https://file.aiquickdraw.com/mathbot/file/1736863308913rszoy69y.jpg

From the uploaded diagram and the given question, let's analyze the statements provided:

### Observations:
1. The segment \( XY \) is marked with equal lengths on both sides of \( X \), suggesting that \( XY \) might be a **segment bisector**.
2. There's no explicit information indicating that \( XY \) is perpendicular to any segment.
3. There’s no marking to indicate \( XY \) bisects an angle, so \( XY \) is **not necessarily an angle bisector**.
4. \( X \) and \( Y \) do not appear to form a right angle vertex (there are no markings for \( 90^\circ \)).
5. \( Y \) could potentially be the midpoint of \( UV \) (depending on equal segment markings).

### Assessing the Statements:
1. **\( XY \) is a segment bisector.**
   - True. The diagram suggests \( XY \) divides the segment \( VW \) into two equal parts.
2. **\( XY \) is a perpendicular bisector.**
   - False. No information is given about perpendicularity.
3. **\( XY \) is an angle bisector.**
   - False. There’s no indication \( XY \) divides any angle into equal parts.
4. **\( X \) is the vertex of a right angle.**
   - False. No angle at \( X \) is marked as \( 90^\circ \).
5. **\( Y \) is the vertex of a right angle.**
   - False. No angle at \( Y \) is marked as \( 90^\circ \).
6. **\( Y \) is the midpoint of a segment in the diagram.**
   - True. \( Y \) appears to be the midpoint of \( UV \).

### Final Correct Statements:
- \( XY \) is a segment bisector.
- \( Y \) is the midpoint of a segment in the diagram.

Would you like a deeper breakdown of any part?  

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### Relative Questions:
1. How do you define a segment bisector and identify it in diagrams?  
2. What distinguishes a perpendicular bisector from a regular segment bisector?  
3. What clues in a diagram help verify that an angle is being bisected?  
4. How do you confirm that a point is a midpoint in geometry?  
5. Can a line segment simultaneously be a perpendicular bisector and a segment bisector?  

### Tip:
Always look for markings (equal lengths, angles, or perpendicular symbols) in geometry diagrams to confirm properties like bisectors or midpoints.

Which of the following statements must be true based on the diagram below? Select all that apply. (Diagram is not to scale.)

Explore how to identify segment bisectors, perpendicular bisectors, angle properties, and midpoints in a geometry diagram. This problem is suitable for Grades 8-10 and includes step-by-step reasoning.

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