**Geometry 3.3 Parallel Lines and Transversals**

**I) Vocabulary:**

A) Transversal: A line that intersects 2 lines at different places.

II) Postulate:

A) If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

B) If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.

C) If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

D) If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

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

**II) Converse of above:**

A) If 2 lines are cut by a transversal such that the corresponding angles are congruent, then the lines are parallel.

B) if 2 lines are cut by a transversal such that the pairs of consecutive interior angles are supplementary, then the lines are parallel.

C) if 2 lines are cut by a transversal such that the pairs of alternate exterior angles are congruent, then the lines are parallel.

D) if 2 lines are cut by a transversal such that the pairs of alternate interior angles are congruent, then the lines are parallel.

**III) Using Properties of Parallel lines:**

A) if two lines are parallel to the same line, then they are parallel to each other.

B) In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.