MathDB
Parallel Edges in a Cube

Source: 2015 AMC 8 #12

November 25, 2015
AMC 8geometry3D geometry

Problem Statement

How many pairs of parallel edges, such as AB\overline{AB} and GH\overline{GH} or EH\overline{EH} and FG\overline{FG}, does a cube have?
<spanclass=latexbold>(A)</span>6<spanclass=latexbold>(B)</span>12<spanclass=latexbold>(C)</span>18<spanclass=latexbold>(D)</span>24<spanclass=latexbold>(E)</span>36<span class='latex-bold'>(A) </span>6 \qquad<span class='latex-bold'>(B) </span>12 \qquad<span class='latex-bold'>(C) </span> 18 \qquad<span class='latex-bold'>(D) </span> 24 \qquad <span class='latex-bold'>(E) </span> 36
[asy] import three; currentprojection=orthographic(1/2,-1,1/2); /* three - currentprojection, orthographic */ draw((0,0,0)--(1,0,0)--(1,1,0)--(0,1,0)--cycle); draw((0,0,0)--(0,0,1)); draw((0,1,0)--(0,1,1)); draw((1,1,0)--(1,1,1)); draw((1,0,0)--(1,0,1)); draw((0,0,1)--(1,0,1)--(1,1,1)--(0,1,1)--cycle); label("DD",(0,0,0),S); label("AA",(0,0,1),N); label("HH",(0,1,0),S); label("EE",(0,1,1),N); label("CC",(1,0,0),S); label("BB",(1,0,1),N); label("GG",(1,1,0),S); label("FF",(1,1,1),N); [/asy]