1. Lesson 3.3 – 3.4: Proving Lines Parallel

2. 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:

3. Practice
Based upon each statement, which two lines are parallel? 1) ∠1 ≅ ∠9 2) ∠3 is suppl. to ∠2 3) ∠6 ≅ ∠16
m n _ a b

4. SOL Question

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

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

7. Postulates vs. Theorems

8. Practice Prove the Alt. Int. ∠s Thm. Given: a||b Prove: ∠3 ≅ ∠6 a 3 b7

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

10. 
Practice

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

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

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

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

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