Parallel, Perpendicular & Intersecting lines worksheet - Free Printable

Let's solve the worksheet step by step and explain each answer.

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Part 1: Identify Parallel, Perpendicular, and Intersecting Lines (Diagrams 1 to 6)

We are given six diagrams with pairs of lines. We need to identify whether the lines are parallel, perpendicular, or intersecting.

#### Definitions:
- Parallel lines: Lines that never meet (same direction, equal distance apart).
- Perpendicular lines: Lines that intersect at a 90° angle (right angle).
- Intersecting lines: Lines that cross each other at any angle (not necessarily 90°).

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#### 1.
Two lines going in the same direction, equally spaced — they will never meet.

✔ Answer: Parallel

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#### 2.
Two lines forming an "X" shape, crossing at a point but not at a right angle.

✔ Answer: Intersecting

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#### 3.
Two lines crossing at a point, forming angles that don't look like 90°.

✔ Answer: Intersecting

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#### 4.
Two lines going in the same direction, equally spaced — parallel.

✔ Answer: Parallel

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#### 5.
Two lines crossing at a point, forming an "X", but not at right angles.

✔ Answer: Intersecting

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#### 6.
Two horizontal lines, same direction, equal distance apart.

✔ Answer: Parallel

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✔ Part 1 Answers:

1. Parallel
2. Intersecting
3. Intersecting
4. Parallel
5. Intersecting
6. Parallel

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Part 2: Identify Relationships Between Labeled Lines

Now we analyze the diagram with labeled lines:

```
A ------------------------> (AB)
P ↑ M ↑ X ↑
| | |
| | |
Q ↓ N ↓ Y ↓
C ------------------------> (CD)
G \-----------------------> H (GH)
```

Let’s analyze each pair:

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#### 1. Line PQ and line GH

- PQ is vertical (up/down).
- GH is diagonal (from top-left to bottom-right).
- They cross at a point → intersecting.
- Not at 90° → not perpendicular.

✔ Answer: Intersecting

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#### 2. Line PQ and line MN

- Both PQ and MN are vertical (going up and down).
- Same direction, same spacing → never meet.

✔ Answer: Parallel

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#### 3. Line CD and line XY

- CD is horizontal (left to right).
- XY is vertical (up and down).
- They cross at a point, forming a right angle → 90°.

✔ Answer: Perpendicular

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#### 4. Line AB and line GH

- AB is horizontal.
- GH is diagonal (slanting from G to H).
- They cross → intersecting.
- Not at 90° → not perpendicular.

✔ Answer: Intersecting

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#### 5. Line PQ and line XY

- Both are vertical (PQ and XY).
- Same direction, parallel.

✔ Answer: Parallel

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#### 6. Line CD and line MN

- CD is horizontal.
- MN is vertical.
- They cross at a point → form a right angle.

✔ Answer: Perpendicular

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#### 7. Line AB and line CD

- Both are horizontal.
- Same direction, same spacing → never meet.

✔ Answer: Parallel

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#### 8. Line MN and line GH

- MN is vertical.
- GH is diagonal.
- They cross → intersecting.
- Not at 90° → not perpendicular.

✔ Answer: Intersecting

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#### 9. Line MN and line XY

- Both are vertical (up/down).
- Same direction, parallel.

✔ Answer: Parallel

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✔ Part 2 Answers:

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

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✔ Final Answer Summary:

#### Part 1:
1. Parallel
2. Intersecting
3. Intersecting
4. Parallel
5. Intersecting
6. Parallel

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

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🔍 Explanation Recap:

- Parallel lines never meet and have the same direction.
- Perpendicular lines intersect at exactly 90° (like a cross).
- Intersecting lines cross at any angle (but not necessarily 90°).

This helps students understand how lines relate in geometry, which is foundational for later math topics like coordinate geometry and angles.

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