Are circles and ovals the only 2d shaped figures with no line segments?

First , let us revise what we already know, When two points are connected with a straight line, we get a line segment. A line segment is represented with a line on the top. Say segment AB is a line segment which is a line between A and B, and can represented as \overline{AB}
Common examples of 2d figures with line segments are a triangle, parallelogram, square, rectangle, a quadrilateral, polygon.
The figures that consist of curved lines and associated points are called curved shapes. The main types that are included under this category are described below:
5, Arches - These figures consist of a curved line that meets a straight line at two adjacent points. The former line may be entirely curved or might be in the form of two parallel lines before joining the straight line. Like the arc of a bridge.
So, to answer your question no, circles and ovals are not the only 2d objects with line segments.