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/horizontal).
- They intersect at a point (visually, HT crosses FQ).
- But they do not form a right angle → not perpendicular.
- So, they are intersecting lines.

✔ Answer: Intersecting

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

- Both FQ and YG are vertical lines.
- They run parallel to each other and never meet.
- No intersection shown, and same direction.

✔ Answer: Parallel

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

- DZ is horizontal.
- YG is vertical.
- They intersect at a right angle (marked with a square).
- 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 (H is on CN, and HT starts there).
- Since HT is not vertical, it doesn't form a 90° angle with CN.
- So they intersect, but not perpendicularly.

✔ Answer: Intersecting

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

- Both are vertical lines.
- They are not the same line and don’t cross.
- 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 (with a right angle marked).
- So they are 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 (right angle marked).
- So they are 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 (where HT ends and YG goes down).
- Not a right angle → not perpendicular.
- So they are 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 (right angle marked).
- So they are perpendicular.

✔ Answer: Perpendicular

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

- HT is diagonal.
- MW is vertical.
- Do they intersect? Yes — HT crosses MW somewhere between M and W.
- Angle is not 90° → not perpendicular.
- So they intersect.

✔ 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 of Definitions Used:

- Parallel lines: Never meet, same direction (e.g., FQ & YG).
- Perpendicular lines: Meet at 90° (right angle), marked with a square.
- Intersecting lines: Cross at any angle except 90° (or if not perpendicular).

Let me know if you'd like this formatted as a printable answer sheet!