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

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.

In a parallelogram ABCD, E and F are the midpoints of the sides AB and DC respectively. Show that the line segments AF and EC trisect the diagonal BD.

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, AC and BC of the DeltaABC. Prove that DE and AF bisects each other.

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 a triangle ABC (see figure), E is the midpoint of median AD, show that (i) ar DeltaABE = ar DeltaACE (ii) ar DeltaABE=1/4ar(DeltaABC)

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

In Delta^(s)ABC and, AB"||"DE, AB=DE, BC=EF and BC"||"EF . Vertices A, B and C are joined to vertices D, E and F respectively (see figure). Show that (i) ABED is a parallelogram (ii) BCFE is a parallelogram (iii) AC = DF (iv) DeltaABC~=DeltaDEF