Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn, intersecting AC in L and AD produced in El. Prove that EL= 2BL

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

P is the mid-point of the side CD of a parallelogram ABCD. A line through C parallel to PA intersects AB at Q and DA produced at R. Prove that DA = AR and CQ = QR.

P is the mid-point of side AB of parallelogram ABCD. A line drawn from B parallel to PD meets CD at Q and AD produce at R. Prove that : (i) AR = 2BC (ii) BR= 2BQ

Through the vertex D of a parallelogram ABCD,a line is drawn to intersect the sides BA and BC produced at E and F respectively. Prove that (DA)/(AE)=(FB)/(BE)=(FC)/(CD)

P is the mid-point of side AB of a parallelogram ABCD .A Line through B parallel to PD meets DC at Q and AD produced at R. Prove that ( i )AR=2BC (ii) BR=2BQ.

The mid-point of side CD of parallelogram ABCD is 'm' in the given figure what is the ratio ON : OB?

P is the mid-point of the side AD of the parallelo- gram ABCD.The line BP meets the diagonal AC in Q and the line CD in R .Then RQ:QB is equal to

In a parallelogram ABCD, the bisector of angleA bisects the line Bcat point X. Prove that AD = 2AB.

The diagonals of a parallelogram ABCD intersect at O.A line through O intersects AB at X and DC at Y. Prove that OX=OY

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