Convex Polygons — A Complete Guide
🔑 What is a Polygon?
A polygon is a closed, flat (2D) shape made up of straight line segments called sides. The points where sides meet are called vertices (singular: vertex). Polygons are named by their number of sides:
3 → Triangle
4 → Quadrilateral
5 → Pentagon
6 → Hexagon
7 → Heptagon
8 → Octagon
📐 Formal Definition: Convex Polygon
A convex polygon is a polygon in which every interior angle is strictly less than $180°$, and for any two points inside the polygon, the line segment connecting them lies entirely inside the polygon.
Equivalently, a polygon is convex if:
- ✅ All interior angles satisfy: $0° < \theta < 180°$
- ✅ All diagonals lie completely inside the polygon
- ✅ No side, when extended, enters the interior of the polygon