If two straight lines meeting one another be parallel to two straight lines meeting one another not in the same plane, they will contain equal angles.
如果两条相交直线分别平行于不在同一平面内的两条相交直线，那么它们所夹的角相等。
For let the two straight lines AB, BC meeting one another be parallel to the two straight lines DE, EF meeting one another, not in the same plane; I say that the angle ABC is equal to the angle DEF. For let BA, BC, ED, EF be cut off equal to one another, and let AD, CF, BE, AC, DF be joined.
设直线AB、BC相交于B，分别平行于直线DE、EF相交于E，且两对直线不在同一平面内。
Now, since BA is equal and parallel to ED, therefore AD is also equal and parallel to BE. [I. 33] For the same reason CF is also equal and parallel to BE.
截取BA、BC、ED、EF彼此相等，连接AD、CF、BE、AC、DF。
Therefore each of the straight lines AD, CF is equal and parallel to BE. But straight lines which are parallel to the same straight line and are not in the same plane with it are parallel to one another; [XI. 9] therefore AD is parallel and equal to CF.
由BA平行且等于ED，得AD平行且等于BE；同理CF平行且等于BE，故AD平行且等于CF，从而AC平行且等于DF。
And AC, DF join them; therefore AC is also equal and parallel to DF. [I. 33] Now, since the two sides AB, BC are equal to the two sides DE, EF, and the base AC is equal to the base DF, therefore the angle ABC is equal to the angle DEF.
三角形ABC与DEF中，两边AB、BC等于DE、EF，底边AC等于DF，所以角ABC等于角DEF。