In a classical course on Euclidean, compass-and-ruler geometry, Thales' theorem has always had a prominent place. However, as the Wikipedia article says,
It is equivalent to the theorem about ratios in similar triangles,
which seems to be conceptually easier for most students (I don't have any hard data for that, but this is both my and my colleagues' experience). So my question is: should we teach Thales' theorem? If yes, should we expect the students to actually use this particular result (as opposed to ratios in similar triangles)?
Note that I am strongly opposed against purely pragmatic approach to teaching – I think that we should teach people many things that are not directly useful, but are an important part of our culture (Latin language being a classical (pun intended;-)) example) – so an argument like "it is not needed to solve problems, so it should not be taught" is not at all convincing.