This document discusses properties of parallel lines cut by a transversal. It introduces two postulates about corresponding angles being congruent if lines are parallel, and lines being parallel if corresponding angles are congruent. It then presents four theorems: if alternate interior angles or same-side interior angles of two lines cut by a transversal are congruent/supplementary, the lines are parallel; and if two lines are perpendicular to the same line, they are parallel. Finally, it lists five ways to prove two lines are parallel using the previous postulates and theorems.

1. 3-3 Properties of Parallel
Lines

2. Postulates
 Postulate 10
If two parallel lines are cut by a
transversal, then corresponding angles are
congruent.
 Postulate 11
If two lines are cut by a transversal and
corresponding angles are congruent, then
the lines are parallel.

3. Theorem 3-5
If two lines are cut by a transversal and
alternate interior angles are
congruent, then the lines are parallel.

4. Theorem 3-6
If two lines are cut by a transversal and
same-side interior angles are
supplementary, then the lines are
parallel.

5. Theorem 3-7
In a plane two lines perpendicular to the
same line are parallel.

6. Ways to Prove Two Lines
Parallel
1. Show that a pair of corresponding angles
are congruent.
2. Show that a pair of alternate interior angles
are congruent.
3. Show that a pair of same-side interior
angles are supplementary.
4. In a plane show that both lines are
perpendicular to a third line.
5. Show that both lines are parallel to a third
line.