Math worksheet titled "Identifying Regular and Irregular Polygons" where students fill out a table to categorize different 2D shapes.

Let's solve this step by step.

We are asked to identify whether each shape is a regular polygon, irregular polygon, or not a polygon, and to fill in the table accordingly.

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🔷 Definitions:

- Polygon: A closed 2D shape made of straight line segments (no curves).
- Regular Polygon: A polygon with all sides equal and all angles equal.
- Irregular Polygon: A polygon that has sides and/or angles that are not all equal.
- Not a polygon: If the shape has curved sides or is not closed.

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Now let’s go through each shape one by one.

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1. Triangle (scalene or random triangle)

- It has 3 straight sides, so it's a polygon.
- Sides: Not necessarily equal → ✘ "Has all equal sides"
- Angles: Not all equal → ✔ "Does not have all equal angles"
- So it’s an irregular polygon.
- Name: Triangle

✔ Fill:
- Has all equal sides: ✘
- Does not have all equal angles: ✔
- Regular polygon: ✘
- Irregular polygon: ✔
- Not a polygon: ✘
- Name: Triangle

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2. Square

- 4 straight sides, closed → ✔ polygon
- All sides equal → ✔ "Has all equal sides"
- All angles = 90° → ✔ all angles equal → ✘ "Does not have all equal angles"
- So it's a regular polygon
- Name: Square

✔ Fill:
- Has all equal sides: ✔
- Does not have all equal angles: ✘
- Regular polygon: ✔
- Irregular polygon: ✘
- Not a polygon: ✘
- Name: Square

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3. Parallelogram

- 4 straight sides, closed → ✔ polygon
- Opposite sides equal, but not all sides equal → ✘ "Has all equal sides"
- Opposite angles equal, but not all angles equal → ✔ "Does not have all equal angles"
- So it's an irregular polygon
- Name: Parallelogram

✔ Fill:
- Has all equal sides: ✘
- Does not have all equal angles: ✔
- Regular polygon: ✘
- Irregular polygon: ✔
- Not a polygon: ✘
- Name: Parallelogram

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4. Heart

- Has curved sides → ✘ not a polygon
- So it's not a polygon

✔ Fill:
- Has all equal sides: ✘
- Does not have all equal angles: ✘
- Regular polygon: ✘
- Irregular polygon: ✘
- Not a polygon: ✔
- Name: Heart (or just "Heart" — not a polygon)

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5. Right-angled triangle

- 3 straight sides, closed → ✔ polygon
- Sides: clearly different lengths → ✘ "Has all equal sides"
- Angles: one 90°, others not equal → ✔ "Does not have all equal angles"
- So it's an irregular polygon
- Name: Triangle (specifically right triangle)

✔ Fill:
- Has all equal sides: ✘
- Does not have all equal angles: ✔
- Regular polygon: ✘
- Irregular polygon: ✔
- Not a polygon: ✘
- Name: Triangle

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6. Rhombus

- 4 sides, all sides equal → ✔ "Has all equal sides"
- But angles are not all equal (unless it's a square) → ✔ "Does not have all equal angles"
- So it's not regular, but still a polygon → irregular polygon
- Name: Rhombus

✔ Fill:
- Has all equal sides: ✔
- Does not have all equal angles: ✔
- Regular polygon: ✘
- Irregular polygon: ✔
- Not a polygon: ✘
- Name: Rhombus

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7. Pentagon (irregular-looking)

- 5 straight sides, closed → ✔ polygon
- Sides and angles appear unequal → ✘ "Has all equal sides", ✔ "Does not have all equal angles"
- So it's an irregular polygon
- Name: Pentagon

✔ Fill:
- Has all equal sides: ✘
- Does not have all equal angles: ✔
- Regular polygon: ✘
- Irregular polygon: ✔
- Not a polygon: ✘
- Name: Pentagon

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8. L-shaped figure

- Made of straight lines, closed → ✔ polygon
- Sides not all equal, angles not all equal → ✘ "Has all equal sides", ✔ "Does not have all equal angles"
- So it's an irregular polygon
- Name: L-shape (or irregular octagon? Let's count sides...)

Wait — how many sides?

It looks like an octagon (8 sides), but irregular.

So name: Irregular octagon or L-shaped polygon

✔ Fill:
- Has all equal sides: ✘
- Does not have all equal angles: ✔
- Regular polygon: ✘
- Irregular polygon: ✔
- Not a polygon: ✘
- Name: Irregular octagon

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9. Cross-shaped figure

- Made of straight lines, closed → ✔ polygon
- Sides not equal, angles not equal → ✘ "Has all equal sides", ✔ "Does not have all equal angles"
- So it's an irregular polygon
- How many sides? Count: 12 sides (each arm has 4 sides, but shared) → actually, it’s a dodecagon (12 sides), irregular.

But commonly called a cross.

So name: Irregular dodecagon or Cross

✔ Fill:
- Has all equal sides: ✘
- Does not have all equal angles: ✔
- Regular polygon: ✘
- Irregular polygon: ✔
- Not a polygon: ✘
- Name: Irregular dodecagon or Cross

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## ✔ Final Table Completed:

| Shape | Has all equal sides | Does not have all equal angles | Regular polygon | Irregular polygon | Not a polygon | Name |
|------|---------------------|-------------------------------|------------------|--------------------|----------------|--------|
| 🌟 Star (example) | ✔ | ✔ | ✘ | ✔ | ✘ | Star / irregular decagon |
| 🔺 Triangle | ✘ | ✔ | ✘ | ✔ | ✘ | Triangle |
| ▪️ Square | ✔ | ✘ | ✔ | ✘ | ✘ | Square |
| ◻️ Parallelogram | ✘ | ✔ | ✘ | ✔ | ✘ | Parallelogram |
| ❤️ Heart | ✘ | ✘ | ✘ | ✘ | ✔ | Heart |
| △ Right triangle | ✘ | ✔ | ✘ | ✔ | ✘ | Triangle |
| ◆ Rhombus | ✔ | ✔ | ✘ | ✔ | ✘ | Rhombus |
| ⬤ Pentagon | ✘ | ✔ | ✘ | ✔ | ✘ | Pentagon |
| ⬛ L-shape | ✘ | ✔ | ✘ | ✔ | ✘ | Irregular octagon |
| ➕ Cross | ✘ | ✔ | ✘ | ✔ | ✘ | Irregular dodecagon |

> Note: For the last two shapes, you can write “L-shape” or “Cross” as common names, though technically they are irregular polygons with 8 and 12 sides respectively.

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✔ Summary of Key Concepts:

- Only straight sides make a polygon.
- Curves disqualify a shape from being a polygon.
- All sides and angles must be equal for a regular polygon.
- If only some are equal, it's irregular.
- The star in the example is a decagon (10 sides) but irregular because angles aren’t equal.

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