1999 AMC 12 第 2 题

Question

下列哪一个命题是假的？

Which one of the following statements is false?

所有等边三角形都彼此全等。

All equilateral triangles are congruent to each other.

所有等边三角形都是凸的。

All equilateral triangles are convex.

所有等边三角形都是等角的。

All equilateral triangles are equiangular.

所有等边三角形都是正多边形。

All equilateral triangles are regular polygons.

所有等边三角形都彼此相似。

All equilateral triangles are similar to each other.

全等表示形状和大小都相同。

Congruent means the same shape and the same size

等边三角形可以有不同边长。

Equilateral triangles can have different side lengths

边长为

1

和边长为

2

的等边三角形形状相同但大小不同，所以它们相似但不全等。每个等边三角形都是凸的、等角的（每个角都是

60^\circ

），也是正多边形，因此唯一错误的命题是所有等边三角形都彼此全等。

所以正确答案是 A。

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.

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