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Identify whether each pair of lines is parallel, perpendicular, or intersecting in this geometry worksheet.

Worksheet titled "Parallel Perpendicular or Intersecting" with nine diagrams of lines and arrows showing different relationships, including parallel, perpendicular, and intersecting lines.

Worksheet titled "Parallel Perpendicular or Intersecting" with nine diagrams of lines and arrows showing different relationships, including parallel, perpendicular, and intersecting lines.

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Show Answer Key & Explanations Step-by-step solution for: Parallel and Perpendicular Lines
Let’s go through each pair of lines one by one and decide if they are parallel, perpendicular, or intersecting.

Remember:
- Parallel lines never meet — they stay the same distance apart, like train tracks.
- Perpendicular lines cross at a perfect right angle (like the corner of a square).
- Intersecting lines cross each other at any angle that’s not 90 degrees.

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Row 1:

1. First image (top left): Two slanted lines going in the same direction, never touching → Parallel
2. Second image (top middle): Lines crossing straight up/down and left/right → forms a plus sign → Perpendicular
3. Third image (top right): Two lines crossing but not at right angles → Intersecting

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Row 2:

4. Fourth image (middle left): Two lines going almost the same way but slightly different slopes → they will eventually meet → Intersecting
5. Fifth image (middle center): Two slanted lines side by side, same slope → Parallel
6. Sixth image (middle right): Two lines crossing diagonally, forming an X → not right angles → Intersecting

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Row 3:

7. Seventh image (bottom left): Two lines crossing to form an X with equal angles → looks like right angles? Wait — actually, it’s symmetric but not necessarily 90°. Let’s check: if you rotate your head, it still looks like a tilted X. But in geometry, unless marked, we assume only obvious right angles count. This is just two lines crossing → Intersecting
*(Note: Some might think it’s perpendicular, but without a square corner mark, we don’t assume it. In this worksheet, only the clear “plus” shape is perpendicular.)*

Wait — let me double-check #7. Actually, looking again: the lines cross at what appears to be 90 degrees — vertical and horizontal? No, they’re diagonal. But if they form four equal angles, then yes — it *is* perpendicular. Hmm… Actually, in many worksheets, if it looks like a perfect X with symmetrical arms, it’s meant to be perpendicular. Let’s compare to #2 — that was clearly perpendicular. #7 also has symmetry. I think it’s intended to be Perpendicular.

But wait — no! Look closely: in #2, one line is perfectly vertical, one perfectly horizontal. In #7, both are diagonal — so even if they cross at 90°, they’re still perpendicular. Yes — perpendicular doesn’t require vertical/horizontal — just 90° between them. So if the X is symmetric, it’s likely 90°. So #7 = Perpendicular

Actually, let’s be safe. In most elementary worksheets, if it’s drawn as a perfect X (equal angles), it’s considered perpendicular. So I’ll go with Perpendicular.

8. Eighth image (bottom middle): One line going down-left, another going up-right — they cross, but not at 90° → Intersecting
9. Ninth image (bottom right): Two lines very close together, same slope → Parallel

Wait — let me recheck all for consistency.

Final decision per item:

1. Parallel
2. Perpendicular
3. Intersecting
4. Intersecting (they’re converging)
5. Parallel
6. Intersecting
7. Perpendicular (symmetric X = 90°)
8. Intersecting
9. Parallel

Yes, that makes sense.

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Final Answer:
Row 1: Parallel, Perpendicular, Intersecting
Row 2: Intersecting, Parallel, Intersecting
Row 3: Perpendicular, Intersecting, Parallel
Parent Tip: Review the logic above to help your child master the concept of worksheet parallel and perpendicular lines.
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