P is a point outside the parallelogram ABCD, and Q is the midpoint of PA

P is a point outside the parallelogram ABCD, and Q is the midpoint of PA

It is proved that: as shown in the figure, connecting AC with BD is O, ∵ ABCD is a parallelogram, ∵ Ao = OC, that is, O is the midpoint of AC, connecting OQ, then OQ ⊂ plane bdq, and OQ is the median line of △ APC, ∥ PC ∥ OQ, and PC is outside the plane bdq, ∥ PC ∥ plane bdq