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)`

In a triangle ABC , E is the midpoint of median AD. Show that ar(BED) = 1/4 ar(ABC)

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

PQR is a Deltaright angled at P and M is a point on QR such that PM bot QR . Show that PM^(2)= QM*MR .

P is a point in the interior of a parallelogram ABCD. Show that (i) ar (DeltaAPB) +ar (DeltaPCD)=1/2ar (ABCD) (ii) ar(DeltaAPD)+ar (DeltaPBC)=ar(DeltaAPB)+ar(DeltaPCD) (Hint : Throught , P draw a line parallel to AB)

In a triangle ABC (see figure), E is the midpoint of median AD, show that (i) ar DeltaABE = ar DeltaACE (ii) ar DeltaABE=1/4ar(DeltaABC)

In the figure, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that (i) ar (DeltaACB) = ar (DeltaACF) (ii) ar (AEDF) = ar (ABCDE)

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)

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

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 triangleABC , medians AC, BE and CF intersect at point G. Prove that ar(GAB)=ar(GBC)=ar(GCA)= 1/3 ar(ABC).