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 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.

If P and Q are the middle points of the sides BC and CD of the parallelogram ABCD, then AP+AQ is equal to

E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that DeltaABE ~ DeltaCFB .

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)

If D ,Ea n dF are three points on the sides B C ,C Aa n dA B , respectively, of a triangle A B C such that AD,BE and CF are concurrent, then show that (B D)/(C D),(C E)/(A E),(A F)/(B F)=-1

ABCD is a trapezium with AB||DC . E and F are points on non-parallel sides AD and BC respectively such that EF is parallel to AB (see the figure). Show that (AE)/(ED)=(BF)/(FC)

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).