Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals

Prove that the sum of the squares of the diagonals of rhombus is equal to the sum of the squares of the sides.

Prove that the sum of the squares of the squares of tha diagonals of a parallelogram is equal to tha sum of the squares of its sides.

Prove that the area of a rhombus is equal to half of the product of the diagonals.

In which of the following quadrilateral sum of squares of all sides is equal to the sum of squares of diagonals?

Prove that in a right triangle, the square of the hypotenure is equal to the sum of the squares of the others two sides.

If the sum of the roots of the quadratic equation ax^2 + bx + c = 0 ( abc ne 0) is equal to the sum of the squares of their reciprocals, the sum of the squares of their reciprocals, then a/c , b/a , c/b are in H.P.

Prove that three times the square of any side of an equilateral triangle is equal to four times the square of the altitude.

If the sum of the roots of the quadratic equation a x^2+b x+c=0 is equl to the sum of the squares of their reciprocals, then prove that a/c , b/a a n d c/b are in H.P.

Prove by vector method, that in a right angled triangle the square of h the hypotenuse is equal to the sum of the square of the other two sides.

If the sum of the roots of the quadratic equation ax^(2) + bx + c = 0 is equal to the sum of the squares of their reciprocals, then prove that 2a^(2)c = c^(2)b + B^(2)a.