Why is arsenic trichloride more likely to be polar than aluminum trichloride?

According to my chemistry teacher, $\ce{AsCl3}$ is more likely to be polar than $\ce{AlCl3}$. Why is this? As I understand it, the difference in electronegativity is what makes a compound more or less likely to be polar, and $\ce{AlCl3}$ has a much greater difference between the two elements' electronegativities. So why isn't it more likely to be polar of the two?




It is because $\ce{AlCl3}$ has a [trigonal planar geometry](https://en.wikipedia.org/wiki/Aluminium_chloride) (leading to no permanent dipole moment) and $\ce{AsCl3}$ has a [pyramidal geometry](https://en.wikipedia.org/wiki/Arsenic_trichloride) (leading to a permanent dipole moment).


 3