2.3 Proving Lines Parallel Review of Previous Postulates

1. 2.3 Proving Lines ParallelReview 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. Section 2.3 Nack

2. 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 Section 2.3 Nack

3. 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 Section 2.3 Nack

4. 2 1   A B 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.  P Section 2.3 Nack