Criteria of parallelism of straight line and plane:
1) If a straight line, lying out of plane, is parallel to
some straight line, lying in the
plane, then it is parallel to this plane.
2) If a straight line and a plane are perpendicular to
the same straight line, then they
are parallel.
Criteria of parallelism of planes:
1) If two intersecting straight lines of the same plane
are parallel correspondingly to
two intersecting straight lines of other plane, then
these planes are parallel.
2) If two planes are perpendicular to the same straight
line, then they are parallel.
Criteria of perpendicularity of straight line and
plane:
1) If a straight line is perpendicular to two interesting
straight lines, lying in a plane,
then it is perpendicular to this plane.
2) If a plane is perpendicular to one of parallel
straight lines, then it is perpendicular
to the other.
Straight line inclined to plane.
A straight line, intersecting a plane and not perpendicular
to it, is called a straight line inclined to plane.
Theorem about three perpendiculars.
A straight line, that lies in a plane and is perpendicular to a projection of
straight line inclined to this plane, is perpendicular to this straight line
inclined to plane.
Criteria of parallelism of straight lines in a space.
1) If two straight lines are perpendicular
to the same plane, then they are parallel.
2) If a straight line lies in one of interesting planes
and it is parallel to another plane,
then it is parallel to line of intersection of these
planes.
Criterion of perpendicularity of planes:
if a plane goes through a straight line that is
perpendicular to another plane, then these planes are perpendicular.
Theorem about common perpendicular to two crossing
straight lines.
Any two crossing straight lines have the only
common perpendicular.
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