In the adjoning figure, D and E are the points on the sides AB and AC respectively of `Delta ABC` and area of `Delta BCE = " area of " Delta BCD`.
Prove that `DE ||BC`

D and E are points on sides AB and AC respectively of Delta ABC such that ar( Delta DBC) = ar( Delta EBC). Prove that DE I I BC.

In the adjoining figure D, E and F are the mid-points of the sides BC, CA and AB respectively of Delta ABC . Prove that: (i) square BDEF is a parallelogram (ii) area of Delta DEF = (1)/(4) xx " area of " Delta ABC (iii) area of square BDEF = (1)/(2) xx " area of " Delta ABC

In the adjoining figure D, E and F are the mid-points of the sides BC, AC and AB respectively. triangle DEF is congruent to triangle :

In Figure,D,E are points on sides AB and AC respectively of ABC, such that ar(BCE)=ar(BCD) .Show that DEBC .

In Delta ABC, D and E are the midpoint of AB and AC respectively. Find the ratio of the areas of Delta ADE and Delta ABC .

If D,E,F are the mid-points of the sides BC,Ca and AB respectively of a triangle ABC ,prove by vector method that Area of Delta DEF=1/4 Area of Delta ABC