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.
