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.