AMC12 2003 B

AMC12 2003 B · Q10

AMC12 2003 B · Q10. It mainly tests Casework, Transformations.

Several figures can be made by attaching two equilateral triangles to the regular pentagon ABCDE in two of the five positions shown. How many non-congruent figures can be constructed in this way?

在图示的五个位置中选取两个位置，把两个等边三角形分别贴在正五边形 $ABCDE$ 上，可以构成若干图形。用这种方式能构造出多少个互不全等的图形？

(A) 1 1

(B) 2 2

(D) 4 4

(E) 5 5

Answer

Correct choice: (B)

正确答案：（B）

Solution

Place the first triangle. Now, we can place the second triangle either adjacent to the first, or with one side between them, for a total of $\boxed{\text{(B) }2}$

先放置第一个三角形。接着放置第二个三角形时，它要么与第一个相邻，要么与第一个之间隔着一条边，因此共有 $\boxed{\text{(B) }2}$ 种。

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