In a parallelogram ABCD, E and F are the mid points of sides AB and CD respectively (see fig.) Show that the line segements AF and EC trisect the diagonal BD.

In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively. Show that the line segments AF and EC trisect the diagonal BD.

E and F are respectively the mid-points of equal sides AB and AC of DeltaABC (see figure) Show that BF = CE.

In the adjacent figure ABCD is a parallelogram P and Q are the midpoints of sides AB and DC respectively. Show that PBCQ is also a parallelogram.

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)

ABCD is a rectangle and P,Q,R and S are the mid points of the sides AB,BC,CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

If D, E and F are three points on the sides BC, CA and AB, respectively, of a triangle ABC such that the lines AD, BE and CF are concurrent, then show that " "(BD)/(CD)*(CE)/(AE)*(AF)/(BF)=-1

If D, E, F are respectivley the mid points of AB, AC and BC respectively in a triangle ABC, then vec BE + vec AF =

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

ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

ABCD is quadrilateral E, F, G and H are the midpoints of AB, BC, CD and DA respectively. Prove that EFGH is a parallelogram.