In the figure , AP || BQ || CR. Prove that ar `(DeltaAQC)` = ar `(DeltaPBR)` .

In the figure, if ar DeltaRAS = ar DeltaRBS and [ar (DeltaQRB) = ar(DeltaPAS) then show that both the quadrilaterals PQSR and RSBA are trapeziums.

In the figure, diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar(DeltaAOD) = ar(Delta BOC).

ABCD is a parallelogram. The diagonals AC and BD intersect each other at ‘O’. Prove that ar(DeltaAOD) = ar(DeltaBOC) . (Hint: Congruent figures have equal area)

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)

In the figure, ΔABC and ΔABD are two triangles on the same base AB. If line segment CD is bisected by bar(AB) at O, show that ar (DeltaABC) = ar (DeltaABD).

P is a point in the interior of a parallelogram ABCD. Show that ar (Delta APD) + ar ( DeltaPBC) = ar ( DeltaAPB) + ar (DeltaPCD)

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

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 the figure, XY is a line parallel to BC is drawn through A. If BE || CA and CF || BA are drawn to meet XY at E and F respectively. Show that ar(DeltaABE) = ar (DeltaACF).

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)