In 2-dimensional Euclidean geometry, two lines are parallel if they do not intersect. Some properties of parallel lines:
The angles that fall on alternate sides of a transversal and between the parallels (called alternate interior angles) are equal. The converse is also true: if alternate interior angles are equal, the lines are parallel.
The two parallels lines are a constant distance apart, so any pair of lines that interesects them at the same angle will make segments with the same length.