5.2 Proving Lines Parallel Advanced Geometry 5.2 Proving Lines Parallel

What other conclusions are possible? Theorem 30: The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle. ?⁰ Question! What other conclusions are possible? 60⁰ 120⁰ 50⁰ 130⁰ 110⁰ ?⁰ 70⁰ ?⁰

Theorem 31: If two lines are cut by a transversal such that two alternate interior angles are congruent, then the lines are parallel. Abbreviate: Alt int || lines If then l ||m. l 1 2 m

Theorem 32: If two lines are cut by a transversal such that two alternate exterior angles are congruent, the lines are parallel. Abbreviate: Alt ext || lines If then l || m. 8 l m 1

Theorem 33: If two lines are cut by a transversal such that two corresponding angles are congruent, the lines are parallel. Abbreviate: Corr || lines l 1 If then l || m. 5 m

Theorem 34: If two lines are cut by a transversal such that two interior angles on the SAME SIDE of the transversal are SUPPLEMENTARY, then the lines are parallel. Abbreviate: Same side int ⦞ supp ⇒ || lines If then a|| b. a 3 5 b

Abbreviate: Same side ext ∡‘s supp ⟹ || lines. Theorem 35: If two lines are cut by a transversal such that two exterior angles and the same side of the transversal are SUPPLEMENTARY, the lines are parallel. Abbreviate: Same side ext ∡‘s supp ⟹ || lines. If are supp, then a||b. a 1 7 b

Theorem 36: If two coplanar lines are PERPENDICULAR to a third line, they are parallel. Abbreviate: 2 coplanar lines ⏊ to a 3rd line ⇒ || If a ⏊ c and b ⏊ c, then a || b a b c

Homework Read Sample Problems 1 - 3 starting on p. 218 Assignment: p. 219 - 223 (1, 2, 4, 5, 7 - 9, 11, 13 – 19, 21 – 23)