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.

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.

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.

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 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 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.

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.

One of the two acute angles of a righ-angled triangle is twice the other.Prove that between the sides adjacent to the right angle, the area of the square drawn on the greater side is thrice the area of the square drawn on the smaller side.