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.

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 .

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) .

In the adjacent figure, we have AC = XD, C and D are mid points of AB and XY respectively. Show that AB = XY.

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 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 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 -

In the adjacent figure ABCD is a parallelogram ABEF is a rectangle show that DeltaAFD~=DeltaBEC .

In a right triangle ABC right-angled at B, if P and Q are points on the side AB and AC respectively, then___

In the adjacent figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC||PR. Show that BC || QR.