1. **Problem Statement:** Given that \(\angle 1 \cong \angle 5\), determine which postulate or theorem justifies that lines \(p\) and \(q\) are parallel. 2. **Understanding the Angles:** \(\angle 1\) and \(\angle 5\) are located on opposite sides of the transversal \(r\) and outside the two lines \(p\) and \(q\). These are called alternate exterior angles. 3. **Relevant Theorem:** The Alternate Exterior Angles Theorem states that if two lines are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel. 4. **Applying the Theorem:** Since \(\angle 1 \cong \angle 5\) and they are alternate exterior angles formed by transversal \(r\) intersecting lines \(p\) and \(q\), by the Converse of the Alternate Exterior Angles Theorem, lines \(p \parallel q\). 5. **Conclusion:** The postulate or theorem that justifies \(p \parallel q\) is the **Alternate Exterior Angles Theorem Converse**. **Final answer:** Alternate Exterior Angles Theorem Converse