Question

D AND E are points on the sides AB and AC of a triangle ABC such that area (triangleDBC)=area(triangleEBC).PROVE THAT DE||BC

Answer 1

By given data you can prove that points D and E are midpoints on AB and AC respectively by using area of triangle formula.
$area = \frac{1}{2} \times base \times height$
Then by using converse of midpoint theorem you can prove DE || BC
$midpoint \: theorem - line \: joining \: to \: midpoint \: of \: one \: side \: parallel \: to \: other \: side \: bisects \: the \: third \: side$

Answer 2

Answer:

Step-by-step explanation:

∆dbc and ∆ebc lie on the same base bc and have equal areas.

And we know that when two triangles lie on a same base and have equal areas they lie between same parallels.

Therefore, de // bc