Geometry and Trigonometry

Plane Geometry

What are some divisions of polygons?

There are two major divisions of polygons: Regular polygons are convex polygons with equal sides and length; thus, all sides and angles are congruent (equal). For example, one of the most famous regular octagons is the stop sign used along roads in the United States: a closed polygon with eight equal sides. The naming of the various polygons can be challenging, though. For example, a polygon called a regular triangle is also called an equilateral triangle; another name for the polygon called a regular quadrilateral is a square. Irregular polygons are those with sides of differing lengths and variable angles. Therefore, unless all the sides of the polygon are of the same length and all the angles are of the same measure, the polygon is said to be irregular.

But don’t be fooled: The names for the various polygons—such as hexagon, nonagon, and pentagon, depending on number of sides—don’t just apply to the regular polygons, but rather to any two-dimensional closed figure with the number of sides as described by its name. For example, the two figures shown on page 185 are both polygons—A is a regular hexagon and B is an irregular hexagon.

Polygons are described in other ways, too. Convex polygons are those in which every line drawn between any two points inside the polygon lie entirely within the figure. Opposite from the convex polygons are the concave polygons—those that are essentially “caved in,” with some of the sides bent inward. If a line is drawn between two points inside a concave polygon, the line often passes outside the figure. Another type of polygon is a star polygon, in which a star figure is drawn based on equidistant points connected on a circle.


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