1. 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 :…then the exterior angles on the same side of the transversal are supplementary.
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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
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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
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4. 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
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