1. 3.5 Notes: Proving Lines Parallel
For which of the theorems involving parallel lines and transversal is the converse true?

2. Vocab!
Converse
 Switching the hypothesis and conclusion of a conditional statement.   
What is the Corresponding Angles theorem?
 If p ||q, then ∠1 ≅ ∠3, ∠2 ≅ ∠4, ∠8 ≅ ∠6, ∠5 ≅ ∠7
Converse of Corresponding Angles Theorem  
 If ∠1 ≅ ∠3, ∠2 ≅ ∠4, ∠8 ≅ ∠6, ∠5 ≅ ∠7, then p ||q p q
Use this figure to understand all new definitions. 1 2 3 r 4 8 7 6 5

3. Vocab! If p ||q, then ∠3 ≅ ∠7, ∠2 ≅ ∠6 If ∠3 ≅ ∠7, ∠2 ≅ ∠6, then p ||q  
What is the alternate interior angles theorem?
 If p ||q, then ∠3 ≅ ∠7, ∠2 ≅ ∠6
Converse of Alternate Interior Angles Theorem
 If ∠3 ≅ ∠7, ∠2 ≅ ∠6, then p ||q
What is the alternate exterior angles theorem? 
 If p ||q, then ∠1 ≅ ∠5, ∠4 ≅ ∠8
Converse of Alternate Exterior Angles Theorem
 If ∠1 ≅ ∠5, ∠4 ≅ ∠8, then p ||q

4. Vocab! If p ||q, then ∠2 ≅ ∠3, ∠6 ≅ ∠7 If ∠2 ≅ ∠3, ∠6 ≅ ∠7, then p ||q
What is the consecutive interior angles theorem?
 If p ||q, then ∠2 ≅ ∠3, ∠6 ≅ ∠7
Converse of Consecutive Interior Angles Theorem
 If ∠2 ≅ ∠3, ∠6 ≅ ∠7, then p ||q
Parallel Postulate
 If p ⊥ q & q ⊥ r, then p || q

5. Example 1
Use the diagram to the right a) Given ∠1 ≅ ∠ 3, is it possible to prove that any of the lines shown are parallel? If so, state the postulate or theorem that justifies your answer. Yes, a || b because of the converse of corresponding angles theorem b) Given m ∠ 1 = 103 and m ∠ 4 = 100, is it possible to prove that any of the lines shown are parallel? If so, state the postulate or theorem that justifies your answer No it is not possible, we do not have enough information.

6. Example 2
Given ∠ 1 ≅ ∠ 5, is it possible to prove that any of the lines shown are parallel? l || n

7. You Try! Find m ∠ ZYN so that 𝑃𝑄 || 𝑀𝑁 . Show your work.
Converse of the alternate exterior angles theorem
11𝑥 −25=7𝑥+35
𝑥=15

8. Converse of the alternate interior angles theorem
You Try!
2. Find x so that 𝐺𝐻 || 𝑅𝑆
Converse of the alternate interior angles theorem
9𝑥−21=7𝑥−3

9. Do on your own!
16. Name 4 pair of alternate-interior angles. 17. Name 4 pair of alternate-exterior angles. 18. Name 8 pair of corresponding angles. 19. Name 8 pair of vertical angles. 20. How many linear pair angles are there in this diagram? 22. Name 2 pair of non-vertical, equal angles from the diagram. 23. Name 2 pair of angles that are supplementary but are NOT linear pairs.