1. 5.2 Proving Lines Parallel
Advanced Geometry
5.2 Proving Lines Parallel

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

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