Thales understood similar triangles and right triangles, and what is more, used that knowledge in practical ways. The story is told in DL (loc. cit.) that he measured the height of the pyramids by their shadows at the moment when his own shadow was equal to his height. A right triangle with two equal legs is a 45-degree right triangle, all of which are similar. The length of the pyramid's shadow measured from the center of the pyramid at that moment must have been equal to its height.
Apparently Thales's measurement had to wait for that special moment when his shadow was equal to his height because was not able to generalize that whatever the ratio of his own height to his own shadow length, the ratio of pyramid height to pyramid shadow length would be equal; because he knew that isosceles right triangles were similar but he did not know of the more general AAA triangle similarity.