What methods can prove two planes are parallels ?

Two lines are a1x+b1y+c1 = 0 and a2x+b2y+c2 are
parallel

if a1/a2 = a2/b2 in a plane or 2
dimension.

Two planes a1x+b1y+c1z+d1 = 0
and

a2x+b2y+c2z+d2 = 0  are parallel if a1/a2= b1/b2= c1/c2
i a 3 dimenssional space or solilid geometry.

So the above
condition proves the planes are parallel.

Also like
parallel straight keeps a constant distance between them, the parallel planes also
maintain a constant distance between them.

The perpendiculr
to the parallel planes  are also parallel.