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In the given image, we are tasked with determining which pairs of lines are parallel and justifying the answer using a specific theorem. The diagram shows several intersecting lines, and we are presented with six possible answers, each involving a different pair of lines and the application of various theorems.

### Let's analyze this:
- The diagram indicates two sets of transversal lines intersecting two potential pairs of parallel lines.
- We can use the **Converse of the Alternate Interior Angles Theorem** or **Converse of the Corresponding Angles Theorem** to determine which pairs of lines are parallel. 

### Answer justification:
Looking at the arrangement, lines \( K \parallel C \) and \( H \parallel N \) are transversals. Given the position of the angles, we can use the **Converse of the Corresponding Angles Theorem** to deduce that:
- Line \( KH \parallel CN \).

Thus, the correct answer is option **E**, as it states:
- \( KC \parallel HN \) by the **Converse of the Corresponding Angles Theorem**.

Would you like further details or clarification on this? 

Here are 5 related questions to explore this topic further:
1. What is the Converse of the Alternate Interior Angles Theorem?
2. How do corresponding angles prove parallelism in a transversal diagram?
3. What is the difference between alternate interior and alternate exterior angles?
4. Can same-side interior angles be used to prove parallel lines?
5. How can you identify transversal lines in a complex figure?

**Tip:** When working with parallel lines and a transversal, identifying angle relationships (corresponding, alternate, or same-side) is key to proving which lines are parallel.

In the given figure, which lines are parallel? Justify your answer. The possible answers include using the Converse of the Alternate Interior Angles Theorem, Same-Side Interior Angles Postulate, and Corresponding Angles Theorem.

Learn how to determine which lines are parallel in a transversal diagram using the Converse of the Alternate Interior Angles Theorem, Same-Side Interior Angles Postulate, and Corresponding Angles Theorem. Suitable for students in Grades 8-10.

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