So NB=MC

Because GM and BC are parallel

So triangle AGM is similar to triangle ABC.

So AG/AB=AM/AC

So AG/AB=FN/FB

So BG/AB=BN/FB.

Angle NBG= angle FBA

So the triangle NBG is similar to the triangle FBA.

So NG//FA//EB

So NG//EB

And because GM//BC

So MNG plane BCE plane