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

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.

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 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 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.

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.

ABCD is a squre. E and F are respectivley the mid-points of BC and CD. If R is the mid-points of EF. Prove that ar (AER) = ar(AFR).

If D,E and F are the mid-points of the sides BC,CA and AB, respectively of a DeltaABC and O is any point, show that (i) AD+BE+CF=0

If in a triangle AB=a,AC=b and D,E are the mid-points of AB and AC respectively, then DE is equal to

The sides BC, CA and AB of a triangle ABC are of lengths a, b and c respectively. If D is the mid-point of BC and AD is perpendicular to AC, then the value of cos A cos C is: