Question

In the figure $△ABC,D,E,F$ are the midpoint of sides $BC,CA$ and $AB$ respectively. Show that
$BDEF$ is parallelogram

Answer 1

Given:- $△ABC$ in which $D,E$ and $F$ are the mid-points of sides $BC,CA$ and $AB$ respectively.

To prove:- $BDEF$ is a parallelogram.

Proof:-

We know that line segments joining the mid-point of two sides of a triangle is parallel to the third side.

Now, in $△ABC$,

$F$ is mid-point of $AB$.

$E$ is mid-point of $AC$.

$\therefore EF\parallel BC$

$\Rightarrow EF\parallel BD(\because \text{Parts of parallel lines are parallel})$

Similarly,

$DE\parallel BF$

Now, in $BDEF$ both pairs of opposite sides are parallel.

$\therefore BDEF$ is a parallelogram.

Hence proved.