For, since A is similar to C,
it is equiangular with it and has the sides about the equal angles proportional. [VI. Def. 1]
Again, since B is similar to C,
it is equiangular with it and has the sides about the equal angles proportional.
Therefore each of the figures A, B is equiangular with C and with C has the sides about the equal angles proportional;
therefore A is similar to B.
Q. E. D.