Prove that if AB and CD are intersecting lines, then AD and BC are also intersecting lines.

Given: AB and CD are crossing lines.

Prove: AD and BC are crossed lines.

Evidence:

Let’s use the method by contradiction. Suppose that AD and BC are not crossed lines. Then they lie in the same plane. This means that all four points lie in this plane: A, B, C and D. But then the lines AB and CD lie in the same plane – this contradicts the condition of the problem, which means that our assumption is incorrect, and the lines AD and BC intersect, as needed to be proved.