ADVANCED GEOMETRY 5 2 Proving Lines Parallel THEOREM

ADVANCED GEOMETRY 5. 2 Proving Lines Parallel

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 ? ⁰ 110⁰ 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 1 2 l m || lines If then l ||m.

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

Theorem 33: If two lines are cut by a transversal such that two corresponding angles are congruent, the lines are parallel. Abbreviate: Corr 1 || lines l If 5 m then l || 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: Abbreviate Same side int ⦞ supp ⇒ || lines If 3 5 then a|| b. a b

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. a 1 If 7 b are supp, then a||b.

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