Question

Question 7
D and E are points on sides AB and AC respectively of $\Delta ABC$ such that ar (DBC) = ar (EBC). Prove that DE || BC.

Answer 1

Since $\Delta BCE$ and $\Delta BCD$ are lying on a common base BC and also have equal areas,
$\Delta BCEand\Delta BCD$ will lie between the same parallel lines.
$\Rightarrow DE||BC$