how would the symmetry and polarity of a molecule be affected in the case of non-identical attached atoms
In order to answer this question, we try to compare two kinds of compounds.
For example: methane (CH4) and bromochloromethane (CH2BrCl)
. H . | . H -- C --H . | . H
There are FOUR C-H bonds.
The first compound, CH4 is symmetrical in all directions. All the H's exerts equal amount of electronegative force towards C therfore all the directions cancels out which makes the compound non-polar.
. H . | . H -- C --Cl . | . Br
There are TWO C-H bonds, ONE C-Br bond and ONE C-Cl bond.
For the second compound, imagine the two H's of CH4 is replaced by a Br and a Cl. CH2BrCl is not symmetrical. The presence of non-identical atoms in the compound makes it not symmetrical. It's polarity as well will change. Br and Cl exerts a force with C differently as what H can do to C. Since there are different atoms attached in the C it will now become polar.
Hope this helps :)