Menelaus’s Theorem

Menelaus’s theorem relates the way two cevians of a triangle divide each other and the sides of a triangle. Menelaus’s theorem is named for Menelaus of Alexandria.

Stated mathematically, Menelaus's theorem claims that, given triangle ABC, and a transversal line that crosses the extended sides of BC, AC, and AB at points D, E, and F respectively, with D, E, and F distinct from A, B, and C, then Or, stated another way:

It is important to know that this theorem uses signed lengths of segments. Any segment that goes from left to right is positive. Any segment that goes from right to left is negative. Maniplulative 2 demonstrates positive and negative line segments.