Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 2 - Section 2.1 - The Parallel Postulate and Special Angles - Exercises - Page 76: 29


The answer is below.

Work Step by Step

The first five steps are the same as we did in 28: 1. We know that if two lines are cut by a transversal, then the corresponding angles are congruent. 2. By definition, the alternate exterior angle of one angle forms a vertical angle with its corresponding angle. 3. According to the vertical angle theorem, vertical angles are congruent. 4. Thus, the second corresponding angle, which is equal to the first angle, in congruent to the alternate exterior angle of the first angle. 5. Therefore, alternate exterior angles are congruent. 6. An alternate exterior angle of an angle forms a 90 degree angle with the same side exterior angle. 7. Because the alternate angle equals the original angle, this means that the same side exterior angles are supplementary.
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