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To solve the problem, we need to identify pairs of equal angles in the given diagram using the properties of parallel lines and transversals. Let's analyze the diagram:

### Key Angle Relationships:
1. **Corresponding Angles**: These are equal when a transversal crosses parallel lines.
2. **Alternate Interior Angles**: These are equal when a transversal crosses parallel lines.
3. **Vertical Angles**: These are equal because they are opposite each other.

### Given Angles:
- \( a \) and \( e \)
- \( b \) and \( d \)
- \( c \) and \( g \)
- \( f \) and \( h \)

### Analysis:
- **\( a \) and \( e \)** are corresponding angles, so they are equal.
- **\( b \) and \( d \)** are corresponding angles, so they are equal.
- **\( c \) and \( g \)** are corresponding angles, so they are equal.
- **\( f \) and \( h \)** are corresponding angles, so they are equal.

### Correct Answer:
The correct response should be the one that states:
- \( a = e \)
- \( b = d \)
- \( c = g \)

Thus, the correct choice is **option A: \( a = e \), \( b = d \), and \( c = g \)**.

Would you like any further details on this problem, or do you have any questions?

Here are some related questions:
1. What is the difference between corresponding and alternate interior angles?
2. How can vertical angles be identified in any diagram?
3. Why are corresponding angles equal when a transversal cuts through parallel lines?
4. How would the relationships change if the lines were not parallel?
5. Can you explain why the sum of angles around a point is always 360 degrees?

**Tip:** In any geometry problem involving parallel lines and a transversal, always look for corresponding and alternate interior angles first; they often hold the key to solving the problem.

Learn how to solve a geometry problem involving parallel lines and transversals by identifying pairs of equal angles. This problem covers key geometric concepts, including corresponding angles, alternate interior angles, and vertical angles. Suitable for high school students.

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