Geometry Worksheets | Lines Worksheets - Free Printable

Let's solve this step by step based on the image you've provided. The goal is to identify each pair of lines as either parallel, perpendicular, or intersecting.

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🔍 First, analyze the diagram:

We have several lines and points labeled. Let’s identify key features:

- Line FQ: Vertical line from F to Q (going down).
- Line CN: Horizontal line from C to N (going right).
- Line DZ: Horizontal line from D to Z (same level as CN).
- Line YG: Vertical line from Y to G.
- Line MW: Vertical line from M to W.
- Line HT: Diagonal line from H to T (going down and to the right).
- Right angles are marked at intersections like:
- F and D on FQ with CN and DZ → indicates perpendicularity.
- M and W on MW with CN and DZ → also perpendicular.
- Y and G on YG with CN and DZ → perpendicular.

So:
- All vertical lines: FQ, YG, MW
- All horizontal lines: CN, DZ
- Diagonal line: HT

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Now let’s go through each question:

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✔ 1) Line FQ and Line HT are __________ lines.

- FQ is vertical.
- HT is diagonal (not vertical or horizontal).
- They intersect at a point (visually, HT crosses FQ).
- But they are not perpendicular (angle ≠ 90°), nor parallel.
- So: Intersecting lines.

> ✔ Answer: Intersecting

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✔ 2) Line FQ and Line YG are __________ lines.

- Both are vertical lines.
- They are not the same line, but run in the same direction.
- Since they are both vertical and never meet (they're separated horizontally), they are parallel.

> ✔ Answer: Parallel

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✔ 3) Line DZ and Line YG are __________ lines.

- DZ is horizontal.
- YG is vertical.
- They intersect at point G (where DZ meets YG).
- The angle between them is 90° (right angle marked).
- So they are perpendicular.

> ✔ Answer: Perpendicular

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✔ 4) Line CN and Line HT are __________ lines.

- CN is horizontal.
- HT is diagonal.
- They intersect at some point (likely near the center).
- Not at a right angle → not perpendicular.
- Not parallel → different directions.
- So: Intersecting

> ✔ Answer: Intersecting

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✔ 5) Line FQ and Line MW are __________ lines.

- Both are vertical lines.
- They don’t overlap, but run in the same direction.
- Never meet → parallel

> ✔ Answer: Parallel

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✔ 6) Line DZ and Line FQ are __________ lines.

- DZ is horizontal.
- FQ is vertical.
- They intersect at point D (marked with a right angle).
- So: Perpendicular

> ✔ Answer: Perpendicular

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✔ 7) Line CN and Line FQ are __________ lines.

- CN is horizontal.
- FQ is vertical.
- They intersect at point F (with a right angle shown).
- So: Perpendicular

> ✔ Answer: Perpendicular

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✔ 8) Line YG and Line HT are __________ lines.

- YG is vertical.
- HT is diagonal.
- They intersect at point T (end of HT and YG).
- Not at a right angle → not perpendicular.
- Not parallel → different directions.
- So: Intersecting

> ✔ Answer: Intersecting

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✔ 9) Line CN and Line YG are __________ lines.

- CN is horizontal.
- YG is vertical.
- They intersect at point Y (with a right angle shown).
- So: Perpendicular

> ✔ Answer: Perpendicular

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✔ 10) Line HT and Line MW are __________ lines.

- HT is diagonal.
- MW is vertical.
- They intersect somewhere along the path (visually, HT crosses MW).
- Not at a right angle → not perpendicular.
- Not parallel → different directions.
- So: Intersecting

> ✔ Answer: Intersecting

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📝 Final Answers:

| Question | Answer |
|--------|------------------|
| 1) | Intersecting |
| 2) | Parallel |
| 3) | Perpendicular |
| 4) | Intersecting |
| 5) | Parallel |
| 6) | Perpendicular |
| 7) | Perpendicular |
| 8) | Intersecting |
| 9) | Perpendicular |
| 10) | Intersecting |

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✔ Summary:

- Parallel: Lines that never meet and have same direction (e.g., vertical or horizontal lines).
- Perpendicular: Lines that intersect at 90° (right angle).
- Intersecting: Lines that cross at any angle other than 90° (or even if they do, unless specified).

This worksheet helps reinforce understanding of geometric relationships between lines.

Let me know if you'd like a printable version or explanation for younger students!