Understanding Polygons: Types, Properties, and Classifications

Polygon

A polygon is a flat geometric figure bounded by a closed traverse that does not intersect itself.

Classifying Polygons

Polygons are basically classified into:

• Regular Polygons
• Irregular Polygons

Regular Polygons

A regular polygon has all sides of equal length and all its vertices lie on a circle. They are classified as:

• Equilateral Triangle: A regular polygon with 3 sides.
• Square: A 4-sided regular polygon.
• Regular Pentagon: A regular polygon with 5 sides.
• Regular Hexagon: A 6-sided regular polygon.
• Regular Heptagon: A regular 7-sided polygon.
• Regular Octagon: An 8-sided regular polygon, and so on.

Regular Polygon

Irregular Polygons

An irregular polygon has sides that are not of equal length and/or its vertices do not lie on a circle. According to the number of its sides, they are called:

• Triangle: A polygon with 3 sides.
• Quadrilateral: A polygon with 4 sides.
• Pentagon: A polygon with 5 sides.
• Hexagon: A polygon of 6 sides.
• Heptagon: A 7-sided polygon.
• Octagon: A polygon of 8 sides, and so on.

Irregular Polygon

Triangles

A triangle is a three-sided polygon. According to the magnitude of their angles, triangles are classified as:

• Isosceles Triangle: Has 2 equal angles.
• Scalene Triangle: Has 3 different angles.
• Right Triangle: Has 1 right angle.
• Obtuse Triangle: Has 1 obtuse angle.
• Acute Triangle: Has 3 acute angles.

Triangle: A Polygon with 3 Sides

Quadrilaterals

A quadrilateral is a 4-sided polygon. They are classified as:

• Parallelogram: A quadrilateral in which opposite sides are parallel. These are further classified as:
  • Rectangle: A parallelogram in which all four angles are right angles, but the adjacent sides are not of equal length.
  • Rhombus: A parallelogram that has no right angles, but its sides are of equal length.
  • Rhomboid: A parallelogram with no right angles and its adjacent sides are not of equal length.
• Trapezoid: A quadrilateral with only two parallel sides, further defined as:
  • Right Trapezoid: A trapezoid having two right angles.
  • Isosceles Trapezoid: A trapezoid in which the non-parallel sides are of equal length.
• Irregular Quadrilateral: A quadrilateral that has no parallel sides.

Quadrilateral: A Polygon with 4 Sides