Consider a pair of lines cut by a transversal. The pairs of interior angles with different vertices that lie on the same side of the transversal are called same-side interior angles or consecutive interior angles. Alternatively, same-side interior angles are called co-interior angles. In the diagram, two pairs of same-side interior angles can be identified. If two parallel lines are cut by a transversal, then the consecutive interior angles are supplementary. The same logic in reverse can be applied. If two lines and a transversal form consecutive interior angles that are supplementary, then the lines are parallel.

If	Then
${\ell }_1\parallel {\ell }_2$	$m\angle 3+m\angle 6=180^{\circ }$ and $m\angle 4+m\angle 5=180^{\circ }$
$m\angle 3+m\angle 6=180^{\circ }$ or $m\angle 4+m\angle 5=180^{\circ }$	${\ell }_1\parallel {\ell }_2$

These statements are supported by the Consecutive Interior Angles Theorem and its converse.