https://file.aiquickdraw.com/mathbot/file/1730299473316v6a9gjfx.jpg

To solve this problem, let's analyze what Mason needs to do:

Mason wants to construct segment \( FG \) such that it is congruent to segment \( BE \) in the given figure. This means the length of \( FG \) should be the same as \( BE \).

### Solution Steps
To achieve this:
1. Mason should set his compass to the distance of segment \( BE \).
2. Then, he would use this compass width to mark out \( FG \) to ensure it is the same length as \( BE \).

### Answer Choices Analysis:
- **Option A**: Distance from \( A \) to \( C \) — Not relevant here, as we need the length of \( BE \).
- **Option B**: Distance from \( D \) to \( F \) — Also irrelevant.
- **Option C**: Distance from \( B \) to \( E \) — This matches the length Mason needs to set his compass to in order to make \( FG \) congruent to \( BE \).
- **Option D**: Distance from \( F \) to \( C \) — Irrelevant as well.

### Correct Answer:
The correct answer is **C: the distance from \( B \) to \( E \)**.

Would you like a more detailed explanation, or do you have any questions?

### Related Questions:
1. How do you use a compass to construct a congruent segment?
2. What other tools can be used to ensure accuracy in constructing congruent segments?
3. How can we verify that two segments are congruent without measuring?
4. What are congruent segments, and why are they important in geometry?
5. How can geometric constructions be applied in real-world scenarios?

### Tip:
When constructing a segment congruent to another, always start by measuring the exact length of the original segment with a compass and transfer it directly to ensure precision.

Mason is creating a design using a straightedge and compass. He wants to construct a segment FG, which is congruent to segment BE in the given figure. To what width should Mason set his compass when constructing segment FG?

Learn how to construct a segment congruent to another using a straightedge and compass. In this problem, Mason needs to set his compass to the width of segment BE to create a congruent segment FG. This problem covers key geometric concepts in constructing congruent segments and is suitable for Grade 8 students.

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