1. 3.5 Proving Lines Parallel
Then: You used slope to identify parallel and perpendicular lines.
Now: Recognize angle pairs that occur with parallel line.
2. Prove that two lines are parallel.
Review Converse: exchange the hypothesis and conclusion of a conditional statement.
What is the converse of the following?
If it is raining, then Josh needs an umbrella.

2. Postulate 3.4 Converse of Corresponding Angles
If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. If 2  6, then j k.

3. Theorem 3.5 Alternate Exterior Angles Converse
If two lines in a plane are cut by a transversal so that a pair of alternate exterior angles is congruent, then the lines are parallel.
If 1  8, then j k.

4. Theorem 3.6 Consecutive Interior Angles Converse
If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel.
If m3 +m5 = 180,
then j k.

5. Theorem 3.7 Alternate Interior Angles Converse
If two lines in a plane are cut by a transversal so that a pair alternate interior angles is congruent, then the lines parallel.
If 4  5, then j k.

6. Theorem 3.8 Perpendicular Transversal Converse
In a plane, if two lines are perpendicular to the same line, then they are parallel. If k  t, and l  t, then k  l.

7. Example 1:
Given the following information, determine which lines, if any, are parallel. State the postulate or theorem to justify your answer. a.  3   7 b.  9   11 c.  2   16 d. m 5 + m 12 = 180

8. Example 2:
Find the value of x that makes l  m. Identify the postulate or theorem you used. a.

9. Example 2:
Find the value of x that makes l  m. Identify the postulate or theorem you used. b.

10. Example 2 cont.
Find the value of x that makes l  m. Identify the postulate or theorem you used. c.

11. Example 3: Proof 1
Given:  1  5,  15  5 Prove: l  m, r  s Statements Reasons 1.  15  5 1. _______________________ 2.  13  15 2. _______________________ 3.  5  13 3. _______________________ 4. r  s 4. _______________________ 5.  1  5 5. _______________________ 6. l  m 6. _______________________

12. Example 3: Proof 2
Given: 1 and 2 are complementary BC  CD Prove: BA  CD Statements Reasons 1. BC  CD 1. __________________________ 2. mABC = m  1 + m  2 2. __________________________ 3. 1 and 2 are complementary 3. __________________________ 4. m  1 + m  2 = __________________________ 5. mABC = __________________________ 6. BA  BC 6. __________________________ 7. BA  CD 7. __________________________

13. 3.5 Assignment #8-22 evens, 26,28, 33-35, 44-50 evensp
#8-22 evens, 26,28, 33-35,
44-50 evens
Proofs #26 & 28- on handout