Elementary Geometry for College Students (5th Edition)

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

Chapter 6 - Section 6.2 - More Angle Measures in the Circle - Exercises - Page 299: 39

Answer

If two parallel lines intersect a circle, then we can draw a straight line between the points where each parallel line intersects the circle. Since these two angles involve parallel lines being intersected by a common transversal, they are congruent, for alternate interior angles are congruent. Since all inscribed angles are half of the measure of the arcs they correspond to, if these two angles are congruent, then the arcs created are also congruent.
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