Math worksheet for identifying parallel, perpendicular, and intersecting lines using a diagram with labeled lines.

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.
- FQ and MW are separate, but both go up/down.
- 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 (where DZ starts and FQ goes down).
- Right angle marked → 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 (top of FQ, left end of CN).
- Right angle marked → 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 bottom of YG).
- Not at a right angle → not perpendicular.
- Not parallel.
- 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 (top of YG, right end of CN).
- Right angle marked → Perpendicular

> ✔ Answer: Perpendicular

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

- HT is diagonal.
- MW is vertical.
- They intersect at a point (around the middle of the diagram).
- Not at a right angle → not perpendicular.
- Not parallel.
- 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 of Concepts Used:

- Parallel lines: Same direction, never meet (e.g., vertical vs vertical, horizontal vs horizontal).
- Perpendicular lines: Meet at 90° (right angle shown).
- Intersecting lines: Cross at any angle other than 90°, or even at 90° — but if it's 90°, it's also perpendicular. So "perpendicular" is a subset of "intersecting".

But here, since we’re choosing one category per pair, we use:
- If they form a right angle → Perpendicular
- Else if they cross → Intersecting
- Else → Parallel

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