No. Consider two adjacent faces on a cuboid. Both planes are parallel to the edge at which the intersect. But the fact that they do intersect illustrates that they are not parallel.
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Two planes intersect at a line
For two lines to be parallel they must have the same slope. A line parallel to a line with slope -2 would have a slope of -2.
line
boundary line
SOMETIMES. I just did that problem in my California geometry book. They can either be parallel or skew...making the answer sometimes.