Geometry Postulates and Theorems
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If two parallel lines are intersected by a transversal
then alternate interior angles are congruent.
In a plane if two lines are both perpendicualar to a third line,
then the two lines are parallel.
If two parallel lines are intersected by a transversal
then same-side interior angles are supplementary.
If two lines are both parallel to a third line,
then the two lines are parallel.
If two lines are intersected by a tranversal and alternate interior angles are congruent,
then the lines are parallel.
If two parallel lines are intersected by a third line,
then the lines of intersection are parallel.
If two lines are intersected by a tranversal and same-side interior angles are supplementary
then the lines are parallel.
If two planes are both parallel to a third plane,
then the two planes are parallel.