Question

D and E are points on sides AB and AC respectively of △ ABC such that ar (△ BCD) = ar (△ BCE). Prove that DE || BC.

Answer 1

From the figure we know that △ BCD and △ BCE have equal area and lie on the same base BC.

We know that

Altitude from D of △ BCD = Altitude from E of △ BCE

So we know that △ BCD and △ BCE lie between the same parallel lines

We get

DE || BC

Therefore, it is proved that DE || BC.