two right-angle triangles, then we can find the stopicIdes using the Pythagoras theorem.