Elementary Geometry for College Students (5th Edition)

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

Chapter 6 - Section 6.1 - Circles and Related Segments and Angles - Exercises: 23a

Answer

We know that when arcs are congruent, they have congruent central angles.

Work Step by Step

An arc takes up a certain portion of a given circle. Just like we can related the percentage of a pizza that is eaten to the number of slices (each slice has an arc equal to 1/8 the circumference of the circle), we can relate the angle to the percentage of the circle that the arc takes up. Thus, because congruent arcs take up the same amount of the circle, congruent arcs correspond to congruent central angles.
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