Equilateral Triangle - Famous Theorems

Famous Theorems

Morley's trisector theorem states that, in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle.

Napoleon's theorem states that, if equilateral triangles are constructed on the sides of any triangle, either all outward, or all inward, the centers of those equilateral triangles themselves form an equilateral triangle.

A version of the isoperimetric inequality for triangles states that the triangle of greatest area among all those with a given perimeter is equilateral.

Viviani's theorem states that, for any interior point P in an equilateral triangle, with distances d, e, and f from the sides, d + e + f = the altitude of the triangle, independent of the location of P.

Pompeiu's theorem states that, if P is an arbitrary point in an equilateral triangle ABC, then there exists a triangle with sides of length PA, PB, and PC.