1951 AMC 12 第 27 题
先试着解答 1951 AMC 12 第 27 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 1951 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。
27.
过三角形内一点，从三个顶点分别向对边画直线，将原三角形分成六个三角形区域。则：
Through a point inside a triangle, three lines are drawn from the vertices to the opposite sides, forming six triangular sections. Then:
每一对相对的三角形都相似
The triangles are similar in opposite pairs
每一对相对的三角形都全等
The triangles are congruent in opposite pairs
每一对相对的三角形面积都相等
The triangles are equal in area in opposite pairs
形成三个相似的四边形
Three similar quadrilaterals are formed
以上关系均不成立
None of the above relations is true
小提示：
内点及三条顶点与对边相交的直线都是任意的
The interior point and the three cevians are arbitrary
大提示：
将该点移到非常靠近某一边的位置，检验所声称的相对区域面积关系
Move the point very close to one side to test the claimed opposite-area relation
解答：
题目没有给出任何角度或长度条件，足以保证相对区域相似或全等。它们的面积也不必相等：将内点放在非常靠近某一边的位置，可使邻接该边的区域任意小，却不会迫使其相对区域也变小。六个区域中也没有四边形。
因此，正确答案是 E。
No angle or length condition forces opposite sections to be similar or congruent. Their areas also need not match: placing the interior point very close to one side makes the sections adjoining that side arbitrarily small without forcing their opposite sections to be small. No quadrilaterals are among the six sections.
Thus, the correct answer is E.
其他年份的第 27 题
- 1950 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 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
- 1981 AMC 12
- 1982 AMC 12
- 1983 AMC 12
- 1984 AMC 12
- 1985 AMC 12
- 1986 AMC 12
- 1987 AMC 12
- 1988 AMC 12
- 1989 AMC 12
- 1990 AMC 12
- 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