Parallel lines and a transversal

A transversal crosses two lines. When the two lines are parallel, corresponding angles are equal, alternate angles are equal, and interior angles on the same side of the transversal total \(180^\circ\). Identify the actual rays, not just a remembered letter shape.

Example

Lines \(l\) and \(m\) are parallel. If the marked upper angle is \(58^\circ\), its corresponding lower angle is \(58^\circ\). The adjacent angle on the lower straight line is \(122^\circ\). State “corresponding angles, \(l\parallel m\)” before using the equality.

These facts can also establish parallelism: for example, equal alternate angles imply that the two lines are parallel. Do not assume parallel lines merely because a sketch looks parallel.