P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar (APB) = ar (BQC).

D,E and F are mid-points of the sides BC, CA and AB respectively of triangleABC . Prove that ar(||gmBDEF)= 1/2 ar (triangleABC)

D and E are points on sides AB and AC respectively of a DeltaABC such that ar (DeltaBCE) = ar (DeltaBCD) . Show that DE || BC .

D and E are points on sides AB and AC respectively of DeltaABC such that ar (DBC) = ar (EBC). Prove that DE II BC .

D,E and F are mid-points of the sides BC, CA and AB respectively of triangleABC . Prove that ar(triangleDEF) = 1/4 ar (triangleABC)

If P and Q are the middle points of the sides BC and CD of the parallelogram ABCD, then AP+AQ is equal to

ABCD, DCFE and ABFE are parallelograms. Show that ar(ADE) = ar(BCF)

If E, F, G and H are respectively the mid-points of the sides of a parallelogram ABCD, show that ar(EFGH) =1/2 ar(ABCD).

P,Q,R and S are the mid-poins of the sides AB,BC,CD and DA respectively of quad. ABCD. Show that PQRS is a parallelogram such that ar(||gmPQRS) = 1/2 ar(quad.ABCD)

E is any point on median AD of a triangle ABC . Show that ar (ABE) = ar (ACE).