Lesson 3.3 – 3.4: Proving Lines Parallel

Converse Transversal Theorems Conv. of Corr. ∠s Postulate: Conv. of Alt. Int. ∠s Thm: Conv. of Alt. Ext. ∠s Thm: Conv. of Same Side Int. ∠s Thm: Conv. of Same Side Ext. ∠s Thm:

Practice Based upon each statement, which two lines are parallel? 1) ∠1 ≅ ∠9 2) ∠3 is suppl. to ∠2 3) ∠6 ≅ ∠16 m n 1 2 3 4 _ 5 6 7 8 9 10 11 12 13 14 15 16 a b

SOL Question

Practice Given m ⃦n, ∠2 ≅ ∠4 Prove: a ⃦b Statements Reasons 1) m ⃦n 2) ∠1 ≅ ∠2 3) ∠2 ≅ ∠4 4) ∠1 ≅ ∠4 5) a ⃦b m n 1 2 _ 4 3 a b

Proofs Writing proofs: Two-column proofs: First step: Final step:

Postulates vs. Theorems

Practice Prove the Alt. Int. ∠s Thm. Given: a||b Prove: ∠3 ≅ ∠6 a 3 b 7

Practice Prove the Same Side. Ext. ∠s Thm. Given: a||b Prove: ∠1 and ∠7 are supplementary. 1 a b 5 7

 Practice

|| and ⊥ Lines Multiple Parallels Thm: Perpendicular Transversal Thm:

Practice Prove the Multiple Parallels Thm. Given: r || s s || t Prove: r || t r s t

Practice Prove the Perpendicular Transversal Thm. Given: AB, a ⊥ b and a ⃦ c. Prove: b ⊥ c b 1 a 2 c

Classwork Lesson 3.3, #1 – 7. Note, for #7 use a two-column proof.

Homework 10/3: Lesson 3.3, #13 – 33 odd Read Lessons 3.5 – 3.6