Straight-lines joining equal and parallel (straight lines) on the same sides are themselves also equal and parallel. * Let $AB$ and $CD$ be equal and parallel (straight lines), and let the straight lines $AC$ and $BD$ join them on the same sides. * I say that $AC$ and $BD$ are also equal and parallel.
Let \(\overline{AB}\), \(\overline{CD}\) be two equal parallel segments. Then the segments joining their adjacent endpoints, (\(\overline{AC}, \overline{BD}\)) are themselves parallel and equal in length: \(\overline{AC}=\overline{BD}\) and \(\overline{AC}\parallel\overline{BD}\). In other words, the quadrilateral \({ABCD}\) forms a parallelogram.
Proofs: 1