Ohio Assessments for Educators (OAE) Mathematics Practice Exam

How would you categorize a polygon that can have diagonals lying outside of it?

1. Convex Polygon

2. Concave Polygon

3. Regular Polygon

4. Irregular Polygon

The correct answer is: Concave Polygon

A polygon that has diagonals lying outside of it is classified as a concave polygon. In geometry, a concave polygon is defined by at least one interior angle that is greater than 180 degrees. This characteristic allows for the possibility of one or more diagonals extending outside the figure itself. For instance, if you visualize a concave polygon like a star or a dart shape, you can identify that connecting non-adjacent vertices can lead to lines that pass outside of the overall shape. In contrast, a convex polygon has all its interior angles less than 180 degrees, ensuring that all diagonals lie entirely within the polygon. Regular polygons are both convex and have all sides and angles equal, while irregular polygons can be either convex or concave, but they must simply not have equal sides and angles.