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Alternate Exterior Angles Theorem

The Alternate Exterior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate exterior angles are congruent .

So, in the figure below, if k l , then

1 7 and 4 6 .

Two parallel lines cut by a transversal n, with angles labeled 1 through 8


Since k l , by the Corresponding Angles Postulate ,

1 5 .

Also, by the Vertical Angles Theorem,

5 7 .

Then, by the Transitive Property of Congruence,

1 7 .

You can prove that 4 and 6 are congruent using the same method.

The converse of this theorem is also true; that is, if two lines k and l are cut by a transversal so that the alternate exterior angles are congruent, then k l .