Question

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

Answer 1

There exists one plane through any three noncollinear points. Since the points cannot be on the same line, at least two lines would have to pass through any of the three points.

Answer 2

The correct answer is:
there must be at least two lines on any plane because a plane is defined by 3 non-collinear points.

Explanation:
Since a plane is defined by 3 non-collinear points, we could have: a line and a point not on that line; two intersecting lines; two parallel lines; or simply 3 non-collinear points.
For 3 non-collinear points: If none of the 3 points are collinear, then we could have 3 lines, 1 going through each point. These lines may or may not intersect. If two of the 3 points are collinear, then we have a line through those 2 points as well as a line through the 3rd point.. Again, these lines may intersect, or they may be parallel.