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The given question asks which lines must be parallel, based on the given information that ∠8 ≅ ∠12.

1. **Identifying the angles**: ∠8 and ∠12 are alternate exterior angles. According to the **Converse of the Alternate Exterior Angles Theorem**, if two lines are cut by a transversal and the alternate exterior angles are congruent, the two lines must be parallel.

2. **Conclusion**: Since ∠8 ≅ ∠12, lines **c** and **d** must be parallel because they are cut by the transversal and form congruent alternate exterior angles.

Thus, the correct answer is:
- **c ‖ d, Converse of the Alternate Exterior Angles Theorem**.

Would you like further details or explanations?

Here are 5 related questions to expand understanding:
1. What are alternate interior angles, and how do they relate to parallel lines?
2. How does the Converse of the Corresponding Angles Theorem work?
3. Can you explain the Same-Side Interior Angles Theorem in detail?
4. How do we determine when lines are parallel using transversal properties?
5. What are some real-world applications of the Parallel Line Theorems?

**Tip**: When working with parallel lines, always look for angle relationships formed by a transversal, as they often provide clues for determining parallelism.

Given ∠8 ≅ ∠12, which lines, if any, must be parallel based on the given information? Justify your conclusion.

Learn how to determine parallel lines using the Converse of the Alternate Exterior Angles Theorem. In this problem, ∠8 and ∠12 are congruent, leading to the conclusion that lines c and d are parallel. Suitable for students in Grades 8-10.

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