Before you study Pythagoras theorem, you are advised to study:
What is Right Angle Triangle ?
Pythagoras was a Greek philosopher of 6th century B.C. who had given a theorem used in rightangles triangle and hence this theorem was named after him and called as Pythagoras Theorem.
Pythagoras Property or Pythagoras Theorem says that "The Square of the Hypotenuse of a Right Angle Triangle is Equals to the Sum of Squares of its Legs"
In short we can write it as:
(Hypotenuse)^{2} = (Leg 1)^{2} + (Leg 2)^{2}
Since legs are the other two sides of right angle triangle, so we can also write it as:
(Hypotenuse)^{2} = (Side 1)^{2} + (side 2)^{2}
Example: In the following figure of △ ABC: right angled at B:
Leg 1 = AB = 5 cm
Leg 2 = BC = 12 cm
And we have to find hypotenuse i.e. AC ?
Apply Pythagoras Theorem and we get:
(Hypotenuse)^{2} = (Leg 1)^{2} + (Leg 2)^{2}
Or we can also write it as:
(AC)^{2} = (AB)^{2} + (BC)^{2}
Put the values of leg 1 and leg 2 from above and we get
(AC)^{2} = (5)^{2} + (12)^{2}
Solve brackets on R.H.S and we get:
(AC)^{2} = 25 + 144
Solve addition expression on R.H.S. and we get:
(AC)^{2} = 169
Take square root of both sides and we get:
AC = 13
Hence, hypotenuse = 13 cm
Since, you have learn that Pythagoras Theorem applies to right angle triangle only, so this also concludes that:
In a triangle, if Pythagoras theorem hold true then triangle must be Right Angle Triangle
Here, you must also note that Hypotenuse is the Longest Side in Right Angle Triangle.

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