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:-
AC2 > AB2 and AC2 > BC2
⇒ 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 BC2 = AB2 + AC2 52 = 42 + 32,
then measure of ∠A should be 90°.
Note.: If the pythagoras property holds, the triangle must be right angled.
It is a set of three natural numbers a, b, c such that a2 + b2 = c2. 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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