Understanding Polygons | Types, Properties, and Relationships

Polygon

A polygon is a two-dimensional closed figure formed by straight line segments

A polygon is a two-dimensional closed figure formed by straight line segments. It is made up of line segments that are connected end-to-end to form a closed shape. These line segments are called sides of the polygon. The point where two sides meet is called a vertex of the polygon.

In order to qualify as a polygon, it must meet the following criteria:

1. It must be a closed figure, which means all the sides must connect to form a complete shape with no open ends.
2. It must be two-dimensional, meaning it lies on a flat surface.
3. All the sides must be straight line segments. Curved figures are not considered polygons.
4. It must have at least three sides. A polygon with three sides is called a triangle, with four sides is called a quadrilateral, and so on.

Polygons can be classified based on the number of sides they have. Some common classifications include:
– Triangle: A polygon with three sides.
– Quadrilateral: A polygon with four sides.
– Pentagon: A polygon with five sides.
– Hexagon: A polygon with six sides.
– Heptagon: A polygon with seven sides.
– Octagon: A polygon with eight sides.
– Nonagon: A polygon with nine sides.
– Decagon: A polygon with ten sides.

Polygons can also be classified based on the types of angles they have:
– Equiangular polygon: A polygon with all angles congruent (equal).
– Convex polygon: A polygon in which all internal angles are less than 180 degrees and all diagonals remain inside the polygon.
– Concave polygon: A polygon in which at least one internal angle is greater than 180 degrees, causing some diagonals to go outside the polygon.

Polygons are commonly encountered in geometry problems and can be studied in depth to understand their properties and relationships between their sides, angles, and diagonals.

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