Theorem. If two right lines (AB, CD) be parallel to the same right line (EF), they are parallel to one another.
Dem.—Draw any secant GHK. Then since AB and EF are parallel, the angle AGH is equal to GHF [xxix.]. In like manner the angle GHF is equal to HKD [xxix.]. Therefore the angle AGK is equal to the angle GKD (Axiom i.). Hence [xxvii.] AB is parallel to CD.