Question
D and E are points on sides AB and AC respectively of ΔABC such that ar(ΔDBC) = ar(ΔEBC). Prove that DE || BC.
Solution
Given: D and E are points on sides AB and AC respectively of ΔABC such that ar(ΔDBC) = ar(ΔEBC).
To Prove: DE || BC.
Proof: ∵ ΔDBC and ΔEBC are on the same base BC and have equal areas.
Their altitudes must be the same.
∴ DE || BC.
