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 .

ABCD is a parallelogram and P is the midpoint of the side bar(BC) . Prove that bar(AC) " and " bar(DP) meet in a common point of trisection.

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

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

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

If E, F G and H are respectively the midpoints of the sides AB, BC, CD and AD of a parallelogram ABCD, show that ar(EFGH) =1/2 ar (ABCD) .

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.

ABCD is a cyclic quadrilateral. The two sides AB and CD are produced to meet in the point P and other two sides AD and BC are produced to meet in the point R . The two circumcircle of DeltaBCPandDeltaCDR intersect at the point T . Prove that points P , T , R are collinear.