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

User Brandan
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1 Answer

3 votes

The correct answer is:

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

Step-by-step 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.

User Dejan Munjiza
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