Are bf3 and nf3 symmetric or asymmetric molecules? explain your reasoning

The shape of the molecule depends on how many electrons and bonds you have in the outer shell of the central atom. 
For NH3, N is the central atom. It has 3 covalent bonds and a lone pair. Thus the repulsion of the lone pair electrons and the bond electrons will force them to arrange at the corners of a tetrahedral. The molecule will look as a trigonal pyramid (since the lone pair is not "visible" in the structure. 

For BH3, B is the central atom and has no lone pair apart from the three bonds. So the repulsion of the bond electrons will force them to be in a planar trigonal arrangement.

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