# what is the statement of pythagorian theorum

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.