Concave Polygon

Pronunciation: /ˈkɒn keɪv ˈpɒ liˌgɒn/ Explain
concave polygon
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.

convex 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.


  1. concave polygon. Encyclopedia Britannica. Merriam-Webster. Last Accessed 8/6/2018. polygon.
  2. Beman, Wooster Woodruff; and Smith, David Eugene. New Plane and Solid Geometry. pg 54. Ginn & Company. 1899. Last Accessed 8/6/2018. Buy the book
  3. Lyman, Elmer A.. Plane and Solid Geometry. pg 57. American Book Company. 1908. Last Accessed 8/6/2018. Buy the book

Cite this article as:

McAdams, David E. Concave Polygon. 6/25/2018. All Math Words Encyclopedia. Life is a Story Problem LLC.

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Revision History

6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (McAdams, David E.)
1/19/2010: Corrected description of figure 1, added manipulative 1. (McAdams, David E.)
1/18/2010: Added "References". (McAdams, David E.)
7/30/2007: Initial version. (McAdams, David E.)

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