Polygons
Polygons are closed plane figures bounded by three or more line segments. In the world of geometry, polygons abound. The term refers to a multisided geometric form in the plane. The number of angles in a polygon always equals the number of sides.
Polygons are named to indicate the number of their sides or number of noncollinear points present in the polygon. For example, a triangle has three sides and three vertices, a rectangle has four sides and four vertices; others: pentagon, five and five; hexagon, six and six; heptagon, seven and seven; octagon, eight and eight; nonagon, nine and nine; decagon, ten and ten; and an n-gon has n number of sides and n number of vertices.
A square is a special type of polygon, as are triangles, parallelograms, and octagons. The prefix of the term, poly comes from the Greek word for many, and the root word Gon comes from the Greek word for angle.
A regular polygon is one whose whose sides and interior angles are congruent. Regular polygons can be inscribed by a circle such that the circle is tangent to the sides at the centers, and circumscribed by a circle such that the sides form chords of the circle. Regular polygons are named to indicate the number of their sides or number of vertices present in the figure. Thus, a hexagon has six sides, while a decagon has ten sides. Examples of regular polygons also include the familiar square and octagon.
Not all polygons are regular or symmetric. Polygons for which all interior angles are less than 180° are called convex. Polygons with one or more interior angles greater than 180° are called concave.
The most common image of a polygon is of a multisided perimeter enclosing a single, uninterrupted area. In reality, the sides of a polygon can intersect to form multiple, distinct areas. Such a polygon is classified as reflex.
In a polygon, the line running between non-adjacent points is known as a diagonal. The diagonals drawn from a single vertex to the remaining vertices in an n-sided polygon will divide the figure into n-2 triangles. The sum of the interior angles of a convex polygon is then just (n-2)* 180.
If the side of a polygon is extended past the intersecting adjacent side, it defines the exterior angle of the vertex. Each vertex of a convex polygon has two possible exterior angles, defined by the continuation of each of the sides. These two angles are congruent, however, so the exterior angle of a polygon is defined as one of the two angles. The sum of the exterior angles of any convex polygon is equal to 360 degrees.
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