Pythagorean Theorem

We can define Pythagorean theorem as follows. If one of the angle in a measures 90 ° , this kind of triangle is called right triangle. Let ABC be a right triangle in which the measure of angle B = 90°.

Name of the sides in Right Triangle

The side AC is called the hypotenuse of the right triangle. The side which is opposite to 90 degree is called the hypotenuse side and it is the longest side and is opposite to the right angle. Greek mathematician Pythagoras has found that the length of the square on the hypotenuse is equal to the sum of the length of the squares on the other two sides. That is AC 2 = AB 2 + BC 2. This is knows as Pythagoras theorem.

The Pythagorean-Theorem is the most famous mathematical contribution.The later discovery that the square root of 2 is irrational and therefore, that cannot be expressed as a ratio of two integers, extremely troubled Pythagoras and his followers. They were consume in their belief that any two lengths were integral multiples of some unit length. Many efforts were made to suppress the knowledge that the square root of 2 is irrational.

Pythagorean Theorem-Example problems

1.Find the length of the missing side.

By using Pythagoras theorem

AB= 5 cm , BC = 12 cm

we know AC 2 = AB 2 + BC 2

AC 2 = 5 2 + 12 2
AC 2 = 25 + 144
AC 2 = 169
AC 2 = √169
AC 2 = √13 x 13
AC 2 = 13 cm

2. Find the length of the missing side.Here angle C is 90°.

AB = √5 cm , AC = 1 cm

By using Pythagoras theorem

AB 2 = AC 2 + BC 2
(√5) 2 = 1 2 + BC 2
5 = 1 + BC 2
5 - 1 = BC 2
√4= BC 2
√2 x 2 = BC 2
2 = BC 2
BC = 2 cm

3.In a right triangle ABC right angled at C then AB = √7 cm , AC = 2 cm find BC.

By using Pythagoras theorem

AB 2 = AC 2 + BC 2
(√7) 2 = 2 2 + BC 2
7 = 4 + BC 2
7 - 4 = BC 2
3 = BC 2
BC = √3 cm

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