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High school mathematics point, line and surface proof problem,
Because: cube, q is the midpoint on BD.

So: A, Q and C are on a line, and Q is the midpoint of AC.

And because: p is the midpoint of AD 1

So PQ is the center line of triangle ACD 1, that is, PQ∑CD 1.

So the PQ parallel plane DCC 1D 1