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.

Answer: A

Concepts:equilateral triangle congruence (geometry)similarity

Difficulty rating: 880

Solution:

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.

1999 AMC 12 Problem 2

Answer: A

Difficulty rating: 880

Solution:

Problem 2 in Other Years