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The image you've uploaded outlines the steps to construct a line through point \( X \) that is parallel to line \( k \) using a compass and straightedge.

Here’s a breakdown of the steps to complete the construction:

### Step 1: 
- **Draw the points** \( X \) and line \( k \). Choose a point \( Y \) on line \( k \), and draw the line \( \overleftrightarrow{XY} \).

### Step 2:
- **Draw an arc** with the center at \( Y \) and set the compass to a radius that crosses \( \overleftrightarrow{XY} \) and line \( k \). Label the points where the arc intersects \( \overleftrightarrow{XY} \) and \( k \) as \( A \) and \( B \).
- Without changing the compass setting, **draw another arc** centered at \( Y \), but on the opposite side from the first arc. Label the point where this second arc crosses \( \overleftrightarrow{XY} \) as \( C \).

### Step 3:
- **Draw an arc with the same radius** as \( AB \) and the center at \( A \). Then, using the same compass setting, draw an arc centered at \( C \). Label the intersection of these arcs as \( D \).

### Step 4:
- **Draw the line** \( \overrightarrow{XD} \). This line will be parallel to line \( k \).

Would you like further details or have any specific questions? Here are some related questions for further exploration:

1. What is the significance of using arcs to find parallel lines in compass constructions?
2. Why is it important not to change the compass setting between certain steps?
3. How can you verify that \( \overrightarrow{XD} \) is truly parallel to line \( k \)?
4. What are the common mistakes to avoid in this type of geometric construction?
5. How would this process change if you had to construct a perpendicular line instead?

**Tip:** Always ensure that the compass setting remains the same between steps where you are instructed not to adjust it, as this ensures accuracy in your construction.

You are using a compass and straightedge to construct a line through point X that is parallel to line k. Complete the following steps.

Learn how to construct a line through point X that is parallel to line k using a compass and straightedge. This guide breaks down the steps to perform the construction, including drawing arcs and using geometric principles. Suitable for students in Grades 7-10.

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