In trapezium `ABCD`, `AB` and `DC` are parallel. A straight line parallel to `AB` intersects `AD` and `BC` at the points `E` and `F` respectively. Prove that `DE:EA=CF:FB`.

AD is a median of triangleABC . A straight line parallel to BC intersect AB and AC at P and Q respectively. Prove that AD bisects PQ.

In triangleABC , a straight line parallel to BC intersects AB and AC at P and Q respectively. If AB = 3PB, then PQ : BC =

A straight line drawn through D of the parallelogram ABCD intersects AB and the extended part of CB at the points E and F respectively. Prove that AD:AE=CF:CD .

DeltaABC and DeltaDBC are situated on the same base BC and on the same side of BC . E is any point on the side BC . Two line through the point E and parallel to AB and BD intersects the sides AC and DC at the points F and G respectively. Prove that AD||FG .

In DeltaABC a straight line parallel to BC intersects the sides AB and AC at the points P and Q respectively. If AP=QC , AB=12cm , AQ=2cm , then find the value of CQ .

The diagonals AC and BD of the parallelogram ABCD intersect each other at O . Any straight line passing through O intesects the sides AB and CD at the points P and Q respectively . Prove that OP = OQ.

The straight line parallel to the side BC of DeltaABC intersects the sides AB and AC at the points D and E respectively. Then (AB)/(BD)=(AC)/(CE) .

Two parallel straight lines intersect three concurrent straight lines at the points A , B , C and X,Y,Z respectively. Prove that AB : BC=XY : YZ .

In DeltaPQR the straight line parallel to QR intersects the sides PQ and PR at the points E and F respectively. If EQ=2PE and FR=PF+3 , then the length of PR is