ABCD is parallelogram and ABEF is a rectangle and DG is perpendicular on AB.
Prove that (i) ar (ABCD) = ar(ABEF)
(ii) ar (ABCD) = `AB xx DG`

PQRS and ABRS are parallelograms and X is any point on the side BR. Show that (i) ar(PQRS) = ar(ABRS) (ii) ar(DeltaAXS) =1/2 ar(PQRS)

ABCD is a parallelogram and AP and CQ are perpendiculars from vertex A and C on diagonal BD. Show that (i) DeltaAPB~=DeltaCQD (ii) AP=CQ .

Triangle ABC and parallelogram ABEF are on the same base, AB as in between the same parallels AB and EF. Prove that ar (DeltaABC) = 1/2 ar(|| gm ABEF)

ABCD is a parallelogram, E is the mid-point of AB and CE bisects angleBCD . Then angleDEC is

Diagonal AC of a parallelogram ABCD bisects angleA . Show that (i) it bisects angleC alo (ii) ABCD is a rhombus.

If ABCD is a parallelogram, then vec(AB)+vec(AD)+vec(CB)+vec(CD) is equal to

ABC is a right triangle right angled at C. Let BC = a, CA = b, AB = c and let p be the length of perpendicular from C on AB. Prove that (i) pc = ab (ii) (1)/(p^(2)) = (1)/(a^(2)) + (1)/(b^(2)) .

ABCD is trapezium with AB || DC. The diagonal AC and BD intersect at E . If Delta AED ~ Delta BEC . Prove that AD = BC .