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`.

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

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

In the adjacent figure DeltaABC, D is the midpoint of BC. DE_|_AB, DF_|_AC and DE = DF . Show that DeltaBED ~= Delta CFD .

In the figure, ABCD is a quadrilateral. AC is the diagonal and DE || AC and also DE meets BC produced at E. Show that ar(ABCD) = ar (DeltaABE).

In the adjoining figure, D and E are the mid-points of AB and AC respectively. If DE = 4 cm , then BC is equal to :

In the following figure, ABCD is parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersect AD = CQ. If AQ intersect DC at P, Show that ar (BPC) = ar (DPQ)

ABCD is a trapezium in which AB abs DC , BD is a diagonal and E is the mid-point of AD. A line is drawn through E parallel to AB intersecting BC at F. Show that F is the mid-point of BC.

ABCD is a trapezium in which AB||DC, BD is a diagonal and E is the mid point of AD. A line is drawn through E parallel to AB intersecting BC at F. Show that F is the mid point of BC.

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