Use the line segments shown to construct 
   with a length equal to AB + 2CD.

To construct a line segment with a length equal to \( AB + 2CD \), follow these steps:

### Materials:
- A straightedge (ruler)
- A compass
- A pencil

### Steps:

1. **Draw the line segment \( AB \):**
   - Use your straightedge to draw the line segment \( AB \). Label the endpoints \( A \) and \( B \).

2. **Set your compass to the length of \( CD \):**
   - Place the compass point on point \( C \) and the pencil on point \( D \), adjusting the compass to match the length of \( CD \).

3. **Draw a line extension from \( B \):**
   - Extend the line segment \( AB \) using your straightedge. This will be the line along which we will add the length \( 2CD \).

4. **Mark the first segment of \( CD \):**
   - Place the compass point on \( B \) (the endpoint of \( AB \)) and draw an arc along the extended line. Label the intersection of this arc with the extended line as \( P \). Now, the length from \( B \) to \( P \) is equal to \( CD \).

5. **Mark the second segment of \( CD \):**
   - Without changing the compass width, place the compass point on \( P \) and draw another arc along the extended line. Label the intersection of this arc as \( Q \). The length from \( P \) to \( Q \) is also equal to \( CD \).

6. **Final Segment:**
   - Now, the total length of the line segment from \( A \) to \( Q \) is \( AB + 2CD \).

### Summary:
- You have constructed a line segment \( AQ \), where \( AQ = AB + 2CD \).

Would you like more details or have any questions about this?

Here are five related questions to deepen your understanding:

1. How can you use the same method to construct \( AB - CD \)?
2. What is the purpose of extending the line from \( AB \) in this construction?
3. How could this method be applied if you wanted to construct \( AB + 3CD \)?
4. How would you modify the steps if the given segments were curves or not straight lines?
5. How does this construction method work geometrically in terms of segment addition?

**Tip:** Make sure your compass settings remain unchanged while transferring the segment lengths to ensure precision in your construction.

Use the line segments shown to construct with a length equal to AB + 2CD.

Learn how to construct a line segment with length equal to AB + 2CD using geometric tools like a compass and straightedge. Follow this step-by-step guide to apply key concepts of line segment construction. Suitable for students in Grades 6-8.

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