Straight lines parallel to the same straight line are also parallel to one another.
若两条直线都平行于同一条直线，则它们彼此也平行。
三平行直线 AB、EF、CD；横截线 GK 交 AB 于 G，交 EF 于 H，交 CD 于 K。
正文图形由校订坐标生成；点、线、角、圆可与证明和问答联动。
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, the angle AGK is equal to the angle GHF.
设两条直线都平行于第三条直线。
[I. 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.
取一条横截线，分别使用 euclid-elements/book1-prop-029 得到相等的同位角。
[I. 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] and they are alternate.
由公理 1，这两条直线之间对应角也相等。
Therefore AB is parallel to CD.
再由 euclid-elements/book1-prop-028，它们彼此平行。