Worksheet 3: Wednesday - Identify polygon types and count sides in a geometry exercise.

Let's solve the worksheet step by step.

---

Lesson Recap:

- Regular Polygon: All sides are equal and all angles are equal.
- Irregular Polygon: A polygon that is not regular (sides or angles are not all equal).

We are to:
1. Count the number of sides for each shape.
2. Identify the polygon type (e.g., triangle, quadrilateral, pentagon, etc.).
3. Determine if it is regular or irregular based on side/angle equality.

Now let’s analyze each figure:

---

1) Pentagon (5 sides)

- Number of sides: 5
- Polygon type: Pentagon
- Is it regular? Yes — all sides and angles appear equal.
✔ Regular Pentagon

---

2) Octagon (8 sides)

- Number of sides: 8
- Polygon type: Octagon
- Is it regular? Yes — all sides and angles look equal.
✔ Regular Octagon

---

3) Irregular Decagon (10 sides)

- Number of sides: 10
- Polygon type: Decagon
- Is it regular? No — sides and angles vary; has indentations.
✘ Irregular Decagon

---

4) Rectangle (4 sides)

- Number of sides: 4
- Polygon type: Quadrilateral / Rectangle
- Is it regular? No — opposite sides are equal, but adjacent sides are not (unless square). This is a rectangle, so not all sides equal.
✘ Irregular Quadrilateral

---

5) Regular Octagon (8 sides)

- Number of sides: 8
- Polygon type: Octagon
- Is it regular? Yes — all sides and angles seem equal.
✔ Regular Octagon

---

6) Irregular Hexagon (6 sides)

- Number of sides: 6
- Polygon type: Hexagon
- Is it regular? No — it has a "bowtie" shape with inward angles. Sides and angles are unequal.
✘ Irregular Hexagon

---

7) Regular Octagon (8 sides)

- Number of sides: 8
- Polygon type: Octagon
- Is it regular? Yes — symmetric, all sides and angles equal.
✔ Regular Octagon

---

8) Irregular Pentagon (5 sides)

- Number of sides: 5
- Polygon type: Pentagon
- Is it regular? No — sides and angles differ. It looks like a skewed pentagon.
✘ Irregular Pentagon

---

9) Irregular Pentagon (5 sides)

- Number of sides: 5
- Polygon type: Pentagon
- Is it regular? No — one angle is reflex (greater than 180°), and sides are unequal.
✘ Irregular Pentagon

---

10) Regular Octagon (8 sides)

- Number of sides: 8
- Polygon type: Octagon
- Is it regular? Yes — symmetrical, all sides and angles equal.
✔ Regular Octagon

---

✔ Final Answers:

| # | Number of Sides | Polygon Type | Type |
|---|------------------|--------------------|--------------|
| 1 | 5 | Pentagon | Regular |
| 2 | 8 | Octagon | Regular |
| 3 | 10 | Decagon | Irregular |
| 4 | 4 | Rectangle | Irregular |
| 5 | 8 | Octagon | Regular |
| 6 | 6 | Hexagon | Irregular |
| 7 | 8 | Octagon | Regular |
| 8 | 5 | Pentagon | Irregular |
| 9 | 5 | Pentagon | Irregular |
|10 | 8 | Octagon | Regular |

---

🔍 Explanation Summary:

- Count sides carefully.
- Look for symmetry and equal-length sides to determine regularity.
- Shapes with indentations, reflex angles, or unequal sides are irregular.
- Even if a shape has the same number of sides as a regular one, if it's distorted, it's irregular.

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