ABCD is quadrilateral E, F, G and H are the midpoints of `AB, BC, CD and DA` respectively. 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 adjacent figure ABCD is a parallelogram P and Q are the midpoints of sides AB and DC respectively. Show that PBCQ is also 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)

ABCD is a quadrilateral,AB and CD are parallel, P and Q are the midpoints of the sides BC and AD respectively. They, the value of bar(AB)+bar(DC) is -

ABCD is a quadrilateral . 3, 4, 5 and 6 points are market on the sides AB, BC, CD and DA respectively . The number of triangles with vertices on different slides is

In DeltaABC, D, E and F are the midpoints of sides AB, BC and CA respectively. Show that DeltaABC is divided into four congruent triangles, when the three midpoints are joined to each other. (ΔDEF is called medial triangle)

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.

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

AC is a common diagonal to both the parallelograms ABCD and AECF. If the points B , E , D , F are not collinear , prove that BEDF is a parallelogram.

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.