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The question involves identifying which lines are parallel based on the given angles, and using a theorem or postulate to justify the answer.

### Problem Breakdown:
- **Given**: \( \angle 3 \cong \angle 7 \)
- Angles 3 and 7 are **alternate interior angles**.
- According to the **Alternate Interior Angles Converse Theorem**, if alternate interior angles are congruent, then the lines cut by the transversal are parallel.

### Analyzing the Diagram:
- The transversal cutting through angles 3 and 7 appears to be the line \( \ell \), and the lines intersecting at these angles are \( a \) and \( b \).
- Based on the Alternate Interior Angles Converse Theorem, if \( \angle 3 \cong \angle 7 \), then lines \( a \) and \( b \) must be parallel.

### Correct Answer:
- The lines \( a \parallel b \) based on the **Alternate Interior Angles Converse Theorem**.

Thus, the correct choice is:
- **C) \( a \parallel b \); Alternate Interior Angles Converse**

Would you like a more detailed explanation or have any other questions? Here are some related queries to extend this concept:

1. What are alternate exterior angles, and how are they used to determine parallel lines?
2. Can corresponding angles also prove lines are parallel? If so, how?
3. How does the Converse of the Same-Side Interior Angles Theorem work?
4. In what cases would the Converse of the Corresponding Angles Theorem be used instead?
5. How would you prove that lines \( \ell \parallel m \) using angle relationships?

**Tip**: Remember that alternate interior angles are congruent when the lines are parallel, and this relationship works in both directions (both forward and converse).

Use the given information to determine which lines, if any, are parallel. State the postulate or theorem that justifies your answer. Given that ∠3 ≅ ∠7.

Identify parallel lines using the Alternate Interior Angles Converse Theorem. In this problem, angles ∠3 and ∠7 are alternate interior angles, and their congruence shows that lines a and b are parallel. Suitable for students in Grades 8-10.

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