Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 2 - Reasoning and Proof - 2-5 Reasoning in Algebra and Geometry - Got It? - Page 116: 3

Answer

\begin{array}{c|ll}& \textbf{Statement} & \textbf{Reasons} \\\hline1 & \overline{AB}\cong\overline{CD} & \text{Given} \\2 & \text{AB = CD} & \text{Definition of Congruence} \\3 & \text{BC = BC} & \text{Reflexive Property of Equality} \\4 & \text{AB + BC = BC + CD} & \text{Addition Property of Equality} \\5 & \text{AB + BC = AC; BC + CD = BD} & \text{Segment Addition Postulate} \\6 & \text{AC = BD} & \text{Transitive Property of Equality} \\7 & \overline{AC}\cong\overline{BD} & \text{Definition of Congruence} \end{array}

Work Step by Step

In order to apply the Addition Property of Equality, you must first use the Reflexive Property to show that the amount added to each side of the equation is equal.
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