Question

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

Answer 1

D and E are the mid points on sides AB and AC of triangle ABC
Such that ar(BOC)=ar(EBC)
BDC and triangle EBC have same base BC and tbey must have a same altitude
so DE is parallel to BC

Answer 2

see attachment....hope it will helps...