In Fig. 9.17, PQRS and ABRS are parallelograms and X is any point on side BR. Show that:
(i) ar (PQRS) = ar (ABRS)
(ii) ar (AX S) =
ar (PQRS)
(i) It can be observed that parallelogram PQRS and ABRS lie on the same base SR and also, these lie in between the same parallel lines SR and PB
Area (PQRS) = Area (ABRS) (i)
(ii) Consider ΔAXS and parallelogram ABRS
As these lie on the same base and are between the same parallel lines AS and BR,
Area 
(ΔAXS) = Area 
(ABRS) (ii)
From equations (i) and (ii), we obtain
Area (ΔAXS) = Area (PQRS)
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