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)

P, Q, R and S are the mid-point of the sides AB, BC, CD and DA of the parallelogram ABCD respectively. If the area of the ABCD be 88 sq.cm, then the area of the PQRS is

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

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

If E, F and G are the mid-points of the sides AB, BC and CA of the DeltaABC respectively, then prove that the centres of gravity of DeltaABC and DeltaEFG are the same point.

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.

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.