Q : 16 In Fig., and . Show that both the quadrilaterals ABCD and DCPR are trapeziums.
ar(DPC) = ar(DRC) ..........(i)
and ar(BDP) = ar(ARC)............(ii)
from equation (i),
Since DRC and DPC lie on the same base DC and between same parallels.
CD || RP (opposites sides are parallel)
Hence quadrilateral DCPR is a trapezium
Now, by subtracting eq(ii) - eq(i) we get
ar(BDP) - ar(DPC) = ar(ARC) - ar(DRC)
ar(BDC) = ar(ADC) (Since theya are on the same base DC)
AB || DC
Hence ABCD is a trapezium.