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.

Answer 1

F,E are the midpoints of the sides AB and AC respectively.

$\therefore FE||BCandFE=\frac{1}{2}BC$ [By midpoint theorem ]

$\Rightarrow FE||BCandFE=BD\left[DismidpointofBC\right].....\left(1\right)$

Similarly; D, E are the midpoints of BC and AC respectively.

$\therefore ED||ABandED=\frac{1}{2}AB$

$\Rightarrow ED||ABandED=FB\left[FismidpointofAB\right].....\left(2\right)$

BDEF is a quadrilateral in which opposite sides are parallel and equal.

From (1) and (2), we can conclude that BDEF is a parallelogram.