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**3. Pythagoras Property of Right-Angled Triangle **

In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

**Converse of Pythagoras Theorem**

In a triangle if the square of one side is equal to the sum of the squares of the remaining two sides then the angle opposite to the first side is a right angle.

It is clear that:-

AC^{2} > AB^{2} and AC^{2} > BC^{2}

*⇒* AC > AB and AC > BC.

Hence, we can say that in right triangle the hypotenuse is the largest side.

A *∆*ABC is such that AB = 4 cm, AC = 3cm, BC = 5 cm and BC^{2} = AB^{2} + AC^{2} 5^{2} = 4^{2} + 3^{2},

then measure of *∠*A should be 90°.

**Note.: ** If the pythagoras property holds, the triangle must be right angled.

**Pythagorian Triplets **

It is a set of three natural numbers a, b, c such that a^{2} + b^{2} = c^{2}. Such a set of three number it is called as Pythagorean Triplet. For example- (3, 4, 5), (5, 12, 13), (6, 8, 10) etc.

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