# 3.1-3.3 Postulates and Theorems

Postulate:

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

Postulate:

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

Theorem

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

Theorem

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

Theorem

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

Theorem

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line as well

Theorem

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

Theorem

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

Theorem

In a plane, two lines perpendicular to the same line are parallel

Postulate

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

Postulate

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

Theorem

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