# Concave Polygon

Pronunciation: /ˈkɒn keɪv ˈpɒ liˌgɒn/ Explain
 Figure 1: Concave Polygon

Figure 1 is an example of a concave polygon. Note that part of the line between the two points in the figure lie outside the polygon.

 Figure 2: Convex polygon

Figure 2 is an example of a convex polygon. Note that the entire line is contained within the polygon. In fact, a line drawn between any two points that are part of the polygon will be entirely contained within the polygon.

A polygon is a closed shape whose boundaries consist of straight lines. A polygon is concave if, for any two points that are part of the shape, a straight line can be drawn between the two points that lies outside the shape.[1] A property of concave polygons is that if the sides are extended, the extension of at least two sides will intersect one of the other sides. Also, a polygon is concave if any of the interior angles is greater than 180°.

 Click on the blue points and drag them to change the figure. If an angle at a vertex is a straight line, and all the other angles are less than 180 degrees, is the polygon concave or convex? Manipulative 1 - Concave Polygon Created with GeoGebra.

### References

1. concave polygon. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 8/6/2018. http://www.merriam-webster.com/dictionary/concave polygon.
2. Beman, Wooster Woodruff; and Smith, David Eugene. New Plane and Solid Geometry. pg 54. www.archive.org. Ginn & Company. 1899. Last Accessed 8/6/2018. http://www.archive.org/stream/newplaneandsoli02smitgoog#page/n69/mode/1up/search/concave. Buy the book
3. Lyman, Elmer A.. Plane and Solid Geometry. pg 57. www.archive.org. American Book Company. 1908. Last Accessed 8/6/2018. http://www.archive.org/stream/planesolidgeomet00lymarich#page/56/mode/2up/search/concave. Buy the book

McAdams, David E. Concave Polygon. 6/25/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/concavepolygon.html.

### Revision History

1/19/2010: Corrected description of figure 1, added manipulative 1. (McAdams, David E.)
7/30/2007: Initial version. (McAdams, David E.)

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