Which undefined term can contain parallel lines
The correct answer and explanation is:
Correct Answer: Plane
Explanation (300 words):
In geometry, undefined terms are basic ideas that cannot be defined using simpler terms. The three main undefined terms in Euclidean geometry are point, line, and plane. These terms form the foundation from which other geometric definitions are built.
The correct answer to the question “Which undefined term can contain parallel lines?” is the plane.
A plane is a flat, two-dimensional surface that extends infinitely in all directions. It has no thickness and is usually represented visually as a parallelogram or rectangle. In mathematical models and diagrams, parallel lines are typically drawn on a plane to illustrate their properties.
Why the Plane is the Correct Answer
Parallel lines are defined as lines in the same plane that never intersect, no matter how far they are extended. This definition highlights an essential requirement: for lines to be parallel, they must lie on the same plane. If they lie on different planes, they are not considered parallel — they may be skew lines, which do not intersect but are also not parallel because they are not coplanar.
Since a plane is the only undefined term among point, line, and plane that can contain more than one line and define the coplanar nature of the lines, it is the only one that can logically contain parallel lines.
Comparison with Other Undefined Terms
- A point represents a specific location in space and has no dimension.
- A line is one-dimensional and extends infinitely in both directions but cannot contain other lines within it.
Therefore, neither a point nor a single line can contain parallel lines. Only a plane, which can accommodate multiple lines that do not intersect, can do so.
In summary, the plane is the only undefined geometric term that can logically and structurally contain parallel lines, making it the correct and complete answer.