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 7 - Section 7.3 - More about Regular Polygons - Exercises - Page 344: 43

Answer

The length of the chord is directly proportional to the length of the corresponding arc. Therefore, if the arcs are congruent, then the chords are congruent. Since the chords all come together to form different sides, we obtain that the figure is a shape. In addition, since the angle formed by each side corresponds to the angle in the circle that it takes up, we see that the angles add to 360 degrees. Since the shape contains congruent sides and angles that add to 360 degrees, we find that the shape is a regular polygon.
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