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.

D and E lie on the side AB and AC of DeltaABC such that DeltaDBC=DeltaEBC , Prove that DE || BC.

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)

D, E and F are the mid-points of the sides AB, BC and CA of the DeltaABC . Prove that DeltaDEF=1/4DeltaABC .

The points E, F , G and H are on the sides AB, BC , CD and DA respectively of the rectangle ABCD , such that AE = BF = CG = DH . Prove that EFGH is a parallelogram.

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)

D and E are the mid-points of AB and AC respectively of the DeltaABC. AP is the median of BC. AP intersects DE at Q. Prove that DQ = QE and AQ = QP.

D is any point on the side BC of DeltaABC . P and Q are centroids of DeltaABD and DeltaADC respectively. Prove that PQ||BC .

D is any point on the side BC of the DeltaABC . P and Q are the centroids of DeltaABD and DeltaACD . Prove that PQ||BC .

E and F are the mid - points of AB and AC respectively of DeltaABC . The st. line EF is extended to the point D such that EF = FD. Prove that ADCE is a parallelogram.

If D,E and F are the middle points of the sides BC,CA and AB of the DeltaABC , then AD+BE+CF is