2.3 Proving Lines Parallel Review of Previous Postulates If two parallel lines are cut by a transversal: Postulate 11: …then the corresponding angles are congruent. Theorem 2.1.2:…then the alternate interior angles are congruent., Theorem 2.1.3: …then the alternate exterior angles are congruent. Theorem 2.1.4:.. then the interior angles on the same side of the transversal are supplementary Theorem 2.1.5:…then the exterior angles on the same side of the transversal are supplementary. 5/30/2019 Section 2.3 Nack

Theorems for Proving Two lines are Parallel It two lines are cut by a transversal so that: Theorem 2.3.1: … the alternate interior angles are congruent, then these lines are parallel. p.86 Theorem 2.3.2: … the alternate interior angles are congruent, then these lines are parallel.p. 87 Theorem 2.3.3: …the alternate exterior angles are congruent, then these lines are parallel. Theorem 2.3.4:…the interior angles on the same side of the transversal are supplementary, then these lines are parallel. Ex.3 p.88 5/30/2019 Section 2.3 Nack

Theorems for Proving Two lines are Parallel continued Theorem 2.3.5: …the exterior angles on the same side of the transversal are supplementary, then these lines are parallel. Theorem 2.3.6: If two lines are each parallel to a third line, then these lines are parallel to each other. Theorem 2.3.7: If two coplanar lines are each perpendicular to a third line, then these lines are parallel to each other. Ex. 5 and 6 p.89-90 5/30/2019 Section 2.3 Nack

Constructing a line parallel to a given line from a point not on that line. Draw a line to intersect the given line. This will be the transversal. 2. Choose a point on the transversal and construct an angle congruent to the angle the transversal makes with the first line. A B  1 2  P 5/30/2019 Section 2.3 Nack