Elementary Geometry for College Students (5th Edition)

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

Chapter 1 - Section 1.7 - The Formal Proof of a Theorem - Exercises - Page 59: 32

Answer

1. Given 2. Definition o fsupplementary angles 3. Angle Addition Postulate 4. Definition of angle bisectors 5. Substitution 6. Substitution 7. Division Property of Equality 8. Angle Addition Postulate

Work Step by Step

1. $\angle ABC$ is supp. to $\angle CBD$ 2. $m\angle ABC +m\angle CBD=180^{\circ}$ 3. $m\angle ABC = m\angle 1+m\angle2$ $m\angle CBD=m\angle3+m\angle4$ 4. $m\angle 1=m\angle2$ $m\angle3=m\angle4$ 5. $m\angle ABC = 2\times m\angle2$ (Substituting into statement (3.)) $m\angle CBD =2\times m\angle3$ (Substituting into statement (3.)) 6. $2\times m\angle 2 + 2\times m\angle 3=180^{\circ}$ (Substituting into statement (2.)) 7. $m\angle2+m\angle3=90^{\circ}$ ( Dividing both sides of the equation by 2 in statement (5.)) 8. $\angle2+\angle3=\angle EBF$ Therefore $\angle EBF$ is a right angle.
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