Take two less than the number of sides, n, and multiply times 180°: ( n - 2) x 180°.Ī circle is not a polygon, but a icosikaihenagon is a polygon. The interiors of all polygons can be broken up into triangles, which is a handy way to find the sum of their interior angles. Its diagonals, however, lie outside the shape! Names of Polygons Like any parallelogram, though, the antiparallelogram still only has four sides and four interior angles. An antiparallelogram (or crossed parallelogram) has the normal two pairs of congruent, opposite sides, but one pair has been crossed, forming what appears to be two touching triangles. AntiparallelogramĪn unusual complex polygon is the antiparallelogram, which looks a bit like bird wings. They also do not create new vertices where they cross. Because you twisted two sides, you still have those two sides (they do not double in number by crossing).
If you could lift part of the polygon up and twist it, so two sides cross one another, and then put it down flat again, you would have a complex polygon. The complex quadrilateral still only has four sides and four interior angles.Ĭomplex polygons may be hard to imagine unless you think of them with elastic sides. Just as you do not count the crossed sides as four line segments, you do not count the two angles they create as interior angles. A complex quadrilateral is that familiar bowtie shape, but it is considered to have only four sides, because one pair of opposite sides has twisted to cross each other. For every polygon with four or more sides, a complex polygon can be drawn. The family of complex star-shaped polygons generally share the Greek number prefix and use the suffix -gram: pentagram, hexagram, octagram, and so on. Most people can doodle a star on paper quickly, but few people label it a pentagram, complex polygon, or self-intersecting polygon. Complex polygons, also called self-intersecting polygons, have sides that cross over each other. Simple polygons have no self-intersecting sides. It will have two interior angles greater than 180°.
Think of a bowtie-shaped simple hexagon (6 sides). A concave polygon has at least one angle greater than 180°. The kite is convex the dart is concave.Įvery interior angle of a convex polygon is less than 180°. In geometry, you could have a four-sided polygon that points outward in all directions, like a kite, or you could have the same four sides so two of them point inward, forming a dart. Home plate on a softball or baseball field is an irregular pentagon, because it has five sides with two 90° angles.Ī convex polygon closes in an interior area without looking "dented." None of its interior angles point inward. Irregular polygons do not have congruent sides and angles. The number of regular polygons is limitless. Every side is equal in length to every other side, and every interior angle is equal to all other interior angles. Regular polygons have congruent sides and interior angles. A regular polygon has congruent sides and interior angles.An irregular polygon does not have congruent sides and interior angles.Complex polygons have self-intersecting sides! A simple polygon encloses a single interior space (boundary) and does not have self-intersecting sides.A concave polygon has one interior angle greater than 180°. A convex polygon has no interior angle greater than 180° (it has no inward-pointing sides).Let's take a look at the vast array of shapes that are polygons and go into detail. Closing in a space (having an interior and exterior).The three identifying properties of any polygon are that the polygon is:
So a circle or any shape that has a curve is not a polygon. To be a polygon, a flat, closed shape must use only line segments to create its sides. The word " polygon" means "many-angled," from Greek.