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 areas of the squares drawn on the sides of a rhombus is equal to the sum of the areas of two squares drawn on the diagonals of the given square.

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

If the sum of the roots of ax^2+bx+c =0 is equal to the sum of their squares, then

The sum of the squares of first n natural numbers is -

If the area of the square drawn on any side of a triangle is equal to the sum of the areas of the squares drawn on the other two sides of the triangle ,then the triangle will be right-angled triangle, the opposite angle of the greatest side of which will be "......................" .

A triangle ABC is inscirbed in a circle. If half the sum of the square of its three sides is equal to twice the square of the diameter of the circle, then the value of sin^(2)A + sin^(2)B + sin^(2)C will be-

If the sum of the roots of the equation 2x^(2)+4x+C=0 be equal to the sum of their square then

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

If twice the square of the diameter of a circle is equal to half the sum of the square of the sides of inscribed Delta ABC, then sin^2A+sin^2B++sin^2C is equal to: