Question

Question 5 (i)
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.
$\therefore FE||BCandFE=\frac{1}{2}BC$
$\Rightarrow FE||BCandFE=BD\left[DismidpointofBC\right].....\left(1\right)$
Similarly; D, E are the midpoints of BC and AC respectively.
$\therefore ED||ABandED=\frac{1}{2}AB$
$\Rightarrow ED||ABandED=FB\left[FismidpointofAB\right].....\left(2\right)$
From (1) and (2), we can conclude that BDEF is a parallelogram.