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The question is asking which theorem proves that line *a* is parallel to line *b* in the given diagram.

The diagram shows a transversal cutting across two lines, *a* and *b*. The angles formed suggest that the relationship being tested is between the angles created by the transversal.

From the answer choices:

- **A**: This refers to supplementary angles in a linear pair, which doesn't directly address parallelism.
- **B**: Same-side interior angles being supplementary is a theorem related to parallel lines.
- **C**: Corresponding angles theorem states that when two parallel lines are cut by a transversal, corresponding angles are congruent.
- **D**: The alternate interior angles theorem states that alternate interior angles are congruent when the lines are parallel.

Given the diagram, the angles formed by the transversal appear to correspond to **alternate interior angles**. Thus, the correct answer is likely:

**D. Alternate interior angles of parallel lines cut by a transversal are congruent.**

Let me know if you'd like more details or have any questions! 

Here are five related questions:
1. What are alternate exterior angles, and how do they relate to parallel lines?
2. Can same-side interior angles be congruent in any situation?
3. What is the difference between corresponding angles and alternate interior angles?
4. How can you prove two lines are parallel using angles?
5. What is the significance of the transversal in proving parallelism?

**Tip:** Remember, the properties of angles formed by transversals can help you quickly determine if lines are parallel.

Which theorem proves that a//b in the given diagram?

Explore how to use the Alternate Interior Angles Theorem to prove that two lines are parallel. This geometry problem involves transversals, parallel lines, and various angle relationships. Suitable for students in Grades 8-10.

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