Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 7 - Section 7.3 - More about Regular Polygons - Exercises - Page 333: 38


The length of the tangent is directly proportional to the length of the corresponding arc. Therefore, if the arcs are congruent, then the tangents are congruent. Since the tangents 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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