Category:Menelaus's Theorem

This category contains pages concerning Menelaus's Theorem:

Let $ABC$ be a triangle.

Let points $D, E, F$ lie on lines $BC, AC, AB$ respectively (produced if necessary).

Then $D, E$ and $F$ are collinear if and only if:

$\dfrac {AF} {FB} \cdot \dfrac {BD} {DC} \cdot \dfrac {CE} {EA} = -1$

In the above, the line segments $AF, BD, EA$ are determined to have negative length if they lie outside the line segments $AB, BC, CA$.

Source of Name

This entry was named for Menelaus of Alexandria.