symmetry of the antenna structure is it depending on the shape or the feed position?!

hello!
I want to know when we talk about the symmetry of an antenna does it concern only the shape of the antenna literally ? or we take in consideration also the feed point position?
Hope you can help me in understanding this !
thank you!

An antenna constructed from two geometrically symmetrical parts with respect to a plane considered to be a zero potential plane, and intended to be fed directly from a balanced transmission line. This includes feed point also. Example of symmetrical antennas is dipole, Yagi..

Thank you for your reply!
I beg your pardon! but I don't think that I really understand what do you mean by "...a plane considered to be a zero potential plane."
one more question: if we feed the a bowtie/ square patch antenna ..etc for example in unbalanced way can we still take any advantages from the symmetry of the geometry?!

Best regards!