The Eutrigon Theorem

a

b

60°

a

b

c

Δ=Δ+Δ-Δ

The black central triangle with one angle equal to 60° is called a eutrigon. The areas of equilateral triangles constructed on the three faces

a

,

b

, and

c

obey the eutrigon theorem, which gives the area of the black triangle in terms of the areas of the other three triangles.