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Rule

# Consecutive Interior Angles Theorem

If two parallel lines are cut by a transversal, then the consecutive interior angles are supplementary angles.
In the diagram, and are supplementary as well as and

### Proof

Start by noticing that and form a linear pair as well as and

Therefore, these pair of angles are supplementary.
On the other hand, since the lines and are parallel, by the Alternate Interior Angles Theorem, the alternate interior angles are congruent. This allows to write the following relations.
Next, in Equation I, substitute for The last equation implies that and are supplementary. Similarly, in Equation II, substitute for As before, the last equation implies that and are supplementary, which completes the proof.