Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 5 - Section 5.6 - Segments Divided Proportionally - Exercises - Page 267: 22b

Answer

DB is longer

Work Step by Step

Since CAB is 80 degrees, this means that angle BAD is 40 degrees. In addition, CAD is equal to 40 degrees using the same logic. This means that DA is an angle bisector. Thus, if the line segment CB was perpendicular to DA, DB would be the same length as CD. However, since it is at an angle where BDA is greater that ADC, this means that DB is longer.
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