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Unformatted text preview: (9-3 The Parallel Postulate)
A) Existence vs. Uniqueness of parallels a. To start chapter 9 we proved that parallels exist
b. In order to present the converses of the theorems in the preceding sections we must state uniqueness of parallels B) Postulate 18 (The Parallel Postulate) a. Through a given external point there is only one parallel to a given line. i. C) Theorem 9-9 (The PAI Theorem) a. If two parallel lines are cut by a transversal, then alternate interior angles are congruent D) Corollary 9-9.1 (The PCA Corollary) a. If two parallel lines are cut by a transversal, each pair of corresponding angles are congruent b. E) Corollary 9-9.2 a. If two parallel lines are cut by a transversal, the interior angles on the same side of the transversal are supplementary b. F) Theorem 9-10 a. In a plane, if a line intersects on of two parallel lines in only one point, then it intersects the other i. G) Theorem 9-11 a. In a plane, if two lines are each parallel to a third line, then they are parallel to each other. H) Theorem 9-12 a. In a plane, if a line is perpendicular to one of two parallel lines it is perpendicular to the other i. Example) ...
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- Spring '09
- Algebra, Euclidean geometry, Mathematical terminology, Axiom