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 - Page 287: 31

Answer

Statements 1. $\overline{MN} \parallel \overline{OP}$ in Circle $O$ 2. $\angle{1} \cong \angle{2}$ 3. $m\angle{1} = m\angle{2}$ 4. $m\angle{1} = \frac{1}{2}(m\overparen{MQ})$ 5. $m\angle{2} = m\overparen{NP}$ 6. $\frac{1}{2}(m\overparen{MQ}) = m\overparen{NP}$ 7. $m\overparen{MQ} = 2(m\overparen{NP})$

Work Step by Step

Reasons 1. Given 2. If lines are $\parallel$ then alternate interior angles are congruent 3. Congruent angles have equal measures 4. Measure of inscribed $\angle$ = $\frac{1}{2}$ of intercepted arc 5. Measure of central $\angle$ = Measure of intercepted arc 6. Substitution 7. Multiplication Property of Equality
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