Q. 164.3( 230 Votes )
In Fig.9.29, ar (DRC) = ar (DPC) and ar (BDP) = ar (ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums.
It is given that:
Area (ΔDRC) = Area (ΔDPC)
As ΔDRC and ΔDPC lie on the same base DC and have equal areas, therefore, they must lie between the same parallel lines
DC || RP
Therefore, DCPR is a trapezium. It is
Also given that:
Area (ΔBDP) = Area (ΔARC)
Area (BDP) − Area (ΔDPC) = Area (ΔARC) − Area (ΔDRC)
Area (ΔBDC) = Area (ΔADC)
Since ΔBDC and ΔADC are on the same base CD and have equal areas, they must lie between the same parallel lines
AB || CD
ABCD is a trapezium.
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