https://r2.erweima.ai/mathbot/image/17260084547357m8t2ozs.jpg

To answer the question based on the provided diagram and the condition \( \overline{ED} \cong \overline{DB} \):

### Let's analyze the options:

1. **\( \overline{EB} \) is bisected by \( \overline{DF} \):**
   - This statement implies that \( \overline{DF} \) divides \( \overline{EB} \) into two equal parts. However, there's no clear indication in the diagram that \( \overline{DF} \) bisects \( \overline{EB} \). Hence, this is **false**.

2. **A is the midpoint of \( \overline{FC} \):**
   - Point A is where \( \overline{FC} \) and \( \overline{EB} \) intersect, but the diagram does not indicate that A is the midpoint of \( \overline{FC} \) since no equal segments on \( \overline{FC} \) are marked around A. This is **false**.

3. **\( \overline{FC} \) bisects \( \overline{DB} \):**
   - There is no indication that \( \overline{FC} \) bisects \( \overline{DB} \). The figure suggests no such relation, so this is also **false**.

4. **\( \overline{EB} \) is a segment bisector:**
   - Given \( \overline{ED} \cong \overline{DB} \), it indicates that \( \overline{EB} \) bisects \( \overline{ED} \) and \( \overline{DB} \), making this statement **true**.

5. **\( FA = \frac{1}{2} FC \):**
   - There is no direct indication from the diagram that suggests this proportion is true, as no division of the segment \( \overline{FC} \) is shown. This is **false**.

6. **\( \overline{DA} \cong \overline{AB} \):**
   - There are no equal markings to indicate that \( \overline{DA} \) and \( \overline{AB} \) are congruent. Thus, this is **false**.

### Conclusion:
- The only correct statement is:
   - **\( \overline{EB} \) is a segment bisector.**

Would you like further clarification or details on any of the reasoning?

### Related Questions:
1. What does it mean for one segment to bisect another?
2. How can we identify the midpoint of a segment from a diagram?
3. What are the properties of congruent segments?
4. How can we prove if a line bisects an angle?
5. What is the significance of the point of intersection between two lines?

**Tip:** Always look for congruent markings and intersection points in a geometry diagram to deduce segment relationships.

Given that ED is congruent to DB, which statements about the figure are true? Check all that apply.

In this geometry problem, explore concepts of congruence and segment bisectors. Analyze a diagram where ED is congruent to DB, and identify which statements about the figure are true. This problem is suitable for students in Grades 9-12.

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