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The dipole "arrow" you are referring to is called a vector because it has direction. As far as including the C-H bond in the analysis, the C-Cl bond has a much greater difference in electronegativity. The C-Cl bond is going to contribute much more to the polarity of the molecule. Once you have established that there is at least one polar bond in the molecule that is not cancelled out (as we did with the C-Cl bonds) the entire molecule becomes polar.
For the cis-dichloroethene and trans-dichloroethene, did Dr. Lavelle say which one had rotational ability? Both have carbon and carbon linked by a double bond, so wouldn't both forms have pi-bonds and both can't rotate?
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