Concave polygons


Concave polygons are polygons for which a line segment joining any two points in the interior does not lies completely within the figure

The word interior is important. You cannot choose one point inside and one point outside the figure

The following figure is concave:


Concave polygon



Segment AB does not entirely lie within the polygon. That is why the polygon is concave

Notice that it is quite possible to find other segments that will lie inside the figure, such as segment FE.

However, if you can find at least one segment that does not lie within the figure, the figure is concave

The following figure is also concave


Concave octagon


It is easy to construct a concave figure if the figure has at least 4 sides

Just make sure that one interior angle is bigger than 180 degrees.

In other words, an interior angle should be a reflex angle

Why am I saying at least 4 sides? It is possible to make a concave triangle?

The answer is no!

Since the sum of the interior angles in any triangle must add up to 180 degrees, no interior angles can be more than 180. It is impossible!




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