Q10 of 31 Page 162

Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar (AOD) = ar (BOC)

It can be observed that ΔDAC and ΔDBC lie on the same base DC and between the same parallels AB and CD


Area (ΔDAC) = Area (ΔDBC)


Area (ΔDAC) − Area (ΔDOC) = Area (ΔDBC) − Area (ΔDOC)


Area (ΔAOD) = Area (ΔBOC)


More from this chapter

All 31 →
8

XY is a line parallel to side BC of a triangle ABC. If BE || AC and CF || AB meet XY at E and F respectively, show that ar (ABE) = ar (ACF)

 9

The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed (see Fig. 9.26). Show that ar (ABCD) = ar (PBQR).


[Hint: Join AC and PQ. Now compare ar (ACQ) and ar (APQ)]

 11

In Fig. 9.27, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that:

(i) ar (ACB) = ar (ACF)


(ii) ar (AEDF) = ar (ABCDE)


 12

A villager Itwaari has a plot of land of the shape of a quadrilateral. The Gram Panchayat of the village decided to take over some portion of his plot from one of the corners to construct a Health Centre. Itwaari agrees to the above proposal with the condition that he should be given equal amount of land in lieu of his land adjoining his plot soas to form a triangular plot. Explain how this proposal will be implemented.