Question

一个立方体有多少对平行棱，例如 $\overline{AB}$ 和 $\overline{GH}$ ，或 $\overline{EH}$ 和 $\overline{FG}$ ？

How many pairs of parallel edges, such as $\overline{AB}$ and $\overline{GH}$ or $\overline{EH}$ and $\overline{FG},$ does a cube have?

$6$

$12$

$18$

$24$

$36$

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立方体有 $12$ 条棱。对任意一条棱，都有另外 $3$ 条棱与它平行。

这样每一对平行棱都被数了两次，所以平行棱对数为 $\dfrac{12\cdot3}{2}=18$ 。

所以正确答案是 C。

A cube has $12$ edges. For any edge, there are $3$ other edges parallel to it.

This counts each pair twice, once from each edge in the pair, so the number of pairs of parallel edges is $\dfrac{12\cdot3}{2}=18$ .

Thus, C is the correct answer.