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.

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 Delta ABC , D and E are the mid-points of AB and AC respectively, then the area of Delta ADE is :

If in a triangle AB=a,AC=b and D,E are the mid-points of AB and AC respectively, then DE is equal to

In the adjacent figure, we have AC = XD, C and D are mid points of AB and XY respectively. Show that AB = XY.

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.

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

In the adjoining figure, D and E are the mid-points of AB and AC respectively. If DE = 4 cm , then BC is equal to :

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