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.


Answer :

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


Therefore,


ABCD is a trapezium.

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