AMC8 2015
AMC8 2015 · Q12
AMC8 2015 · Q12. It mainly tests Basic counting (rules of product/sum), Geometry misc.
How many pairs of parallel edges, such as $\overline{AB}$ and $\overline{GH}$ or $\overline{EH}$ and $\overline{FG}$, does a cube have?
一个立方体有多少对平行边，例如 $\overline{AB}$ 和 $\overline{GH}$ 或 $\overline{EH}$ 和 $\overline{FG}$？
(A)
6
6
(B)
12
12
(C)
18
18
(D)
24
24
(E)
36
36
Answer
Correct choice: (C)
正确答案：（C）
Solution
Each of the 12 edges is parallel to 3 other edges giving 36 possible pairs of parallel edges. But each pair of parallel edges is counted twice in this process, so there are 18 pairs of parallel edges.
12 条棱中的每一条都与另外 3 条棱平行，因此共有 36 对平行的棱。但在这个过程中每一对平行棱被计算了两次，所以共有 18 对平行棱。
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