https://file.aiquickdraw.com/mathbot/file/1730114951249tt1sl4q7.jpg

To determine the number of pairs of parallel lines in the given figure, let's analyze the setup:

The figure shows a grid with horizontal and vertical lines.

1. **Horizontal Lines**: There are four horizontal lines labeled \(CF\), \(EH\), \(GI\), and \(KJ\).
   - These lines are parallel to each other.

2. **Vertical Lines**: There are three vertical lines labeled \(AE\), \(BG\), and \(DK\).
   - These lines are also parallel to each other.

Now, let's count the pairs:

- **Horizontal Pairs**:
  - We can form \(\binom{4}{2} = 6\) pairs from the four parallel horizontal lines.

- **Vertical Pairs**:
  - We can form \(\binom{3}{2} = 3\) pairs from the three parallel vertical lines.

Adding both types of pairs:
\[
6 + 3 = 9
\]

So, there are **9 pairs of parallel lines** in total.

The correct answer is not listed in the options, as none of the choices match 9 pairs.

Would you like more details on parallel line pair counting or need further assistance? 

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Here are some related questions for further exploration:

1. How do you calculate the number of pairs in a set of parallel lines?
2. What distinguishes parallel lines in a plane?
3. Can you identify parallel line pairs in a 3D space diagram?
4. How do you determine if lines in various geometric shapes are parallel?
5. What are real-life examples of parallel lines?

**Tip:** When identifying parallel lines in a grid, focus on each distinct direction (horizontal and vertical) separately before combining.

How many pairs of parallel lines are there in the given figure?

This problem involves finding the number of pairs of parallel lines in a grid. It explores key geometric concepts such as parallel lines and uses combinatorics to count line pairs. Ideal for students in Grades 6-8.

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