Given AD¯¯¯¯¯¯¯¯ || GJ¯¯¯¯¯¯¯AD¯ || GJ¯. Refer to the figure and provide an appropriate name for ∠EHC∠EHC and ∠CHJ∠CHJ.

Given that \( \overline{AD} \parallel \overline{GJ} \), we can analyze the angles \( \angle EHC \) and \( \angle CHJ \) with respect to this parallelism and the other lines in the figure.

1. **Naming \( \angle EHC \)**:
   - \( \angle EHC \) is formed by the intersection of line \( \overline{BH} \) (vertical line) with the diagonal line \( \overline{GH} \).
   - Since \( \overline{AD} \parallel \overline{GJ} \) and \( \overline{BH} \) is a transversal, \( \angle EHC \) is the **Alternate Interior Angle** with \( \angle HDC \).
   - Therefore, \( \angle EHC \) can be referred to as the **Alternate Interior Angle**.

2. **Naming \( \angle CHJ \)**:
   - \( \angle CHJ \) is formed at the intersection of the diagonal line \( \overline{GH} \) with \( \overline{HK} \).
   - Given \( \overline{AD} \parallel \overline{GJ} \) and \( \overline{HK} \) as a transversal, \( \angle CHJ \) is also an **Alternate Interior Angle** with \( \angle AHD \).
   - Therefore, \( \angle CHJ \) can be referred to as the **Alternate Interior Angle**.

### Summary:
- \( \angle EHC \) is an **Alternate Interior Angle**.
- \( \angle CHJ \) is an **Alternate Interior Angle**.

Would you like any further details or explanations on this? Here are some related questions that might help you explore this topic further:

1. What properties do alternate interior angles have when lines are parallel?
2. How can you prove that \( \overline{AD} \parallel \overline{GJ} \)?
3. What are the measures of \( \angle EHC \) and \( \angle CHJ \) if you know other angle measures in the diagram?
4. Are there any corresponding angles in the diagram related to \( \overline{AD} \parallel \overline{GJ} \)?
5. What role do transversal lines play in identifying angle relationships?
6. How do alternate interior angles help in proving lines are parallel?
7. Can you identify any other pairs of alternate interior angles in the diagram?
8. How would you describe the relationship between \( \overline{AE} \) and \( \overline{BF} \) if \( \overline{AD} \parallel \overline{GJ} \)?

### Tip:
When dealing with parallel lines and a transversal, always look for alternate interior angles, corresponding angles, and same-side interior angles as they often reveal important geometric relationships and properties.

Explore how alternate interior angles are defined and identified when parallel lines are present. This detailed explanation uses a geometric diagram to illustrate the concept clearly. Suitable for high school students studying geometry.

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