Which undefined term is used to define an angle? line plane point ray
The correct answer and explanation is:
The correct answer is ray.
Explanation:
In geometry, certain basic terms are called undefined terms because they are so fundamental that they are not formally defined using other terms. Instead, all other definitions and theorems build upon them. The three primary undefined terms in geometry are point, line, and plane.
- Point: An exact location in space with no size or dimension.
- Line: A straight one-dimensional figure extending infinitely in both directions, with no thickness.
- Plane: A flat two-dimensional surface that extends infinitely in all directions.
Although these three are the main undefined terms, the concept of a ray is also crucial in defining other geometric figures, particularly angles.
Why Ray?
An angle is formed when two rays share a common endpoint.
- A ray starts at one point (called the endpoint) and extends infinitely in one direction.
- When two rays share the same endpoint, the space between them is what we call an angle.
This means that an angle is defined as the figure formed by two rays with a common endpoint. The common endpoint is called the vertex of the angle, and the rays are the sides of the angle.
Why Not Point, Line, or Plane?
- A point alone cannot define an angle because it has no length or direction.
- A line extends infinitely in both directions and cannot define an angle by itself; two lines intersecting could define an angle, but the angle itself is defined by rays.
- A plane is a flat surface and cannot define an angle directly; an angle can lie within a plane but is not defined by it.
Summary
- The three fundamental undefined terms are point, line, and plane.
- The ray is a defined term but is used to define angles.
- An angle is formed by two rays sharing a common endpoint.
Thus, the undefined term used to define an angle is ray.