3-2 Properties of Parallel Lines

Postulates Postulate 10 Postulate 11 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.

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

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

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

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