1. Proving Lines are Parallel Unit IC Day 12

2. Do now: Complete the statements If two parallel lines are cut by a transversal, then Corresponding angles are ____________ Alternate Interior angles are ___________ Alternate Exterior angles are ____________ Consecutive Interior angles are _____________

3. Conditional Statements and Converse Statements Conditional statement: has a hypothesis and a conclusion, often in “if-then” form. ◦ If [hypothesis], then [conclusion]. ◦ Example: If [it is Sunday], then [I don’t have school]. Converse: Switch the hypothesis and the conclusion. ◦ A true conditional statement may have a false converse! ◦ Example: If [I don’t have school], then [it is Sunday]. If the conditional statement and its converse are both true, then the statement is considered biconditional.

4. Corresponding Angles Converse (Postulate 16) If two lines are cut by a transversal so that corresponding angles are _____________, then the lines are _____________.

5. Alternate Interior Angles Converse (Thm. 3.8) If two lines are cut by a transversal so that alternate interior angles are __________, then the lines are ___________.

6. Consecutive Interior Angles Converse (Thm. 3.9) If two lines are cut by a transversal so that consecutive interior angles are ____________, then the lines are ____________.

7. Alternate Exterior Angles Converse (Thm. 3.10) If two lines are cut by a transversal so that alternate exterior angles are __________, then the lines are __________.

8. Note: Linear pairs and vertical angles have nothing to do with parallel lines! ◦ Angles making up a linear pair are always _________________. ◦ Vertical angles are always _____________.

9. Ex. 1: Proof of Alternate Interior Angles Converse

10. Ex. 2: Proving Lines are Parallel Note: Figure not drawn to scale.

11. Ex. 3: Proving Lines are Parallel

12. Ex. 4: Making Lines Parallel Fill in the blanks. Then solve the problem. The two angles labeled in the picture below are ________________ angles. In order for m to be parallel to n, the two angles must be ______________.

13. Ex. 5: Making Lines Parallel Find the value of x that would make j || k. Be able to justify your answer!

14. Ex. 6: Are the Lines Parallel? Be able to justify your answer!

15. Ex. 7: Challenge Problem Be able to justify your answer!