Question

Explain why there must be at least two lines on any given plane.

a) Due to the nature of planes and lines.
b) Due to the definition of a plane.
c) Because a single line cannot define a plane.
d) There is no requirement for multiple lines on a plane.

Answer 1

A plane is a two-dimensional surface that requires at least two lines to be defined.

Step-by-step explanation:

A plane is a two-dimensional surface that extends infinitely in all directions. In order to define a plane, you need at least two lines. This is because a single line cannot define a plane, as it does not have enough points to create a two-dimensional surface.

For example, if you have two lines that are not parallel and do not intersect, they can be used to define a plane. All points that lie on both lines will be on the plane. Any point in space can be uniquely determined by its position relative to the two lines, allowing us to construct a plane.

Therefore, there must be at least two lines on any given plane.