Parallel, Intersecting, and Perpendicular Lines Worksheet - Identify and classify line relationships.

Problem Overview:

The task involves identifying whether pairs of lines in given diagrams are parallel, intersecting, or perpendicular. Let's solve each part step by step.

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Definitions Recap:

1. Parallel Lines: Lines that never intersect, no matter how far they are extended. They maintain a constant distance from each other.
2. Intersecting Lines: Lines that cross each other at a single point.
3. Perpendicular Lines: Lines that intersect at a right angle (90 degrees).

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Part 1: Definitions and Examples

The worksheet provides examples for each type of line relationship:
- Parallel Lines: Lines \( AB \) and \( CD \) are parallel. They never cross, even if extended infinitely.
- Intersecting Lines: Lines \( XY \) and \( UV \) are intersecting. They cross each other at a single point \( W \).
- Perpendicular Lines: Lines \( EF \) and \( GH \) are perpendicular. They form right angles where they cross.

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Part 2: Classify Each Pair of Lines

Now, we analyze each diagram to determine the relationship between the lines.

#### Diagram 1:
- Lines: \( l \) and \( m \)
- Observation: The lines do not appear to intersect and maintain a constant distance.
- Conclusion: Parallel

#### Diagram 2:
- Lines: \( l \) and \( m \)
- Observation: The lines intersect at a single point.
- Conclusion: Intersecting

#### Diagram 3:
- Lines: \( l \) and \( m \)
- Observation: The lines intersect at a single point, and the angles formed look like right angles.
- Conclusion: Perpendicular

#### Diagram 4:
- Lines: \( l \) and \( m \)
- Observation: The lines intersect at a single point.
- Conclusion: Intersecting

#### Diagram 5:
- Lines: \( l \) and \( m \)
- Observation: The lines do not appear to intersect and maintain a constant distance.
- Conclusion: Parallel

#### Diagram 6:
- Lines: \( l \) and \( m \)
- Observation: The lines intersect at a single point, and the angles formed look like right angles.
- Conclusion: Perpendicular

#### Diagram 7:
- Lines: \( l \) and \( m \)
- Observation: The lines do not appear to intersect and maintain a constant distance.
- Conclusion: Parallel

#### Diagram 8:
- Lines: \( l \) and \( m \)
- Observation: The lines intersect at a single point.
- Conclusion: Intersecting

#### Diagram 9:
- Lines: \( l \) and \( m \)
- Observation: The lines intersect at a single point, and the angles formed look like right angles.
- Conclusion: Perpendicular

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Final Answers:

1. Parallel
2. Intersecting
3. Perpendicular
4. Intersecting
5. Parallel
6. Perpendicular
7. Parallel
8. Intersecting
9. Perpendicular

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Boxed Final Answer:

\[
\boxed{\text{Parallel, Intersecting, Perpendicular, Intersecting, Parallel, Perpendicular, Parallel, Intersecting, Perpendicular}}
\]