SOLUTION: Given two parallel lines cut by a transversal, prove that a pair of alternate interior angles are congruent.

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AB and CD are parallel segements cut by transversal EF with G at point of intersection of AB and EF and H at CD and EF:
angle EGB = angle GHD ~ corresponding angles
* angle EGB = angle AGH ~ vertical angles
angle AGH = angle GHD
Now, a repeat of the properties would show the other two interior angles are congruent.