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

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

Views

We have  $\Delta$ ABC and points D and E are on the sides AB and AC such that ar($\Delta$DBC ) = ar ($\Delta$EBC)

Since $\Delta$DBC and $\Delta$EBC are on the same base BC and having the same area.
$\therefore$ They must lie between the same parallels DE and BC
Hence DE || BC

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