Figures which are similar to the same rectilineal figure are also similar to one another.

For let each of the rectilineal figures A, B be similar to C; I say that A is also similar to B.

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.