what is the statement of pythagorian theorum
Pythagoras Theorem: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
For Example: A right triangle ABC right angled at B.
To Proove: AC2 = AB2 + BC2.
Proof:We draw BD ⊥ AC.
As per previous theorem, we can write, Δ ADB ~ Δ ABC.
So, AD/AB = AB/AC (Since sides are proportional) i.e. AD x AC = AB2 – (1)
Similarly, as per previous theorem, we can write, Δ BDC ~ Δ ABC.
So, CD/BC = BC/AC (Since sides are proportional) i.e. CD x AC = BC2 – (2)
On adding (1) and (2), we get,
⇒AD x AC + CD x AC = AB2 + BC2
⇒AC (AD + CD) = AB2 + BC2
⇒AC x AC = AB2 + BC2
⇒AC2 = AB2 + BC2.