1951 AMC 12 第 29 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。
29.
下列各组数据中，唯一不能确定三角形形状的是：
Of the following sets of data, the only one that does not determine the shape of a triangle is:
两边之比及其夹角
The ratio of two sides and the included angle
三条高之比
The ratios of the three altitudes
三条中线之比
The ratios of the three medians
一条高与其对应底边之比
The ratio of the altitude to the corresponding base
两个角
Two angles
小提示：
确定形状，是指在相似意义下确定三角形
Determining shape means determining the triangle up to similarity
大提示：
单独一个高与底边之比只固定一种面积比例，但不同形状的三角形可以具有相同的这一比值
A single altitude-to-base ratio fixes an area ratio but can occur in differently shaped triangles
解答：
选项 A 和 E 可在相似意义下确定各角。三条高之比确定相应边长的倒数之比，三条中线之比也能确定边长之比。但仅有一个比值 ，无法确定其余边长或角；许多不相似的三角形都可以具有这一比值。
因此，正确答案是 D。
Choices A and E determine the angles up to similarity. Ratios of all three altitudes determine reciprocal side ratios, and ratios of all three medians determine side ratios. But a single ratio does not determine the remaining side lengths or angles; many non-similar triangles can share it.
Thus, the correct answer is D.
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