Planar Polygons: Properties and Classification

Defining Polygons

A polygon is a closed two-dimensional figure formed by connecting a finite number of straight line segments. These segments are called edges or sides, and the points where the segments meet are called vertices.

Categorizing Polygons by Number of Sides

Polygons are classified based on the number of sides and vertices they possess. This number is always equal for a given polygon. For example, a triangle has three sides and three vertices, a pentagon has five sides and five vertices, and so forth.

Quadrilaterals: A Specific Polygon Class

Quadrilaterals constitute a significant category of polygons. They are characterized by the presence of four sides and four vertices. This fundamental characteristic allows for further sub-classification into various types, including squares, rectangles, rhombuses, trapezoids, and kites, each distinguished by specific properties relating to side lengths, angles, and parallel sides.

Geometric Properties of Polygons

The sum of the interior angles of a polygon with n sides is given by the formula (n - 2) x 180°. For quadrilaterals (n = 4), the sum of interior angles is always 360°.

Further Exploration of Quadrilaterals

Types of Quadrilaterals

• Parallelograms: Possess two pairs of parallel sides. This category includes rectangles, rhombuses, and squares.
• Trapezoids: Have at least one pair of parallel sides.
• Kites: Have two pairs of adjacent sides of equal length.