Definitions, Postulates, and Theorems Relating to Parallelism
Two lines are
skew
lines if they do not lie in the same plane. Two lines are
parallel
lines if they are coplanar and they do not intersect.
Parallel Postulate:
Through a point not on a given
line there is only one parallel
to that line.
A
transversal
of two coplanar lines is a line which intersects them in different
points.
If two parallel lines are cut by a transversal, then the corresponding angles
formed are congruent.
If two parallel l
ines are cut by a transversal, then the alternate interior angles
formed are congruent.
If two parallel lines are cut by a transversal, then the alternate exterior angles
formed are congruent.
If two parallel lines are cut by a transversal, then the same

side interior
angles formed are supplementary.
If two parallel lines are cut by a transversal, then the same

side exterior
angles formed are supplementary.
If two lines are cut by a transversal so that corresponding angles are
congruent, then the lines
are parallel.
If two lines are cut by a transversal so that alternate interior angles are
congruent, then the lines are parallel.
If two lines are cut by a transversal so that alternate exterior angles are
congruent, then the lines are parallel.
If two
lines are cut by a transversal so that same

side interior angles are
supplementary, then the lines are parallel.
If two lines are cut by a transversal so that same

side exterior angles are
supplementary, then the lines are parallel.
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