Use the paragraph proof to complete the two-column proof.
What statement and reason belong in line 4?
\begin{tabular}{|c|c|} \hline Statements & Reasons \\ \hline [tex]$C E = C D + D E$[/tex] & 1. segment addition \\ [tex]$D F = E F + D E$[/tex] & \\ \hline [tex]$C D = E F$[/tex] & 2. given \\ \hline [tex]$D F = C D + D E$[/tex] & 3. substitution property of equality \\ \hline [tex]$C E = D F$[/tex] & 4. transitive property of equality \\ \hline [tex]$A B = C E$[/tex] & 5. given \\ \hline [tex]$A B = D F$[/tex] & 6. transitive property of equality \\ \hline \end{tabular}
To fill in line 4 of the two-column proof, let's examine the statements and reasons given in the paragraph proof.
So far, we have: 1. [tex]$C E = C D + D E$[/tex] (segment addition) 2. [tex]$C D = E F$[/tex] (given) 3. [tex]$D F = C D + D E$[/tex] (substitution property of equality)
From the paragraph proof, we know that since [tex]$C E$[/tex] and [tex]$D F$[/tex] equal the same quantity ([tex]$C D + D E$[/tex]), we can state that [tex]$C E = D F$[/tex] using the transitive property of equality.
Thus, line 4 should state: - Statement: [tex]$C E = D F$[/tex] - Reason: Transitive property of equality
Therefore, placing this into the two-column proof:
