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

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 "......................" .

Answer any one : If in a triangle, the area of the square drawn on one side is equal to the sum of the areas of the squares drawn on other two sides, then prove that the angle opposite to the first side will be a right angle.

Prove that if the difference of the areas of the squares drawn on any two sides of a triangle be equal to the area of square drawn ono its third side, then the triangle is a right-angled triangle.

Prove that the area of the square drawn on the diagonal of a square is twice the area of the given square.

Prove that if equilateral triangles are drawn on the sides of a right-angled triangles then the area of the equilateral triangle, drawn on the hypotenuse is equal to the sum of the areas of the other two equilateral triangals drawn on its other two sides.

In a right-angled triangle, the area of a square drawn on the hypotenuse is equal to the "…..............." of the areas of the squares drawn on other two sides.

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

Prove that the area of the equilateral triangle described on the side of a square is half the area of the equilateral triangles described on its diagonal.