1956 AMC 12 第 26 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。
26.
下列哪一组已知条件不能唯一确定所指三角形？
Which one of the following combinations of given parts does not determine the indicated triangle?
底角和顶角；等腰三角形
base angle and vertex angle; isosceles
triangle
顶角和底边；等腰三角形
vertex angle and the base; isosceles triangle
外接圆半径；等边三角形
the radius of the circumscribed circle; equilateral
triangle
一条直角边和内切圆半径；直角三角形
one arm and the radius of the inscribed circle; right
triangle
两个角及其中一个角的对边；不等边三角形
two angles and a side opposite one of them; scalene
triangle
答案：A
小提示：
判断每组信息是否同时确定大小和形状
Ask whether each set of information fixes scale as well as shape
大提示：
若没有给出任何长度，两个角只能确定一类相似三角形
Two angles determine only a similarity class unless some length is also supplied
解答：
在等腰三角形中，一个底角和顶角可以确定三个角，但没有指定任何边长。因此，任意大小的相似三角形都满足同样的已知条件，三角形不能唯一确定。其余每个选项都直接给出或通过半径给出了足够的长度信息，可以同时确定大小和形状。
因此，正确答案是 A。
In an isosceles triangle, a base angle and the vertex angle determine all three angles, but no side length is specified. Therefore triangles of every scale have the same given data, so the triangle is not determined. Each other choice includes enough length information, directly or through a radius, to fix the scale as well as the shape.
Thus, the correct answer is A.
其他年份的第 26 题
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1957 AMC 12
- 1958 AMC 12
- 1959 AMC 12
- 1960 AMC 12
- 1961 AMC 12
- 1962 AMC 12
- 1963 AMC 12
- 1964 AMC 12
- 1965 AMC 12
- 1966 AMC 12
- 1967 AMC 12
- 1968 AMC 12
- 1969 AMC 12
- 1970 AMC 12
- 1971 AMC 12
- 1972 AMC 12
- 1973 AMC 12
- 1974 AMC 12
- 1975 AMC 12
- 1976 AMC 12
- 1977 AMC 12
- 1978 AMC 12
- 1979 AMC 12
- 1980 AMC 12
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- 1991 AMC 12
- 1992 AMC 12
- 1993 AMC 12
- 1994 AMC 12
- 1995 AMC 12
- 1996 AMC 12
- 1997 AMC 12
- 1998 AMC 12
- 1999 AMC 12