Another example: take a right cylinder. Every tangent aircraft to the cylinder is parallel come the cylinder"s axis.
You are watching: Two lines parallel to a plane are parallel
Think in the floor of your room together the gray airplane and think in the wall of your room as the blue plane. The blue line will be the line in between the wall surface in prior of the wall blue and also the ceiling.
A very straightforward example is two different planes containing the exact same line: both are parallel to that line and to any type of other line parallel come it.
If friend take any type of two intersecting planes they will both it is in parallel come the line developed by their intersection, yet they can"t it is in parallel to each other since they intersect.
In the image above both planes space parallel to the line defined by point out A and also B.
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Because in three-dimensional space, the airplane that room anchored come a heat still have one an ext degree of freedom. They deserve to rotate approximately the line. Therefore the two planes that space parallel to the very same line can be at an infinite variety of angles to each other.
Making lines parallel in 3D is much easier than making planes parallel, since planes have extra dimension. You have the right to think that a airplane as one intersection of 2 lines.
So as you can see over there is one more line involved. Omitting that extra line is what renders your explain incomplete. Not necessarily false. It might still it is in true in one case out that infinity.
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If you had actually two lines crossing each various other (not have to at the ideal angle) and you had actually two planes that were parallel come both of the lines, climate you might guarantee the the two planes space parallel, because then you would have anchored both of the plane"s dimensions, not simply one.