Question

D and E are points on AB and AC respectively of triangle ABC such that area of triangle =area of triangle BCE. Prove that DE is parallel to BC.

Answer 1

∆ABC AND ∆ BCE ARE ON SAME BASE BC
THEREFORE THEY MUST LIE BETWEEN SAME PARALLEL DE( BY PROPERTY)

Answer 2

Step by Step Explanation:

Triangle BCD and triangle BCE lie on same base BC and ar(BCD)=ar(BCE)

=> They lie between same parallels   [Converse of Triangle Area Theorem]

=> BC ll DE

Converse of Triangle Area Theorem:

    Two triangles lie on same base and areas of triangles are equal, then they lie between same parallels.

I hope this would help you.