If `D ,Ea n dF` are the mid-points of sides BC, CA and AB respectively of a ` A B C ,` then using coordinate geometry prove that Area of △DEF= 1/4 (Area of △ABC)

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

If D(3,-2) , E(-3,1) and F(4,-3) are the mid-points of the sides BC, CA and AB respectively of Delta ABC , find the co-ordinates of point A , B and C .

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.

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.

Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , respectively of a triangle A B Cdot Then prove that vec A D+ vec B E+ vec C F= vec0 .

Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , respectively of a triangle A B Cdot Then prove that vec A D+ vec B E+ vec C F= vec0 .

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 an equilateral Delta ABC. Show that Delta DEF is also an equilateral triangle.

In Delta ABC, D,E and F are mid-point of sides AB ,BC and AC respectively , Prove that AE and DF bisect each other.

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) =