Draw and label an example of two parallel lines that are perpendicular to a third line.

Euclid used a somewhat different parallel postulate in trying to avoid the notion of the infinite.  He observed that when two parallel lines are intersected by a third line, called a transversal, then if you measure two angles formed by these three lines, on the same side of the transversal and between the parallels, they will add to  (that is, they will be supplementary).  Such angles are called same-side interior angles: