1959 AMC 12 第 3 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
3.
若一个四边形的两条对角线互相垂直，则该图形一定属于下列哪一大类：
If the diagonals of a quadrilateral are perpendicular to each other, the figure would always be included under the general classification:
菱形
rhombus
矩形
rectangle
正方形
square
等腰梯形
isosceles trapezoid
以上都不是
none of these
小提示：
找一个对角线垂直、但不属于前四种特殊类型的四边形
Look for a quadrilateral with perpendicular diagonals that is not one of the four named special types
大提示：
一般的筝形可作为反例
A general kite supplies a useful counterexample
解答：
筝形的对角线可以互相垂直，但它未必是菱形、矩形、正方形或等腰梯形。因此，仅有对角线垂直这一条件不能保证它属于前四类中的任何一类。
因此，正确答案是 E。
A kite can have perpendicular diagonals without being a rhombus, rectangle, square, or isosceles trapezoid. Therefore perpendicular diagonals alone do not force any of the first four classifications.
Thus, the correct answer is E.
其他年份的第 3 题
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