Pythagoras Theorem

When we add the squares of 3 and 4 we get 52 or in other words 9+16=25. This property was first found as these numbers. Later with the help of geometry and algebra it was proved that the sides of a right angled triangle follow the rule a2 + b2 = c2, where a,b and c are the length of the sides of the triangle. This theorem was later called as Pythagoras Theorem.

Let us derive this theorem.

The triangles BCD and ABC are similar
we have, BD/AB = DC/BC = BC/AC             (i)
Also triangles ABC and ADB are similar
we have, AD/AB = AB/AC = BD/CB             (ii)
As triangles ABC is similar to ADB.
From above AD/AB = AB/AC ;
AB2 = AD·AC = (AC − DC)AC
=AC2 − DC·AC       from (i)
=AC2 − BC2

Pythagoras Theorem is in a triangle ABC
right angled at B
AB2 + BC2 = AC2