Question

prove that the sum of square of diagonal of parallelogram is equal to sum of square of its sides ​

Answer 1

In parallelogram the diagonal bisect at 90 degree

thus we could apply the formula of Pythagoras theorem.

let it's diagonals be x, y

let it's side be s

thus

$s^2= (x/2)^2 +(y/2)^2$

$s^2 = (x^2+y^2)4$

$4s^2=x^2+y^2$

{Pythagoras theorem says:

$h^2=p^2 + b^2$

}

thus we could see that sum of square of its sides equal to the sum of square of diagonals of parallelogram