Exact conditions for the symmetry of a loop

It is well known that a loop looks the same from both ends provided that it s topology is approximately symmetrical with respect to the midpoint of the line. However, to the best of the author's knowledge, no explicit proof ha s ever been given to confirm or refute this property. In this short contrib ution, it is mathematically proved for the first time that a telephone line , regardless of its topology, is always a symmetric channel (same frequency ;transfer function from either side) provided that the source and load impe dances be the same.