∫N is the midpoint of a1c.

You MN⊥ plane A 1DC

∴ face A 1DC⊥ face AA 1D 1

MN∑ad 1

And MN crosses A 1C to n.

∴M is the midpoint of AB.

Still ~ ~

1. 1. Prove that NO, n and o are midpoint, NO//CD⊥AO, NO//AB//CD.

Because MN⊥ plane A 1DC, so MN⊥NO, from the above NO//AB//CD, it can be seen that AONM is the same plane, AO⊥CD and AO⊥AD, that is, AO⊥ plane A 1DC, so AO.

I can't help it, right ~ the second one is a bit messy ~ I ate too much on holiday ~ I lost all my knowledge ~