Straight lines parallel to the same straight line are also parallel to one another.
Let each of the straight lines AB, CD be parallel to EF; I say that AB is also parallel to CD.
For let the straight line GK fall upon them; Then, since the straight line GK has fallen on the parallel straight lines AB, EF,
But the angle AGK was also proved equal to the angle GHF;
Therefore AB is parallel to CD.
Q. E. D. 1