Alternate Interior Angle Theorem
So, in the figure below, if , then and .
Since , by the Corresponding Angles Postulate ,
Therefore, by the definition of congruent angles ,
Also, and are supplementary, so
Substituting for , we get
Subtracting from both sides, we have
You can prove that using the same method.
The converse of this theorem is also true; that is, if two lines and are cut by a transversal so that the alternate interior angles are congruent, then .