Key Concepts: Two-Dimensional Figures

Polygons

A Polygon is a closed figure formed by three or more Line segments (sides) that meet at their endpoints (vertices). Key properties:

• Each side intersects exactly two other sides at their endpoints.
• No two sides with a common endpoint are collinear.

Classifying Polygons by Sides

• Triangle: 3 sides
• Quadrilateral: 4 sides
• Pentagon: 5 sides
• Hexagon: 6 sides
• Heptagon: 7 sides
• Octagon: 8 sides
• Nonagon: 9 sides | Decagon: 10 sides | Dodecagon: 12 sides

Convex vs. Concave

• Convex Polygon: All interior angles are less than 180°. Any Line segment connecting two interior points lies entirely inside.
• Concave Polygon: At least one interior Angle is greater than 180°.

Regular Polygon

A regular Polygon is both equilateral (all sides congruent) and equiangular (all angles congruent).

Perimeter

The perimeter of a Polygon is the sum of the lengths of its sides.