Question

In figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at  O,  show that ar(ABC)/ar(DBC) =AO/DO

Answer 1

Given: Two triangles ΔABC and ΔDBC which stand on the same base but on opposite sides of BC.

Construction: We draw AE ⊥ BC and DF ⊥ BC.
Proof: In ΔAOE and ΔDOF, we have