Let's solve the problem step by step.
The task is to determine whether each pair of lines in the diagram is
parallel,
perpendicular, or
intersecting.
---
Definitions:
-
Parallel lines: Lines that never meet and are always the same distance apart. They have the same slope and do not cross.
-
Perpendicular lines: Lines that intersect at a
90-degree angle (right angle).
-
Intersecting lines: Lines that cross each other at any angle (not necessarily 90 degrees). If they are perpendicular, they are also intersecting, but we usually classify them as "perpendicular" when the angle is exactly 90°.
---
Now let’s analyze each pair of lines in the image:
---
1. Top-left pair
- Two lines slanting in the same direction, equally spaced.
- They never meet and are equidistant.
✔ Parallel
---
2. Top-center pair
- One vertical line, one horizontal line crossing each other.
- They form four right angles (90°).
✔ Perpendicular
---
3. Top-right pair
- Two lines crossing each other at an angle that is
not 90°.
- They intersect but not at a right angle.
✔ Intersecting
---
4. Middle-left pair
- Two lines going in the same direction (upward), very close together.
- Same slope, never meeting.
✔ Parallel
---
5. Middle-center pair
- Two lines slanting in the same direction, equally spaced.
- Never meet, same orientation.
✔ Parallel
---
6. Middle-right pair
- Two lines crossing each other at an angle that appears to be
90°.
- The lines look like a “+” rotated 45° — forming right angles.
✔ Perpendicular
---
7. Bottom-left pair
- Two lines crossing each other at an angle that is
not 90°.
- They intersect but not perpendicularly.
✔ Intersecting
---
8. Bottom-center pair
- Two lines crossing at an angle that is
not 90°.
- Not parallel, not forming right angles.
✔ Intersecting
---
9. Bottom-right pair
- Two lines slanting in the same direction, equally spaced.
- Parallel and never meet.
✔ Parallel
---
Final Answers:
1.
Parallel
2.
Perpendicular
3.
Intersecting
4.
Parallel
5.
Parallel
6.
Perpendicular
7.
Intersecting
8.
Intersecting
9.
Parallel
---
Answer Key (to fill in the blanks):
```
Parallel
Perpendicular
Intersecting
Parallel
Parallel
Perpendicular
Intersecting
Intersecting
Parallel
```
You can write these under each corresponding diagram.
Let me know if you'd like this formatted for printing or with labels!
Parent Tip: Review the logic above to help your child master the concept of parallel lines and perpendicular lines worksheet.