Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is a concave polygon characterized by?

1. All diagonals are inside the polygon

2. Some diagonals lie outside the polygon

3. All sides are equal in length

4. All angles are equal

The correct answer is: Some diagonals lie outside the polygon

A concave polygon is characterized by the presence of at least one interior angle that is greater than 180 degrees. This condition causes some diagonals to lie outside the polygon. When you connect non-adjacent vertices in a concave polygon, certain line segments (diagonals) will extend beyond the shape, illustrating the property that distinguishes concave polygons from convex ones, where all diagonals remain entirely within the figure. In contrast, the other characteristics mentioned do not accurately describe concave polygons. For instance, convex polygons have all their diagonals inside the figure, while equilateral polygons have all sides equal, and regular polygons feature all angles equal. Therefore, the defining feature of a concave polygon being that some diagonals extend outside the polygon correctly identifies its unique and distinguishing properties.