1991 AMC 12 第 4 题
先试着解答 1991 AMC 12 第 4 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1991 AMC 12 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
4.
下列哪一种三角形不可能存在？
Which of the following triangles cannot exist?
锐角等腰三角形
An acute isosceles triangle
等腰直角三角形
An isosceles right triangle
钝角直角三角形
An obtuse right triangle
不等边直角三角形
A scalene right triangle
不等边钝角三角形
A scalene obtuse triangle
答案：C
小提示：
直角三角形已经有一个 角
A right triangle already contains an angle of
大提示：
钝角三角形必须有一个大于 的角
An obtuse triangle must contain an angle greater than
解答：
直角三角形有一个 角，另外两个正角之和只有 。所以另外两个角都不可能是钝角，三角形不可能既是直角三角形又是钝角三角形。
因此正确答案为 C。
A right triangle has one angle, leaving only for its other two positive angles together. Neither remaining angle can therefore be obtuse. Hence a triangle cannot be both right and obtuse.
Thus the correct answer is C.
其他年份的第 4 题
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