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 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 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.

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

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.

If D, E and F are respectively, the mid-points of AB, AC and BC in DeltaABC , then BE + AF is equal to

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).

D,E and F are mid-points of the sides BC, CA and AB respectively of triangleABC . Prove that ar(triangleDEF) = 1/4 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.

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(PRQ)= 1/2 ar(ARC).