AMC 8 2009 Problem 20
AMC8 2009 年第 20 题
三角形★★★☆☆
How many non-congruent triangles have vertices at three of the eight points in the array shown below?
以下图所示阵列 8 个，点中的 3 个为顶点，可以形成多少个不全等的三角形？
- A.5
- B.6
- C.7
- D.8
- E.9
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
Assume the base of the triangle is on the bottom four points because a congruent triangle can be made by reflecting the base on the top four points. For a triangle with a base of length 1, there are 3 triangles. For a triangle with a base of length 2, there are 3 triangles. For length 3, there are 2. In total, the number of non-congruent triangles is 3+3+2=8.
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