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 two lines each. 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 at any angle (not necessarily 90°).

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1.
Two lines going in the same direction, not crossing → Parallel lines

✔ Answer: Parallel

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2.
Two lines forming an "X" shape — they cross at a point → Intersecting lines
But do they form a right angle? Not clearly visible; they don't look like 90° → So just intersecting, not perpendicular.

✔ Answer: Intersecting

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3.
Two lines crossing at a point, but not at a right angle → Intersecting lines

✔ Answer: Intersecting

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4.
Two lines slanting in the same direction, same slope, not meeting → Parallel lines

✔ Answer: Parallel

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5.
One horizontal line and one diagonal line crossing → They intersect at a point → Intersecting lines

✔ Answer: Intersecting

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6.
Two horizontal lines, same direction, equal distance apart → Parallel lines

✔ 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 in the diagram

We are given a grid-like figure with labeled lines:
- Horizontal lines: AB, CD
- Vertical lines: PQ, MN, XY
- Diagonal line: GH

Let’s analyze each pair:

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1. Line PQ and line GH are ________ line.

- PQ is vertical (up-down)
- GH is diagonal (from top-left to bottom-right)
- They intersect at a point
- The angle is not 90° → not perpendicular

✔ Answer: Intersecting

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2. Line PQ and line MN are ________ line.

- Both are vertical lines
- Same direction, parallel, never meet
- Equal distance apart

✔ Answer: Parallel

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3. Line CD and line XY are ________ line.

- CD is horizontal
- XY is vertical
- They intersect at a point
- Since one is horizontal and one is vertical → they form a right angle (90°)

✔ Answer: Perpendicular

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4. Line AB and line GH are ________ line.

- AB is horizontal
- GH is diagonal
- They intersect at a point
- Not at 90° → not perpendicular

✔ Answer: Intersecting

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5. Line PQ and line XY are ________ line.

- Both are vertical lines
- Same direction, parallel

✔ Answer: Parallel

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6. Line CD and line MN are ________ line.

- CD is horizontal
- MN is vertical
- They intersect at a point
- Form a right angle → Perpendicular

✔ Answer: Perpendicular

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7. Line AB and line CD are ________ line.

- Both are horizontal
- Same direction, parallel

✔ Answer: Parallel

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8. Line MN and line GH are ________ line.

- MN is vertical
- GH is diagonal
- They intersect at a point
- Not at 90° → not perpendicular

✔ Answer: Intersecting

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9. Line MN and line XY are ________ line.

- Both are vertical lines
- Same direction, parallel

✔ Answer: Parallel

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✔ Final Answers for Part 2:

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

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📌 Summary of Key Concepts:

| Relationship | Description |
|-------------|-------------|
| Parallel | Lines that never meet; same direction |
| Perpendicular | Lines that meet at 90° (like a cross) |
| Intersecting | Lines that cross at any angle (not necessarily 90°) |

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✔ Final Answer Sheet:

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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