Question

$D,E$ and $F$ are respectively the mid-point of the sides $BC,CA$ and $AB$ of a $△ABC$
Show that
$BDEF$ is a parallelogram.

Answer 1

R.E.F image

Given : D,E and F are mid points

To Prove : BDEF is a parallelogram

proof : F and E are mid points of AB and AC

So, by mid-point theorem

$FE=\frac{1}{2}BC$ and $FE\parallel BC$

As,$BD=\frac{1}{2}BC$

so $FE=BD$ and $FE\parallel BD$

Since one pair of opposite side of a quadrilateral are equal

and parallel

so, the quadrilateral is parallelogram.

Hence, BDEF is a parallelogram.