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.

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

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

The areas of a square of sides x and a triangle of base x are equal, then the height of the triangle is

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

The area of a square and an equilateral triangle are equal. If the diagonal of the square be 12sqrt(2)m, then find the area of the triangle.

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.

If one side of a triangle is double the other, and the angles on opposite sides differ by 60^0, then the triangle is

A perpendicular AD is drawn on BC from the vertex A of the acute Delta ABC . Prove that AC^(2) = AB^(2) +BC^(2) -2BC.BD OR Prove that the square drawn on the opposite side of theacute angle of an acute triangle is equal to the areas of the sum of the squares drawn on its other two sides being subtracted by twice the area of the rectangle formed by one of its sides and the projection of the other side to this side.