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Math Question

Consider the figure to the right. Given: \( \overline{C T} \cong \overline{P M}, \overline{C T} \| \overline{P M} \) Prove: \( \overline{C A} \cong \overline{M A} \) Shown below are the statements and reasons for the proof. They are not in correct order. \begin{tabular}{|l|l|} \hline \multicolumn{1}{|c|}{ Statements } & \multicolumn{1}{|c|}{ Reasons } \\ \hline I. \( \quad \triangle C A T \cong \triangle M A P \) & AAS \\ \hline II. \( \quad \angle C A T \cong \angle P A M \) & Vertical Angles Theorem \\ \hline III. \( \quad \overline{C T} \cong \overline{P M}, \overline{C T} \| \overline{P M} \) & Given \\ \hline IV. \( \quad \overline{C A} \cong M A \) & CPCTC \\ \hline V. \( \quad \angle C T A \cong \angle M P A \) & Alternate Interior Angles Theorem. \\ \hline \end{tabular} Which of these is the most logical order for the statements and reasons?

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