What is the definition of a polygon in geometry?

A polygon in geometry is defined as a closed figure formed by connecting line segments. This means that the sides of the polygon are straight lines that come together at vertices, creating a complete and enclosed shape. The defining characteristic is that it must be "closed," meaning all the line segments must connect back to the starting point without any gaps.

This definition encompasses various types of polygons, such as triangles, quadrilaterals, pentagons, and so on, depending on the number of sides or vertices they possess. The fact that the lines are straight is fundamental to polygons, which distinguishes them from other geometric figures that may include curves or open shapes.

The other options refer to different concepts; three-dimensional shapes describe solids that have volume, such as cubes or spheres. An open figure formed by curves does not meet the structural requirements of a polygon, while a shape with only straight lines could suggest a line or a polygon but does not specify the crucial aspect of being closed. Thus, the key aspect of the correct answer lies in the closed figure formed specifically by connecting line segments.