Parallelism implies Equal Corresponding Angles

Theorem
Given two infinite straight lines which are cut by a transversal, if the lines are parallel, then the corresponding angles are equal.

Proof

 * Parallel Cut by Transversal.png

Let $AB$ and $CD$ be parallel infinite straight lines.

Let $EF$ be a transversal that cuts them.

From Parallelism implies Equal Alternate Interior Angles:
 * $\angle AGH = \angle DHG$

By the Vertical Angle Theorem:
 * $\angle EGB = \angle AGH = \angle DHG$