In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides



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What is Pythagoras theorem?

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.


b

c



a

Hypotenuse side

Proof

Let’s consider the following figure



a b

b c c a

a b


b a

There are two squares shown in the above figure,

One has the length of “c” (blue colored) and the other one has the length of “a+b”


  • Area of the outer square is equal to area of inner square and area of 4 right angled triangles

    • Area of outer square = (a+b)2

    • Area of inner square = c2

    • Area of a right angled triangle = ½ ab

Hence,

(a+b)2 = c2+4 (½ ab)

a2+2ab+c2= c2+2ab

From above equation we can conclude that,



a2+b2=c2

Applications



Mostly Pythagoras theorem is used in trigonometry , for example calculating length of lake , height of buildings and length of bridges .
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