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 DeltaABC . Find the ratio of the areas of DeltaDEF" and "DeltaABC .

ABC is an isosceles triangle right angled at B. Similar triangles ACD and ABE are constructed on sides AC and AB. Find the ratio between the areas of Delta ABE and Delta ACD

In Delta ABC the coordinates of vertex A are (0,-1), D(1,0) and E(0,1) are the midpoints of sides AB and AC respectively. If F is the midpoint of side BC find the area of Delta DEF . Also find area of Delta 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 points, then prove that OA+OB+OC=OD+OE+OF

In triangle ABC,D is the midpoint of AB, E is the midpoint of DB and F is the midpoint of BC. If the area of DeltaABC is 96, the area of DeltaAEF is

If the coordinates of the midpoints of the sides of Delta ABC are (1,1), (2,-3) and (3,4) , find the coordinates of the vertices of Delta ABC

In DeltaABC, D, E and F are the midpoints of sides AB, BC and CA respectively. Show that DeltaABC is divided into four congruent triangles, when the three midpoints are joined to each other. (ΔDEF is called medial triangle)

E and F are respec­tively the midpoints of equal sides AB and AC of triangle ABC (see the given figure). Show that BF = CE.

In DeltaABC , D , E and F are respectively the midpoints of sides AB, BC and CA( see the given figure). Show that DeltaABC is devided into four congruent triangles by joining D, E and F.

Points A, B, C lie on the parabola y^2=4ax The tangents to the parabola at A, B and C, taken in pair, intersect at points P, Q and R. Determine the ratio of the areas of the triangle ABC and triangle PQR