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: 23b

Answer

We know that when central angles are congruent, the corresponding arcs are congruent as well.

Work Step by Step

We can use the same analogy that we used on the previous problem. 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, if two angles are congruent, then they correspond to the same amount of arc taken up. Thus means that when central angles are congruent, the corresponding arcs are congruent as well.
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