In geometry, certain terms are considered undefined, meaning they are fundamental concepts that are not explicitly defined using other terms. They serve as the basic building blocks upon which other geometric concepts are defined. The three primary undefined terms in geometry are:
Point: A point represents a location in space, having no size, length, width, or depth. It is usually represented by a dot and labeled with a capital letter.
Line: A line is a continuous, straight arrangement of infinitely many points that extend indefinitely in both directions. It has no thickness or width and is often represented by a straight line with two arrowheads.
Plane: A plane is a flat, two-dimensional surface that extends infinitely in all directions. It has no thickness and is usually represented by a parallelogram or a shaded region.
Defined terms in geometry, on the other hand, are concepts that are built upon the undefined terms. Some examples of defined terms include:
- Line segment: A part of a line that has two endpoints.
- Ray: A part of a line that has one endpoint and extends indefinitely in one direction.
- Angle: The figure formed by two rays sharing a common endpoint.
- Polygon: A closed, two-dimensional figure formed by a finite number of line segments.
- Circle: The set of all points in a plane that are equidistant from a fixed point, called the center.
These defined terms are derived from the undefined terms and serve as a basis for constructing more complex geometric concepts and relationships.