What methods can prove two planes are parallels ?
The following techniques are used to prove that 2 planes P, Q are parallels:
- the result of (P) intersecting (Q) is null set, or the result of (P) intersecting (Q) = (P) = (Q).
- (P) and (Q) are parallels both with the same plane
- 2 concurrent lines, parallel with the (Q) plane, belong to the plan (P).
- (P) and (Q) are perpendicular to the same line.
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.