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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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