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

\(\because \) \(\triangle{BCE}\) and \(\triangle{BCD}\) are lying on a common base BC and also have equal areas.

\(\therefore\) \(\triangle{BCE}\) and \(\triangle{BCD}\) will lie between the same parallel lines.
\(\Rightarrow \) DE || BC

Hence, it is proved that DE || BC