There must be at least two lines on any given plane because a plane is defined by at least three non-collinear points, and from any two of these points, a line can be drawn. Since three non-collinear points form a plane, at least two distinct lines must exist on that plane. A single line alone cannot define a plane because one line can lie in infinitely many planes; two lines (not parallel or collinear) fix the orientation and structure of a specific plane. Thus, a plane inherently contains at least two lines to establish its two- dimensionality and spatial relationships.

Explanation

• A plane is a flat, two-dimensional surface extending infinitely in all directions, defined by three non-collinear points (points not lying on the same line).

• Two points define a line , so three non-collinear points yield at least two different lines connecting these points.

• Having only one line would not fix a plane uniquely, as one line can belong to infinitely many planes. At least two distinct lines are needed to set the orientation and structure of the plane.

• The existence of at least two lines on a plane ensures the plane's two-dimensional nature and allows for constructing shapes, intersections, and directions within it.

This geometric fact underpins how planes are structured and understood in mathematics and real-world applications.