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)`

If M and N are the mid - points of the sides BC and CD respectively of a parallelogram ABCD, then AM + AN equals

If E, F G and H are respectively the midpoints of the sides AB, BC, CD and AD of a parallelogram ABCD, show that ar(EFGH) =1/2 ar (ABCD) .

In the figure D, E are points on the sides AB and AC respectively of DeltaABC such that ar(DeltaDBC) = ar(DeltaEBC) . Prove that DE || BC.

P is a point in the interior of a parallelogram ABCD. Show that ar (Delta APD) + ar ( DeltaPBC) = ar ( DeltaAPB) + ar (DeltaPCD)

P is a point in the interior of a parallelogram ABCD. Show that (i) ar (DeltaAPB) +ar (DeltaPCD)=1/2ar (ABCD) (ii) ar(DeltaAPD)+ar (DeltaPBC)=ar(DeltaAPB)+ar(DeltaPCD) (Hint : Throught , P draw a line parallel to AB)

In the figure, ΔABC, D, E, F are the midpoints of sides BC, CA and AB respectively. Show that (i) BDEF is a parallelogram (ii) ar(DeltaDEF)=1/4ar(DeltaABC) (iii) ar(BDEF)=1/2ar(DeltaABC)

DF and BE are the highest on sides AB and AD respectively in parallelogram ABCD. if the area of the parallelogram is 1470cm^2 , AB=35cm and AD=49cm, find the length of BE and DF.

In the below given figure P and Q are points on the sides AB and AC respectively of triangle ABC such that AQ = 3cm, QC= 5cm and PQ ||BC . Find the ratio of areas traingle APQ and triangle ABC .

In the figure, ΔABC and ΔABD are two triangles on the same base AB. If line segment CD is bisected by bar(AB) at O, show that ar (DeltaABC) = ar (DeltaABD).