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 286: 23d

Answer

We know that when arcs are congruent, their corresponding chords are congruent as well.

Work Step by Step

Consider an arc an its corresponding chord in a given location. Since a circle is symmetric, we can rotate the arc and the chord around the circle without changing anything. Therefore, we find that as long as the length of the arc remains the same, the length of the chord remains the same, meaning that when arcs are congruent, their corresponding chords are congruent as well.
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