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

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

Write down the converse of following statements: If the sum of squares of two sides foa triangle is equal to the square of third side of a triangle, then the triangle is right angled.

Find an A.P whose sum of n terms is equal to three times the square of n.

For any triangle, prove that the sum of the sides of the triangle is greater than the sum of the medians of the triangle.

Equilateral triangles are drawn on the three sides of a right angled triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides.

Prove that the sum of two odd numbers is even.

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

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

Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.