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To solve the problem, we need to determine whether there is enough information to prove that \( EF \parallel CD \) (i.e., lines \( EF \) and \( CD \) are parallel) based on the given diagram and information about angles.

### Given Information:
- Transversal \( AB \) intersects lines \( EF \) and \( CD \) at points \( G \) and \( H \), respectively.
- \( \angle BGE \cong \angle DHG \).

### Analysis:
1. **Transversal and Angles**: 
   The transversal \( AB \) intersects the two lines \( EF \) and \( CD \). We are given that \( \angle BGE \) is congruent to \( \angle DHG \). These angles are alternate interior angles formed by the transversal.

2. **Parallel Line Condition**: 
   By the **Alternate Interior Angles Converse Theorem**, if two lines are intersected by a transversal and the alternate interior angles are congruent, then the lines are parallel.

### Conclusion:
Since \( \angle BGE \cong \angle DHG \) are alternate interior angles, and they are congruent, this information is sufficient to conclude that \( EF \parallel CD \).

Thus, the answer is:
- **Yes**, there is enough information to prove that \( EF \parallel CD \) by the **Alternate Interior Angles Converse Theorem**.

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Do you need more details or have any questions?

Here are 5 related questions for further understanding:
1. How do you identify alternate interior angles in different transversal scenarios?
2. What are other methods to prove two lines are parallel besides the alternate interior angles converse?
3. Can corresponding angles be used to prove parallel lines? How?
4. What are the conditions for two lines to be considered parallel geometrically?
5. How does the concept of parallel lines extend to non-Euclidean geometries?

**Tip**: When proving lines parallel, always check for congruent corresponding or alternate interior angles created by a transversal.

Is there enough information to prove EF || CD? If yes, by what converse?

Learn how to prove EF || CD using the Alternate Interior Angles Converse Theorem in geometry. This problem explains the key concepts of transversals and congruent angles, suitable for students in Grades 8-10.

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