I was wondering how Thales would prove that the perpendicular from a point outside a line, to the line, is the smallest linear segment linking the two.

My proof (I wonder if it would be similar to one by Thales...)

Given that the Pythagorean theorem hadn't yet been discovered (Pythagoras was a student of the student of Thales, Anaximander), it couldn't be used back then ^^

Any ideas? (or better yet, is the answer known from historical documents?)

Thanks for any help!