The diagonal BD of parallelogram ABCD intersect AE at F as shown in the figure. If E is any point on BC, then prove that `DFxxEF=FB=FA`.

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

Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar (AOD) = ar (BOC) . Prove that ABCD is a trapezium.

Throught the mid-point M of the sides of a parallelogram ABCD, the line BM is drawn intersecting AC at L, and AD produced to E. Prove that EL = 2 BL .

In the given figure, diagonals AC and BD of quadrilateral ABCD interset at O such that OB = OD. If AB = CD, then show that : (i) ar (DOC) = ar (AOB) (ii) ar (DCB) = ar (ACB) (iii) DA || CB or ABCD is a parallelogram .

E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. show that DeltaABE ~DeltaCFB

ABCD is a parallelogram. AC and BD are the diagonals intersect at O. P and Q are the points of tri section of the diagonal BD. Prove that CQ" ||" AP and also AC bisects PQ (see figure).

In the adjacent figure ABCD is a parallelogram and E is the midpoint of the side BC. If DE and AB are produced to meet at F, show that AF = 2AB .

ABCD is a parallelogram. The circle through A, B and C intersect CD (produced if necessary) at E. Prove that AE = AD.

ABCD is a parallelogram. The circle through A, B and C intersect CD (produced if necessary) at E. Prove that AE = AD.