In the given diagram, we are asked to identify the postulate or theorem that proves lines $r \parallel s$, given that $\angle 3 \cong \angle 6$.

Analysis:

• $\angle 3$ and $\angle 6$ are corresponding angles formed by the transversal between lines $r$ and $s$.
• According to the Corresponding Angles Postulate, if two lines are cut by a transversal and the corresponding angles are congruent, then the two lines are parallel.

Conclusion:

Since $\angle 3 \cong \angle 6$, by the Corresponding Angles Postulate, lines $r$ and $s$ are parallel. Therefore, $r \parallel s$.

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Here are 5 related questions you might find useful:

1. What are alternate interior angles, and how do they relate to parallel lines?
2. How can we prove that two lines are parallel using the Converse of the Corresponding Angles Postulate?
3. How do you differentiate between corresponding, alternate interior, and alternate exterior angles?
4. What are the consequences of parallel lines in geometry (e.g., equal distances, same slope in coordinate geometry)?
5. How does the Transversal Theorem apply to this type of problem?

Tip: Always remember that corresponding angles are in matching positions relative to the transversal and the two lines. If they're equal, the lines are parallel!