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The given diagram presents a set of intersecting lines, and the question asks which two statements are true regarding parallelism (denoted by "∥") or perpendicularity (denoted by "⊥") among certain line segments.

### Step-by-step breakdown:
1. **Identify the lines**:
    - **\( \overleftrightarrow{FG} \), \( \overleftrightarrow{HB} \), \( \overleftrightarrow{AC} \), \( \overleftrightarrow{DE} \)** are labeled, and we need to determine their relationships based on the diagram.
  
2. **Examine perpendicularity**:
    - If lines are perpendicular (⊥), they form a 90° angle at the intersection.
  
3. **Examine parallelism**:
    - If lines are parallel (∥), they never intersect and maintain equal distance between them.

### Analyzing each option:
- **First option**: \( \overleftrightarrow{FG} \perp \overleftrightarrow{HB} \) and \( \overleftrightarrow{AC} \perp \overleftrightarrow{HB} \)
    - In the diagram, neither \( \overleftrightarrow{FG} \) nor \( \overleftrightarrow{AC} \) appears to form 90° angles with \( \overleftrightarrow{HB} \).
  
- **Second option**: \( \overleftrightarrow{FG} \parallel \overleftrightarrow{DE} \) and \( \overleftrightarrow{DE} \parallel \overleftrightarrow{AC} \)
    - From the diagram, \( \overleftrightarrow{FG} \) and \( \overleftrightarrow{DE} \) appear to be parallel as they maintain the same direction.
    - \( \overleftrightarrow{DE} \parallel \overleftrightarrow{AC} \) is also likely true as the two lines are shown to be parallel.
  
- **Third option**: \( \overleftrightarrow{HB} \perp \overleftrightarrow{AC} \) and \( \overleftrightarrow{FG} \parallel \overleftrightarrow{DE} \)
    - This does not seem valid because \( \overleftrightarrow{HB} \) is not perpendicular to \( \overleftrightarrow{AC} \).

- **Fourth option**: \( \overleftrightarrow{FG} \perp \overleftrightarrow{HB} \) and \( \overleftrightarrow{FG} \parallel \overleftrightarrow{DE} \)
    - \( \overleftrightarrow{FG} \) and \( \overleftrightarrow{DE} \) are parallel but \( \overleftrightarrow{FG} \) is not perpendicular to \( \overleftrightarrow{HB} \).

### Conclusion:
The second option, \( \overleftrightarrow{FG} \parallel \overleftrightarrow{DE} \) and \( \overleftrightarrow{DE} \parallel \overleftrightarrow{AC} \), appears to be the correct choice based on the diagram's geometry.

Would you like more details or explanations about parallelism and perpendicularity? Here are five related questions to deepen understanding:

1. How do we determine if two lines are parallel in a diagram?
2. What properties define perpendicular lines?
3. Can two non-intersecting lines always be assumed parallel?
4. How does the transitive property of parallelism apply here?
5. Can a pair of lines be both perpendicular and parallel at different points?

**Tip**: When working with geometric diagrams, pay close attention to the angles formed at intersections to determine perpendicularity.

Which two statements about parallelism or perpendicularity are both true based on the given diagram?

Solve a geometry problem by determining which two statements about parallelism and perpendicularity are true based on an intersecting line diagram. Ideal for students in Grades 8-10.

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