What defines a convex polygon?

What defines a convex polygon?

• A. All vertices point outward
• B. At least one angle is greater than 180 degrees
• C. All diagonals lie within the interior of the polygon
• D. It has at least one side longer than the others

Answer: (C)

A convex polygon is defined by the property that all its diagonals lie within the interior of the polygon. This characteristic ensures that, for any two points inside the polygon, the line segment connecting them remains entirely inside the shape. In a convex polygon, the angles formed between any adjacent sides are all less than 180 degrees, which prevents any indentations or inward points in the shape. The definition is essential in distinguishing convex polygons from concave polygons, where at least one diagonal will lie outside the interior. Consequently, the property of the diagonals staying within the bounds of the polygon is a key identifying feature of convex polygons.

A convex polygon is defined by the property that all its diagonals lie within the interior of the polygon. This characteristic ensures that, for any two points inside the polygon, the line segment connecting them remains entirely inside the shape. In a convex polygon, the angles formed between any adjacent sides are all less than 180 degrees, which prevents any indentations or inward points in the shape.

The definition is essential in distinguishing convex polygons from concave polygons, where at least one diagonal will lie outside the interior. Consequently, the property of the diagonals staying within the bounds of the polygon is a key identifying feature of convex polygons.