Problem Analysis:
The task involves identifying the relationships between various line segments in a geometric diagram. The relationships to be determined are:
1.
Parallel lines: Lines that never intersect and are always the same distance apart.
2.
Perpendicular lines: Lines that intersect at a 90-degree angle.
3.
Intersecting lines: Lines that cross each other at any angle (not necessarily 90 degrees).
The given statements need to be evaluated based on the provided diagram.
---
Step-by-Step Solution:
####
1. Identify Key Observations from the Diagram:
-
Horizontal Lines:
- \( \overline{AB} \) and \( \overline{CD} \) are parallel (they are both horizontal and do not intersect).
- \( \overline{IJ} \) is vertical and intersects both \( \overline{AB} \) and \( \overline{CD} \) at right angles.
-
Vertical Lines:
- \( \overline{GH} \) is vertical and intersects \( \overline{EF} \) at a point.
- \( \overline{IJ} \) is also vertical and intersects \( \overline{AB} \) and \( \overline{CD} \) at right angles.
-
Diagonal Line:
- \( \overline{EF} \) is diagonal and intersects both \( \overline{GH} \) and \( \overline{IJ} \).
####
2. Evaluate Each Statement:
#####
Left Column:
1.
\( \overline{AB} \) and \( \overline{CD} \) are parallel lines.
-
True: Both \( \overline{AB} \) and \( \overline{CD} \) are horizontal and do not intersect.
2.
\( \overline{GH} \) and \( \overline{AB} \) are perpendicular lines.
-
True: \( \overline{GH} \) is vertical, and \( \overline{AB} \) is horizontal. Vertical and horizontal lines are always perpendicular.
3.
\( \overline{AB} \) and \( \overline{EF} \) are intersecting lines.
-
True: \( \overline{EF} \) is a diagonal line that crosses \( \overline{AB} \) at a point.
4.
\( \overline{IJ} \) and \( \overline{AB} \) are perpendicular lines.
-
True: \( \overline{IJ} \) is vertical, and \( \overline{AB} \) is horizontal. Vertical and horizontal lines are always perpendicular.
5.
\( \overline{GH} \) and \( \overline{IJ} \) are parallel lines.
-
False: Both \( \overline{GH} \) and \( \overline{IJ} \) are vertical, but they are not parallel because they intersect at a point.
#####
Right Column:
6.
\( \overline{IJ} \) and \( \overline{CD} \) are perpendicular lines.
-
True: \( \overline{IJ} \) is vertical, and \( \overline{CD} \) is horizontal. Vertical and horizontal lines are always perpendicular.
7.
\( \overline{EF} \) and \( \overline{GH} \) are intersecting lines.
-
True: \( \overline{EF} \) is diagonal and crosses \( \overline{GH} \) at a point.
8.
\( \overline{GH} \) and \( \overline{CD} \) are perpendicular lines.
-
True: \( \overline{GH} \) is vertical, and \( \overline{CD} \) is horizontal. Vertical and horizontal lines are always perpendicular.
9.
\( \overline{EF} \) and \( \overline{IJ} \) are intersecting lines.
-
True: \( \overline{EF} \) is diagonal and crosses \( \overline{IJ} \) at a point.
10.
\( \overline{EF} \) and \( \overline{CD} \) are intersecting lines.
-
True: \( \overline{EF} \) is diagonal and crosses \( \overline{CD} \) at a point.
---
Final Answer:
Mark the statements as
True or
False based on the evaluations above:
- Left Column:
1. True
2. True
3. True
4. True
5. False
- Right Column:
6. True
7. True
8. True
9. True
10. True
\boxed{\text{See evaluations above}}
Parent Tip: Review the logic above to help your child master the concept of parallel lines and perpendicular lines worksheet.
