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The question asks which angles are **alternate interior angles** given two parallel lines and a transversal.

### Key Concept:
- **Alternate interior angles** are non-adjacent interior angles that lie on opposite sides of the transversal. 
- These angles are congruent when the lines are parallel.

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### Identifying the Alternate Interior Angles:
- In the diagram:
  - \( \overline{BD} \parallel \overline{EG} \), and line \( \overline{CFH} \) acts as the **transversal**.
  
  - **Alternate interior pairs** will lie between the parallel lines \( BD \) and \( EG \), on **opposite sides** of the transversal \( CFH \).

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### Answer:
- One pair is \( \angle EFC \) and \( \angle DCF \).
  - These angles are on opposite sides of the transversal \( \overline{CFH} \) and between the two parallel lines, which matches the definition of alternate interior angles.

Thus, the correct answer is:

**\( \angle EFC \) and \( \angle DCF \)**

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Do you want further clarification on alternate interior angles or more explanation about why other options are incorrect?

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Here are five related questions for practice:

1. What are corresponding angles in parallel lines cut by a transversal?
2. If two alternate interior angles are \( 65^\circ \), what is the measure of each?
3. What is the relationship between same-side interior angles?
4. How do you prove two lines are parallel using alternate interior angles?
5. Can alternate interior angles be supplementary?

**Tip:** When dealing with parallel lines and a transversal, visualize the angles between the lines to quickly identify patterns like alternate, corresponding, or co-interior angles.

Which angles are alternate interior angles?

Learn how to identify alternate interior angles when two parallel lines are cut by a transversal. This geometry problem explains the key concepts and provides a step-by-step solution suitable for Grades 7-9.

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