D, E, F are mid points of sides BC, CA, AB of `Delta ABC`. Find the ratio of areas of `Delta DEF and Delta ABC`.

D, E and F are respectively the mid-points of sides AB, BC and CA of Delta ABC . Find the ratio of the areas of Delta DEF and Delta ABC .

D,Eand F are respectively the mid - points of sides AB, BC and CA of DeltaABC . Find the ratio of the areas of DeltaDEF and DeltaABC.

Prove that the area of the euilateral traingle described on the side of a square is half the area of the equilatiral triangle described on it's square . OR In Delta ABC D,E, F are the midpoints of te sides BC, AC and AB respectively. Find the rations of the areas of Delta DEF Delta ABC

If D - ((1)/(5) , (5)/(2) ) , E ( 7, 3) and F ((7)/(2), (7)/(2)) are the mid-point of the sides of Delta ABC , find the coordinates of Delta ABC.

Delta ABC and Delta BDE are two equilateral triangles and BD = DC . Find the ratio between areas of Delta ABC and Delta BDE .

D, E and F are the mid-points of sides of Delta ABC . P, Q, R are the mid-points of sides DEF. This process of marking the mid-points and forming a new triangle is continued. How are the areas of these triangles related?

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

D,E and F are respectively the mid-points of the sides BC, CA and AB of triangle ABC show that (i) BDEF is a parallelogram. (ii) ar (DEF) = 1/4 ar (ABC) (iii) ar (BDEF) = 1/2 ar (ABC)

D and E are points on sides AB and AC respectively of Delta ABC such that ar (DBC) = ar EBC). Prove that DE |\| BC.