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)

In the adjacent figure a parallelogram and P, Q are the midpoints of sides AB and DC respectively. Show that PBCQ is also a parallelogram.

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, 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)

In Delta^s ABC and DEF, DE and 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 : ABED is a parallelogram.

In Delta^s ABC and DEF, DE and 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 : BCFE is a parallelogram.