# Parallel Lines Two [[lines]] are **parallel** if one is a _translate_ of the other. That is, one can be obtained from the other by a [[translation]]. Two [[line segments]] are parallel if their extensions are parallel. That is, if one can be translated so that it overlays the other. # Angles and Parallel Lines When a line (called the _transversal_) crosses two parallel lines then many angles are formed and there are many relationships between these angles. ## Corresponding Angles These are angles that are related by _translating_ one angle along the transversal so that it coincides with the other. Corresponding angles are always equal. ## Alternate Angles These are angles that are related by translating, as for corresponding angles, and then a half turn, so that the angles in an alternate pair are related to a pair of corresponding angles by taking the angle [[vertically opposite]] to one of them. Alternate angles are always equal. ## Cointerior Angles Cointerior angles are the two angles formed inside the diagram on the same side of the transversal line. Cointerior angles add up to $180^\circ$. [[!redirects cointerior angles on parallel lines]] [[!redirects angles and parallel lines]] [[!redirects angles in parallel lines]] [[!redirects cointerior angles]] [[!redirects alternate angles]] [[!redirects corresponding angles]] [[!redirects parallel lines]] [[!redirects parallel]]