In geometry, duality can transform a theorem about collinear points into one about concurrent lines. We can simply use a duality principle to predict one theorem from another, before proving it independently. Thus, Menelaus's theorem can be used to predict Ceva's theorem.
Menelaus's theorem states that if ABC is a triangle and D is a line intersecting its three sides at P, Q, and R, then the product PB‾PC‾⋅QC‾QA‾⋅RA‾RB‾\dfrac{\overline{\text{PB}}}{\overline{\text{PC}}}\cdot \dfrac{\overline{\text{QC}}}{\overline{\text{QA}}}\cdot \dfrac{\overline{\text{RA}}}{\overline{\text{RB}}} is equal to 1.
Conversely, such a relation between the signed lengths of the line segments implies that P, Q, and R are collinear.