Postulates and Theorems related to parallel and perpendicular lines

Theorem 3-4

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also.

(Theorem 3-5) AIP

If two lines are cut by a transveral and alternate interior angles are congruent, then the lines are parallel

(Postulate 11) CAP

If two lines are cut by a transversal and corresponding angles are congruent then the lines are parallel.

(Theorem 3-6) SSIP

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

(Theorem 3-2) PAI

If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

(Postulate 10) PCA

If two parallel lines are cut by a transversal, then corresponding angles are congruent.

(Theorem 3-3) PSSI

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

Theorem 3-1

If two parallel planes are cut by a third plane, then the lines of intersection are parallel.

Theorem 3-7

In a plane, two lines perpendicular to the same line are paralell to each other

Theorem 3-8

Through a point outside the line, there is exactly one line parallel to the given line.

Theorem 3-9

Through a point outside the line, there is exactly one line perpendicular to the given line.

Theorem 3-10

Two lines parallel to a third line a parallel to each other