I need to prove that every line l is contained by at least 2 planes

[LCharette]

Homework Statement

Use only incidence axioms to prove that every line is contained by at least two planes.

Homework Equations

The Attempt at a Solution

1. Let l be any line (Given)
2. l has at least two points A and B such that l=AB (I-5(4) Each line has at least two points)
3. Space has at least 3 noncollinear points, that is A,B, and C (I-5(2) Space has at least three noncollinear points)
4. There exists lines AC and BC (I-1 Each two points determines a line)

From here I do not know where to go or even if I am on the right track.

 

[nate808]

5. Since AC and BC are determined by the points A and B, they must also contain the point C (I-3 If a point lies on a line, then it lies on all planes that contain the line)
6. Therefore, l=AB is contained by the planes ABC and BAC (I-2 If two distinct lines intersect, then they intersect in exactly one point.)
7. Since l=AB is contained by two planes, every line is contained by at least two planes.