1999 AMC 12 Problem 2

Question

Which one of the following statements is false?

All equilateral triangles are congruent to each other.

All equilateral triangles are convex.

All equilateral triangles are equiangular.

All equilateral triangles are regular polygons.

All equilateral triangles are similar to each other.

Congruent means the same shape and the same size

Equilateral triangles can have different side lengths

Equilateral triangles with side lengths

1

and

2

have the same shape but different sizes, so they are similar but not congruent. Every equilateral triangle is convex, equiangular (all angles

60^\circ

), and a regular polygon, so the only false statement is that they are all congruent.

Thus, the correct answer is A.

Problem 2 in other years