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) .

E and F are respectively the mid-points of equal sides AB and AC of DeltaABC (see figure) Show that BF = CE.

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

In DeltaABC the midpoints are D,E and F of the sides AB,BC and CA, then DeltaDEF:DeltaABC is

ABCD is a square. E, F, G and H are the mid points of AB, BC, CD and DA respectively. Such that AE = BF = CG = DH . Prove that EFGH is a square.

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)

ABCD is quadrilateral E, F, G and H are the midpoints of AB, BC, CD and DA respectively. Prove that EFGH is a parallelogram.

In the adjacent figure ABCD is a parallelogram and E is the midpoint of the side BC. If DE and AB are produced to meet at F, show that AF = 2AB .

In the adjacent figure ABCD is a parallelogram and E is the midpoint of the side BC. If DE and AB are produced to meet at F, show that AF=2AB .

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.