Proving Lines Parallel

Postulate 3-2: Converse of the Corresponding Angles Postulate If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

Theorem 3-4: Converse of the Alternate Interior Angles Theorem If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.

Postulate 3-6: Converse of the Alternate Exterior Angles Postulate If two lines are cut by a transversal and alternate exterior angles are congruent, then the lines are parallel.

Theorem 3-3: Converse of the Consecutive (Same-Side) Interior Angles Theorem If two lines are cut by a transversal and consecutive interior angles are supplementary, then the lines are parallel.

Consecutive Exterior Angles If two lines are cut by a transversal and consecutive exterior angles are supplementary, then the lines are parallel.

Examples: Proving Lines Parallel Find the value of x which will make lines a and lines b parallel. 2. 1. 3. 4. Answers: 1. 20° 2. 50° 3. 90° 4. 20°

Ways to Prove Two Lines Parallel Show that corresponding angles are equal. Show that alternative interior angles are equal. Show that consecutive interior angles are supplementary. Show that consecutive exterior angles are supplementary. In a plane, show that the lines are perpendicular to the same line.