It looks like the task in your image is asking you to
determine whether each pair of lines is parallel, not perpendicular, as the title suggests. However, the title says "Perpendicular Lines," but the instruction says "State whether the given pair of lines are parallel." This might be a mislabeling — we’ll follow the instruction:
determine if the lines are parallel.
Let’s go through each diagram one by one and analyze whether the lines are
parallel (i.e., they never meet and have the same slope/direction).
---
1)
- One horizontal line going left to right.
- One vertical line going up and down.
- These lines intersect at a right angle (90°).
-
Not parallel — they are
perpendicular.
✔ Answer: No
---
2)
- Line segment
TY is vertical (up-down).
- Line segment
TJ goes diagonally from T to J.
- The two lines share point
T, so they intersect.
- Since they intersect and are not the same line, they are
not parallel.
✔ Answer: No
---
3)
- Two vertical lines with arrows pointing up and down.
- They are both straight up/down and appear to be equidistant.
- Since they are both vertical and do not intersect (assuming infinite extension), they are
parallel.
✔ Answer: Yes
---
4)
- Line
BW and line
DP cross each other.
- They intersect at a point (appears to be near W or P).
- Since they intersect, they are
not parallel.
✔ Answer: No
---
5)
- Line
YD is vertical.
- Line
YC is diagonal from Y to C.
- Both start at point
Y, so they intersect there.
- Not the same line → not parallel.
✔ Answer: No
---
6)
- Line
MW and line
LS are both slanted.
- They appear to be going in the same direction and are equally spaced.
- They do not intersect (they’re like two tracks running side by side).
- So, these lines are
parallel.
✔ Answer: Yes
---
✔ Final Answers:
1)
No
2)
No
3)
Yes
4)
No
5)
No
6)
Yes
---
🔍 Explanation Summary:
-
Parallel lines never meet and have the same direction/slope.
- If lines
intersect at any point, they are
not parallel.
- Vertical lines are parallel only if they are both vertical and don’t converge.
- Diagonal lines are parallel only if they have the same angle and direction.
Let me know if you want to check for
perpendicularity instead!
Parent Tip: Review the logic above to help your child master the concept of angles formed by parallel perpendicular and intersecting lines worksheet.
