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 =

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 .

In triangleABC , a straight line parallel to BC intersects the sides AB and AC at P and Q respectively. If AP = 8cm, CQ = 9cm and AQ = 2BP, then BP=

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.

In triangleABC , a line XY parallel to BC cuts AB at X and AC at Y. If BY bisects angleXYC , then___

In DeltaABC , P is a point on the median AD . Extended BP and CP intersect AC and AB at Q and R respectively. Prove that RQ||BC .

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 triangle ABC, angleABC=angleACB . The bisectors of angleABCandangleACB intersect AC and AB at E and F respectively. Prove that FE||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 .