The diagonals of a quadrilateral ABCD intersects each other at the point O such that `(AO)/(BO)= (CO)/(DO)`. Show that ABCD is a trapezium.

ABCD is a trapezium in which AB||DC and its diagonals intersects each other at the point O. Show that (AO)/(BO)=(CO)/(DO) .

Show that if the diagonals of a quadrilateral bisects each other at right angles. Then it is a rhombus.

Show that the diagonals of a square are equal and bisect each other at right angles.

In the given figure, two chords AB and CD intersect each other at the point P. Prove that AP*PB= CP*DP

Digonals of a trapezium ABCD with AB||DC intersect each other at the point O. If AB= 2 CD, find the ratio of the areas of triangles AOB and COD.

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

Show that if the diagonals of a quadrilateral are equal and bisects each other at right angles, then it is a square.

Show that the diagonals of a rhombus are perpendicular to each other.