The straight lines joining equal and parallel straight lines (at the extremities which are) in the same directions (respectively) are themselves also equal and parallel.
若两条线段相等且平行，连接它们同向端点的线段也相等且平行。
AB 平行且等于 CD；连同向端点 AC 与 BD；连辅助对角线 BC。
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 AB, CD be equal and parallel, and let the straight lines AC, BD join them (at the extremities which are) in the same directions (respectively); I say that AC, BD are also equal and parallel. Let BC be joined.
连接两条相等且平行线段的同向端点，形成两个三角形。
Then, since AB is parallel to CD, and BC has fallen upon them, the alternate angles ABC, BCD are equal to one another. [I. 29] And, since AB is equal to CD, and BC is common, the two sides AB, BC are equal to the two sides DC, CB; and the angle ABC is equal to the angle BCD; therefore the base AC is equal to the base BD, and the griangle ABC is equal to the triangle DCB, and the remaining angles will be equal to the remaining angles respectively, namely those which the equal sides subtend; [I. 4] therefore the angle ACB is equal to the angle CBD.
由平行线角关系，相关内错角相等（euclid-elements/book1-prop-029）。
And, since the straight line BC falling on the two straight lines AC, BD has made the alternate angles equal to one another, AC is parallel to BD. [I. 27] And it was also proved equal to it.
又有一边公共、一边给定相等，由 euclid-elements/book1-prop-026 得三角形全等。
Therefore etc.
于是连接端点的两线段相等，并由角关系得平行。