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Concept

Same-Side Interior Angles

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.
Same-side 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
and
or

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