Question

$D$ and $E$ are points on sides $AB$ and $AC$ respectively of $△ABC$ such that $area\left(DBC\right)=area\left(EBC\right)$. Prove that $DE\parallel BC$

Answer 1

$A\left(△DBC\right)=A\left(△EBC\right)$ ....Given

Both the triangles have a common base $BC$.

$\therefore$ Their heights are equal.

Since both the triangles have a common base and their heights are equal,

the distance between points $B,D$ and distance between points $C,E$ is equal.

Hence, $DE\parallel BC$.