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: 31

Answer

1. Given 2. Definition of congruent angles 3. Definition of angle bisectors 4. Division Property of Equality 5. Substitution 6. Definition of congruent angles

Work Step by Step

1. $\angle ABC\cong \angle EFG$ 2. $m\angle ABC=m\angle EFG$ (if two angles are congruent, they have the same angle measure) 3. $m\angle 1=m\angle 2=\frac{m\angle ABC}{2}$ and $m\angle 3=m\angle 4=\frac{m\angle EFG}{2}$ As both $BD$ and $FH$ are bisectors. 4. $\frac{m\angle ABC}{2}=\frac{m\angle EFG}{2}$ (Dividing both sides by 2 of the equation in statement (2.) 5. $m\angle 1=m\angle 2=m\angle 3=m\angle 4$ 6. $\angle 1\cong \angle 2\cong \angle 3\cong \angle 4$ (two angles are congruent if they have the same angle measure)
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