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

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) square BDEF = (1)/(2) xx " area of " Delta ABC

D, E and F are the mid-points of the sides BC, CA and AB respectively of triangle ABC. Prove that: area of BDEF is half the area of Delta ABC.

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

D, E and F are respectively the mid-points of the sides BC, CA and AB of a DeltaA B C . Show that (i) BDEF is a parallelogram. (ii) a r\ (D E F)=1/4a r\ (A B C) (iii) a r\ (B D E F)=1/2a r\ (A B C)

If D,E and F are the mid-points of the sides BC, CA and AB respectively of a triangle ABC and lambda is scalar, such that vec(AD) + 2/3vec(BE)+1/3vec(CF)=lambdavec(AC) , then lambda is equal to

In the adjoining figure D, E and F are the mid-points of the sides BC, CA and AB of the equilateral DeltaABC. Prove that DeltaDEF is also an equilateral triangle.

In Delta ABC, AB = AC. D , E and F are mid-points of the sides BC, CA and AB respectively . Show that : AD and FE bisect each other.

In Delta ABC, AB = AC. D , E and F are mid-points of the sides BC, CA and AB respectively . Show that : AD is perpendicular to EF.

If D , E and F are the mid-points of the sides BC , CA and AB respectively of the DeltaABC and O be any point, then prove that OA+OB+OC=OD+OE+OF

D, E and F are the mid-points of the sides BC, CA and AB respectively of Delta ABC and G is the centroid of the triangle, then vec(GD) + vec(GE) + vec(GF) =