Maxwell's theorem (geometry)

Maxwell's theorem is the following statement about triangles in the plane.

For a given triangle ${\displaystyle ABC}$ and a point ${\displaystyle V}$ not on the sides of that triangle construct a second triangle ${\displaystyle A'B'C'}$, such that the side ${\displaystyle A'B'}$ is parallel to the line segment ${\displaystyle CV}$, the side ${\displaystyle A'C'}$ is parallel to the line segment ${\displaystyle BV}$ and the side ${\displaystyle B'C'}$ is parallel to the line segment ${\displaystyle AV}$. Then the parallel to ${\displaystyle AB}$ through ${\displaystyle C'}$, the parallel to ${\displaystyle BC}$ through ${\displaystyle A'}$ and the parallel to ${\displaystyle AC}$ through ${\displaystyle B'}$ intersect in a common point ${\displaystyle V'}$.

The theorem is named after the physicist James Clerk Maxwell (1831–1879), who proved it in his work on reciprocal figures, which are of importance in statics.

Wikimedia Commons has media related to Maxwell's theorem.

• Maxwell's Theorem at cut-the-knot.org