Elementary Geometry for College Students (6th Edition)

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

Chapter 6 - Section 6.1 - Circles and Related Segments and Angles - Exercises - Page 277: 35


When a radius intersects a chord at a right angle, we can draw two other radii, one that goes to each end of the bisected chord. Since the intersection of the initial radius is at 90 degrees, the two triangles share a congruent angle. Additionally, the intersecting radius is congruent to itself by the identity property. Finally, the two hypotenuses are congruent since they are both the radius of the circle. Thus, by SAS, the two triangles are congruent. Therefore, since corresponding parts of congruent triangles are congruent, the two sides created by the initial radius are congruent, meaning that it bisects the arc.
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