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)`.

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 .

If a point Q lies between two points P and R such that PQ = QR, prove that PQ = 1/2 PR.

In a parallelogram ABCD, P is the mid point of the side AD. The line BP cuts the diagonal AC in the point Q. Then the ratio AQ:QC=

Prove that a line drawn through the mid-point of one side of a Triangle parallel to another side bisects the third side (Using Basic proportionality theorem).

P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD show that ar(DeltaAPB) = ar Delta(BQC)

In DeltaOAB , L is the midpoint of OA and M is a point on OB such that (OM)/(MB)=2 . P is the mid point of LM and the line AP is produced to meet OB at Q. If bar(OA)=bar(a), bar(OB)=bar(b) then find vectors bar(OP) and bar(AP) interms of bar(a) and bar(b) .

ABCD is a parallelogram and P is themid point of the side AD. The line BP meets the diagonal AC in Q. Then the ratio AQ : QC =