Define a convex polygon.

Define a convex polygon.

• A. A polygon where all interior angles are less than 180 degrees
• B. A polygon with at least one angle greater than 180 degrees
• C. A polygon that can be inscribed in a circle
• D. A polygon with all sides of equal length

Answer: (A)

A convex polygon is defined as a polygon where all interior angles are less than 180 degrees. This characteristic ensures that if you draw a line segment between any two points inside the polygon, the line segment will lie entirely within the boundaries of the polygon. When all interior angles are less than 180 degrees, the shape does not “cave in” or create indentations, which is a defining trait of convexity. In contrast, a polygon with at least one angle greater than 180 degrees will have concave properties, meaning parts of the shape will fold inward. The option regarding a polygon that can be inscribed in a circle refers to cyclic polygons, which can include both convex and concave shapes; therefore, it does not exclusively define a convex polygon. Lastly, a polygon with all sides of equal length describes a regular polygon, but such a polygon can also be either convex or concave. Hence, the condition about angles being less than 180 degrees is the critical aspect that specifically defines convex polygons.

A convex polygon is defined as a polygon where all interior angles are less than 180 degrees. This characteristic ensures that if you draw a line segment between any two points inside the polygon, the line segment will lie entirely within the boundaries of the polygon. When all interior angles are less than 180 degrees, the shape does not “cave in” or create indentations, which is a defining trait of convexity.

In contrast, a polygon with at least one angle greater than 180 degrees will have concave properties, meaning parts of the shape will fold inward. The option regarding a polygon that can be inscribed in a circle refers to cyclic polygons, which can include both convex and concave shapes; therefore, it does not exclusively define a convex polygon. Lastly, a polygon with all sides of equal length describes a regular polygon, but such a polygon can also be either convex or concave. Hence, the condition about angles being less than 180 degrees is the critical aspect that specifically defines convex polygons.