In the given figure PSDA is a parallelogram in which PQ =QR= RS and AP II BQ II CR II VS.Prove that ar(`trianglePQE`) = ar(`triangleDCF`).

In the given figure, ABCD is a parallelogram. E and F are any two points on AB and BC, respectively. Prove that ar (triangleADF)=ar(triangleDCE) .

In the figure, PSDA is a parallelogram. Points Q and R are taken on PS such that PQ = QR = RS " and " PA || QB || RC . Prove that ar (PQE) = ar (CFD) .

In the given figure, ABCD is a parallelogram in which AN and CP are perpendiculars on diagonal BD. Prove that : (i) DeltaADN =DeltaCBP (ii) AN=CP

In the given figure, PQ II BC. Then the value af x is:

In the adjoining figure, MNPQ and ABPQ are parallelogram and T is any point on the side BP. Prove that (i) ar(MNPQ)=ar(ABPQ) (ii) ar(triangleATQ)=(1)/(2)ar(MNPQ) .

In the adjoining figure, ABCD is a parallelogram in which angleBAD=75^@ and angleDBC=60^@ .Calculate (i) angleCDB and (ii) angleADB

In the given figure , PQRS is a parallelogram with PQ = 16 cm and QR = 10 cm . L is a point on PR such that RL:LP=2:3QL is produced to meet RS at M and PS produced at N . Find the length of PN and RM (in cm ) respectively .

In the given figure, ABCD is a quadrilateral in which AD = BC and angleDAB=angleCBA. Prove that (i) DeltaABD~=DeltaBAC, (ii) BD = AC, (iii) angleABD=angleBAC.

In the figure, P is a point in the interior of a parallelogram ABCD. Show that (i) ar (triangleAPB)+ar(trianglePCD=1/2ar(ABCD) (ii) ar (triangleAPD)+ar(trianglePBC)=ar(triangleAPB)+ar(trianglePCD)

In the given figure, if DE||AQ and DF||AR. Prove that EF||QR.