Question
D and E are points on sides AB and AC respectively of $\triangle\text{ABC}$ such that$\text{ar}(\triangle\text{BCD})=\text{ar}(\triangle\text{BCE}).$ Prove that DE || BC.
✓
Answer
Since $\triangle\text{BCD}$ and $\triangle\text{BCE}$ are equal in area and have a same base BC.
Therefore,
Altitude from D of $\triangle\text{BCD}$ = Altitude from E of $\triangle\text{BCE}.$
$\Rightarrow\ \triangle\text{BCD}$ and $\triangle\text{BCE}.$ are between the same parallel lines.
⇒ DE || BC.
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