Then, since the straight line GK has fallen on the parallel straight lines AB, EF, the angle AGK is equal to the angle GHF. [[I. 29](elem.1.29)]

Again, since the straight line GK has fallen on the parallel straight lines EF, CD, the angle GHF is equal to the angle GKD. [[I. 29](elem.1.29)]

But the angle AGK was also proved equal to the angle GHF; therefore the angle AGK is also equal to the angle GKD; [[C.N. 1](elem.1.c.n.1)] and they are alternate.

Therefore AB is parallel to CD.

Q. E. D.

The usual conclusion in general terms (Therefore etc.

) repeating the enunciation is, curiously enough, wanting at the end of this proposition.