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

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 in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Prove that the diagonals of a square are equal.

Prove, by vector method, that the diagonals of a parallelogram bisect each other, conversely, if the diagonals of a quadrilateral bisect each other, it is a parallelogram.

In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.

Explain how a square is. a parallelogram