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

If the diagonals of a quadrilateral bisect each other then it is a

IF the diagonals in a quadrilateral divide each other proportionally then it is…….

One of the diagonals of the quadrilateral ABCD is

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

The diagonal AC of a parallelogram ABCD intersects DP at the point Q, where 'P' is any point on side AB. Prove that CQ times PQ=QA times QD .

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

Diagonals of a trapezium ABCD with AB||DC . Intersect each other at the point 'O'. IF AB=2CD, find the ratio of areas of triangles AOB and COD.

ABCD is a parallelogram. The diagonals AC and BD intersect each other at ‘O’. Prove that ar(DeltaAOD) = ar(DeltaBOC) . (Hint: Congruent figures have equal area)

In the figure, diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar(DeltaAOD) = ar(Delta BOC).

Given statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other. (b) 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 a quadrilateral bisect each other, then it is a parallelogram.