Question

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.

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Solution

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.

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