Prove that two different planes can be drawn through a line.

Given: plane ψ, plane μ, points A, B, C, D of space.

Prove: AB ⊂ ψ, AB ⊂ μ.

Evidence:

Suppose that the line AB lies in the plane ψ (the plane ψ is given by the points A, B, C). Take a point D in the space that does not belong to the plane ψ. According to the first axiom of stereometry, points A, B and D define the plane (μ). Points A and B belong to both the μ plane and the ψ plane. So, according to the third axiom, the planes ψ and μ intersect along a straight line (AB). And then AB ⊂ μ, AB ⊂ ψ.