🔷 Polygon – Definition

• A polygon is a closed 2D shape made of straight line segments only.
  ✅ No curves, ❌ No open shapes
  Examples: Triangle, Quadrilateral, Pentagon, Hexagon

---

📍 Sides (Edges)

• Sides are the straight line segments that form a polygon.
  ✏️ A triangle has 3 sides, a square has 4 sides, etc.

---

🔸 Vertices (Corners)

• Vertices (singular: Vertex) are the points where two sides meet.
  🔺 A triangle has 3 vertices (A, B, C).

---

📐 Angles

• Interior Angles: Angles inside the polygon
• Exterior Angles: Angles formed outside the polygon by extending a side

🧮 Sum of interior angles formula:
(n−2)×180°
(where n = number of sides)

---

✅ Regular vs Irregular Polygons

Type	Meaning	Example
🌈 Regular Polygon	All sides & angles are equal	Equilateral Triangle, Square
🔶 Irregular Polygon	Sides & angles are not equal	Rectangle, Scalene Triangle

---

⚖️ Convex vs Concave Polygons

Type	Description
⭐ Convex Polygon	All interior angles < 180°; no sides go inward
🌀 Concave Polygon	At least one interior angle > 180°; looks “caved in”

---

🧊 Diagonal

• A diagonal is a line segment connecting two non-adjacent vertices inside a polygon.
  🧮 Number of diagonals formula:
  n(n−3)/2

---

🔁 Equilateral, Equiangular & Cyclic Polygons

• Equilateral Polygon: All sides are equal
• Equiangular Polygon: All interior angles are equal
• Cyclic Polygon: All vertices lie on a circle

---

📊 Naming Polygons (by Number of Sides)

Sides	Name
3	Triangle 🔺
4	Quadrilateral ⬛
5	Pentagon ⭐
6	Hexagon 🔷
7	Heptagon
8	Octagon ⯃
9	Nonagon
10	Decagon 🔟

---

🧠 Important Facts to Remember

✨ A polygon must have at least 3 sides
✨ The shortest polygon is a triangle
✨ A circle is NOT a polygon (it has no straight sides)