Identify Parallel/Perpendicular/Intersecting Lines Worksheet for ... - Free Printable

To solve the problem, we need to identify whether the given pairs of lines are parallel, perpendicular, or intersecting based on their geometric relationships in the provided diagram. Let's analyze each pair step by step.

Diagram Analysis:

1. Horizontal Lines:
- \( \overline{AB} \) is horizontal.
- \( \overline{CD} \) is horizontal.
- These two lines are parallel because they never intersect and are equidistant throughout.

2. Vertical Lines:
- \( \overline{IJ} \) is vertical.
- \( \overline{GH} \) is vertical.
- These two lines are parallel because they never intersect and are equidistant throughout.

3. Diagonal Lines:
- \( \overline{EF} \) is diagonal.
- It intersects both horizontal and vertical lines at right angles.

4. Key Observations:
- Horizontal lines (\( \overline{AB} \) and \( \overline{CD} \)) are parallel to each other.
- Vertical lines (\( \overline{IJ} \) and \( \overline{GH} \)) are parallel to each other.
- The diagonal line \( \overline{EF} \) is perpendicular to both horizontal and vertical lines.
- Any two lines that cross each other are intersecting unless they form right angles (then they are perpendicular).

Filling in the Blanks:

#### Left Column:
1. \( \overline{AB} \) and \( \overline{CD} \):
- Both are horizontal and do not intersect.
- Answer: Parallel

2. \( \overline{GH} \) and \( \overline{AB} \):
- One is vertical, and the other is horizontal.
- They intersect at a right angle.
- Answer: Perpendicular

3. \( \overline{AB} \) and \( \overline{EF} \):
- \( \overline{AB} \) is horizontal, and \( \overline{EF} \) is diagonal.
- They intersect at a right angle.
- Answer: Perpendicular

4. \( \overline{IJ} \) and \( \overline{AB} \):
- \( \overline{IJ} \) is vertical, and \( \overline{AB} \) is horizontal.
- They intersect at a right angle.
- Answer: Perpendicular

5. \( \overline{GH} \) and \( \overline{IJ} \):
- Both are vertical and do not intersect.
- Answer: Parallel

#### Right Column:
6. \( \overline{IJ} \) and \( \overline{CD} \):
- \( \overline{IJ} \) is vertical, and \( \overline{CD} \) is horizontal.
- They intersect at a right angle.
- Answer: Perpendicular

7. \( \overline{EF} \) and \( \overline{GH} \):
- \( \overline{EF} \) is diagonal, and \( \overline{GH} \) is vertical.
- They intersect at a right angle.
- Answer: Perpendicular

8. \( \overline{GH} \) and \( \overline{CD} \):
- \( \overline{GH} \) is vertical, and \( \overline{CD} \) is horizontal.
- They intersect at a right angle.
- Answer: Perpendicular

9. \( \overline{EF} \) and \( \overline{IJ} \):
- \( \overline{EF} \) is diagonal, and \( \overline{IJ} \) is vertical.
- They intersect at a right angle.
- Answer: Perpendicular

10. \( \overline{EF} \) and \( \overline{CD} \):
- \( \overline{EF} \) is diagonal, and \( \overline{CD} \) is horizontal.
- They intersect at a right angle.
- Answer: Perpendicular

Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{Left Column:} & \text{Right Column:} \\
\overline{AB} \text{ and } \overline{CD}: \text{Parallel} & \overline{IJ} \text{ and } \overline{CD}: \text{Perpendicular} \\
\overline{GH} \text{ and } \overline{AB}: \text{Perpendicular} & \overline{EF} \text{ and } \overline{GH}: \text{Perpendicular} \\
\overline{AB} \text{ and } \overline{EF}: \text{Perpendicular} & \overline{GH} \text{ and } \overline{CD}: \text{Perpendicular} \\
\overline{IJ} \text{ and } \overline{AB}: \text{Perpendicular} & \overline{EF} \text{ and } \overline{IJ}: \text{Perpendicular} \\
\overline{GH} \text{ and } \overline{IJ}: \text{Parallel} & \overline{EF} \text{ and } \overline{CD}: \text{Perpendicular} \\
\end{array}
}
\]