D, E and F are respectively the mid-points of the sides BC, CA and AB of a `triangle ABC`. Show that:- BDEF is a parallelogram.

D,E and F are respectively the mid points of the sides BC,CA and AB of an equilateral triangle ABC, prove that DEF is also equilateral triangle.

D, E and F are respectively the mid¬ points of the sides BC, CA and AB of triangleABC . Determine the ratio of the areas of triangles DEF and ABC.

D,E and F are respectively the mid points of the sides AB,BC and CA of a triangle ABC. Prove that by joining these mid points D,E and F and the triangle ABC is divided into four congruent triangles.

E and F are respectively the mid-points of equal sides AB and AC of Delta ABC (see Fig. 7.28). Show that BF = CE.

D,E,F are the middle points of the sides [BC],[CA],[AB] respectively of a triangle ABC. Show that : FE is parallel to BC and half of its length.

D,E and F are the middle points of the sides of the triangle ABC, then

D,E and F are mid-points of the sides BC, CA and AB respectively of triangleABC . Prove that ar(||gmBDEF)= 1/2 ar (triangleABC)

In Delta ABC , D, E and F are respectively the mid-points of sides AB, BC and CA . Show that Delta ABC is divided into four congruent triangles by joining D, E and F.

If D, E and F are three points on the sides BC, CA and AB, respectively, of a triangle ABC such that the lines AD, BE and CF are concurrent, then show that " "(BD)/(CD)*(CE)/(AE)*(AF)/(BF)=1

P and Q are respectively the midpoints of sides AB and BC or a triangle ABC and R is the mid-point of AP, show ar(PBQ)=ar(ARC).