The sum of the squared diagonals of a parallelogram

sum squared diagonals parallelogram

     d blue1    - smaller  diagonal

     DD blue    - larger  diagonal

     a black  -  smaller side

     b black  -  larger side

     alpha red  -  acute angle between the diagonals

 

Equation for the sum of the squared diagonals  :

parallelogram F

 

Equation for the difference of squares of the sides:  :

parallelogram F1