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.

ABCD is a parallelogram, P and Q are the mid-points of the sides bar(AB) " and " bar(DC) respectively. Show that bar(DP) " and " bar(BQ) trisect bar(AC) and are trisected by bar(AC) .

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.

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 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)

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 -

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

In DeltaABC , D and E are two such points on the sides AB and AC respectively that DE||BC . If AD=x+3 , BD=3x+19 , AE=x and CE=3x+4 , then the value of x=

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.

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