D, E and F are respectively the mid-points of the sides BC, CA and AB of triangle ABC. Show that BDEF is a parallelogram.
F,E are the midpoints of the sides AB and AC respectively.
∴FE||BC and FE=12BC [By midpoint theorem ]
⇒FE||BC and FE=BD [D is midpoint of BC].....(1)
Similarly; D, E are the midpoints of BC and AC respectively.
∴ED||AB and ED=12AB
⇒ED||AB and ED=FB [F is midpoint of AB].....(2)
BDEF is a quadrilateral in which opposite sides are parallel and equal.
From (1) and (2), we can conclude that BDEF is a parallelogram.