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.
