Question

Let $D$ and $E$ are points on sides $AB$ and $AC$ respectively of triangle $ABC$such that the area of triangle $DBC=$ the area of triangle $EBC$. Prove that $DE\left|\right|BC$.

Answer 1

Area of triangle on the same base :

When $ar(∆DBC)=ar(∆EBC)$

It is clear from the figure that both the triangles have common base $BC$.

These conditions are true when both of the triangles lie between parallel lines.

Thus, $DE$ is parallel to $BC$

Hence,it is proved that $\mathit{D}\mathit{E}\mathbf{}\mathbf{\left|}\mathbf{\right|}\mathbf{}\mathit{B}\mathit{C}$.