Prove that for any quadrilateral with diagonals perpendicular, the area.ls half the product of the diagonals:

Given statement in (a) and (b). Identify the statements given below as contrapositive or converse of each other . If the quadrilateral is a parallelogram then its diagonals bisect each other 1 )If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram 2) if the diagonals of a quadrilateral bisect eachother , then it is a parallogram

Prove that the elastic potential energy density of a stretched wire is half the product of stress and strain.

Prove that any outer angle of a cyclic quadrilateral is equal to the inner angle at the opposite vertex.

Prove that diagonals of trapezium cut each other proportionally.

In the figure, the diagonals of a quadrilateral split it into four triangles. The areas of three of them are shown in the picture: Calculate the area of the whole quadrilateral.

In the figure, squareP=90^o . Sides of triangle APC are extended to B and D. Prove that, the circles drawn with the sides of a quadrilateral with perpendicular diagonals, will meet at a common point. .

B and Si shows diagonal relationship. Compare the products of hydrolysis of their halides.

Draw a right triangle and the perpendicular from the midpoint of the of the hypotenuse to the base Prove that this perpendicular is half the perpendicular side of the large triangle. .

Prove that any outer. angle of a cyclic quadrilateral is equal to the interior angle, at the opposite vertex.

Prove that in any parallelogram, the 'sum of the squares of all sides is equal to the sum of the squares of the diagonals'.