Harold Jocobs' Geometry book(2nd Ed) has a Theorem that states "If two lines form equal corresponding angles with a transversal, then the lines are parallel," and gives a indirect proof. He assumes that the lines are not parallel and shows this assumption leads to a contradiction(since if the lines intersect, the angles are not congruent).
Another textbook(McDougal Littell's Geometry) have Corresponding Angles Postulate that says "If two parallel lines are cut by a transversal then the pairs of corresponding angles are congurent."
The two statements are converse, but Jacobs' book doesn't use a postulate to prove other parallel lines theorems.
Sould the Corresponding Angles Postulate be a theorem, and not a postulate? If it can be proved by indirect proof, shouldn't it be just a theorem like the one in Jacobs' book?
I understand the indirect proof of Jacobs' Theorem, but why do other books use a postulate?