3.5. Alternate Exterior Angles http://www.ck12.org
Alternate Exterior Angles Theorem:If two parallel lines are cut by a transversal, then the alternate exterior angles
are congruent.
The proof of this theorem is very similar to that of the Alternate Interior Angles Theorem.
Converse of the Alternate Exterior Angles Theorem:If two lines are cut by a transversal and the alternate exterior
angles are congruent, then the lines are parallel.
Example A
Using the picture above, list all the pairs of alternate exterior angles.
Alternate Exterior Angles:^6 2 and^6 7,^6 1 and^6 8.
Example B
Findm^6 1 andm^6 3.
m^61 = 47 ◦because they are vertical angles. Because the lines are parallel,m^63 = 47 ◦by the Corresponding Angles
Theorem. Therefore,m^62 = 47 ◦.
(^6) 1 and (^6) 3 are alternate exterior angles.