3-3 part 1 properties of parallel lines
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This document discusses properties of parallel lines cut by a transversal. It introduces two postulates about corresponding angles being congruent if lines are parallel, and lines being parallel if corresponding angles are congruent. It then presents four theorems: if alternate interior angles or same-side interior angles of two lines cut by a transversal are congruent/supplementary, the lines are parallel; and if two lines are perpendicular to the same line, they are parallel. Finally, it lists five ways to prove two lines are parallel using the previous postulates and theorems.
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3-3 part 1 properties of parallel lines
- 1. 3-3 Properties of Parallel Lines
- 2. Postulates Postulate 10 If two parallel lines are cut by a transversal, then corresponding angles are congruent. Postulate 11 If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.
- 3. Theorem 3-5 If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.
- 4. Theorem 3-6 If two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel.
- 5. Theorem 3-7 In a plane two lines perpendicular to the same line are parallel.
- 6. Ways to Prove Two Lines Parallel 1. Show that a pair of corresponding angles are congruent. 2. Show that a pair of alternate interior angles are congruent. 3. Show that a pair of same-side interior angles are supplementary. 4. In a plane show that both lines are perpendicular to a third line. 5. Show that both lines are parallel to a third line.