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 the side CD of a paralellogram ABCD, a line thorugh C parallelogram to PA intersects AB at Q and DA produced by A. Prove that DA=AR and CQ=QR.

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 AR=2BC.

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 BR=2BQ.

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.

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

M is the mid point of the side CD of the parallelogram ABCD. The line BM is drawn intersecting AC in L and AD produced Prove that (i) ALxxLM=CLxxBL

Through the mid point P of the side AD of a parallelogram ABCD, straight line BP is drawn cutting AC at R and CD produced at Q. Prove that bar(QR)=2bar(RB) .

ABCD is a parallelogram and a line through A meets DC at P and BC (produced) at Q. Prove that ar(triangleBPC) = ar(triangleDPQ)

P and Q are the mid-point of the opposite sides AB and CD of a parallelogram ABCD. AQ intersects DP at S and BQ intersects CP at R. Show that PQRS is a parallelogram.

ABCD is a quadrilateral. The straight line through C parallel to the diagonal DB intersects AB produced at E. Prove that the ar(quad. ABCD) = ar (triangleADE) .