If a pair of consecutive interior angles formed by a transversal are supplementary angles, the lines crossed are parallel lines.

For example, in the figure above the lines $A||B$ because $\alpha$ and $\beta$ is a pair of consecutive interior angles with an angle sum of $180^{\circ },$ which makes them supplementary angles. The theorem is named the Converse Consecutive Interior Angles Theorem because the same thing holds true but in opposite order.