Elementary Geometry for College Students (7th Edition)

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 6 - Section 6.1 - Circles and Related Segments and Angles - Exercises - Page 287: 38


We are told MN and PQ are parallel, so it follows that corresponding angles of the same transversal are also parallel. Therefore, angle MNP is congruent to angle NPQ, and angle MQP is congruent to angle NMQ. In addition, because QMN and NPQ are formed by the same congruent arcs and transversal, they are congruent. Thus, by substitution, it follows that base angles are congruent. Since the base angles are congruent, the trapezoid is isosceles.
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