AHSME 1999 Problem 2

Which of the following statements is false? $\mathrm{(A) \ All\ equilateral\ triangles\ are\ congruent\ to\ each\ other.}$ $\mathrm{(B) \ All\ equilateral\ triangles\ are\ convex.}$ $\mathrm{(C) \ All\ equilateral\ triangles\ are\ equianguilar.}$ $\mathrm{(D) \ All\ equilateral\ triangles\ are\ regular\ polygons.}$ $\mathrm{(E) \ All\ equilateral\ triangles\ are\ similar\ to\ each\ other.}$