Question

If $D,E,F$ are midpoints of $AB,BC,AC$ respectively prove that $BDEF$ is a $||gm$

Answer 1

In $△ABC,D,E$ and $F$ are midpoints of $BC,AC$ and $AB$ respectively.

$\because E$ and $F$ are mid point of $AC$ and $AB$ respectively

$\therefore FE||BC\Rightarrow FE||BD---\left(1\right)$

Similarly $DE++AB\Rightarrow DE||FB-----\left(2\right)$

Now, from $\left(1\right)$ and $\left(2\right)$,

opposite pairs are parallel

$\therefore BDEF$ is a parallelogram -----proved.