Q7 of 31 Page 162

D and E are points on sides AB and AC respectively of Δ ABC such that ar (DBC) = ar (EBC). Prove that DE || BC

Since ΔBCE and ΔBCD are lying on a common base BC and also have equal areas,

ΔBCE and ΔBCD will lie between the same parallel lines



Therefore,


DE || BC


More from this chapter

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5

D, E and F are respectively the mid-points of the sides BC, CA and AB of a Δ ABC. Show that:

(i) BDEF is a parallelogram.


(ii) ar (DEF) =ar (ABC)


(iii) ar (BDEF) =ar (ABC)

 6

In Fig. 9.25, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD.


If AB = CD, then show that:


(i) ar (DOC) = ar (AOB)


(ii) ar (DCB) = ar (ACB)


(iii) DA || CB or ABCD is a parallelogram.


[Hint: From D and B, draw perpendiculars to AC]

 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)]