I am looking for the proof of the theorem that the included angle(s) in a semicircle is (are) right angle(s). I thought this was "Thales Theorem" . Theorem 6:1 here, is marked as referring to Thales but is about basic proportionality (a line parallel to the base of a triangle cuts the other 2 sides in the same proportion)

The proof on the Wolfram site uses scalar vectors which I don't (yet) understand and also ( I think) has a slight error , or misprint,  in the explanation.