1999 AHSME Problem 2

Which of the following statements is false?

\text{(A) All equilateral triangles are congruent to each other.}

\text{(B) All equilateral triangles are convex.}

\text{(C) All equilateral triangles are equiangular.}

\text{(D) All equilateral triangles are regular polygons.}

\text{(E) All equilateral triangles are similar to each other.}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.