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: 30

Answer

1. Given ( Defintion of congruent segments) 2. Definition of midpoint 3. Division Property of Equality 4. Substitution 5. Definition of congruent segments

Work Step by Step

1. $AB\cong DC$ ($AB=DC$) 2. $AM=MB=\frac{AB}{2}$ and $DN=NC=\frac{DC}{2}$ As both $M$ and $N$ are midpoints. 3. $\frac{AB}{2}=\frac{DC}{2}$ (Dividing both sides of the equation in statement (1.) 4. $AM=MB=DN=NC$ 5. $AM\cong MB\cong DN\cong NC$ (two segments are congruent if they have the same length)
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