1. Proving Lines Parallel Section 3-2

2. Solve each equation. 1. 2x + 5 = 272. 8a – 12 = 20 3. x – 30 + 4x + 80 = 1804. 9x – 7 = 3x + 29 Write the converse of each conditional statement. Determine the truth value of the converse. 5. If a triangle is a right triangle, then it has a 90° angle. 6. If two angles are vertical angles, then they are congruent. 7. If two angles are same-side interior angles, then they are supplementary. Review:

3. Let’s review section 3-1. Corresponding Angles Postulate: If two parallel lines are cut by a transversal, then corresponding angles are congruent. Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then alternate interior angles are congruent. Same-Side Interior Angles Theorem: If two parallel lines are cut by a transversal, then same-side interior angles are supplementary. Similar Theorems for the Alternate Exterior Angles Theorem and the Same- Side Exterior Angles Theorem were mentioned.

4. The CONVERSES of all of these postulates and theorems are true!

5. CONVERSE OF: Corresponding Angles Postulate If CONVERSE of: If two parallel lines are cut by a transversal, then corresponding angles are congruent.

6. CONVERSE OF: Alternate Interior Angles Theorem If CONVERSE of: If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

7. CONVERSE OF: Same Side Interior Angle Theorem If CONVERSE of: If two parallel lines are cut by a transversal, then same-side interior angles are supplementary.

9. Here’s the Tricky Part! You need to remember which postulates/theorems were the originals and which ones are the converses. The originals start with: If two parallel lines are cut by a transversal, then... The converses start with: If ________ angles are ______, then the two lines must be parallel.

10. Let’s prove the Converse of the Alternate Interior Angles Theorem 1. 2. 3. 4.

11. Which lines, if any, must be parallel if m<1 = m<2? Which lines, if any, must be parallel if m<3 = m<4?

12. Find the value of x for which l || m.

13. Find the value of x for which a || b.

14. Two workers are painting lines for angled parking spaces. The first worker paints a line so that m<1 = 60. The second worker paints a line so that m<2 = 60. Explain why their lines are parallel. If the second workers uses <3, what should m<3 be for parallel lines? Explain.

15. Classwork:

16. Homework:

17. 1. 6 3 2. 1 and 4 are supplementary. 3. 2 4 4. Find the value of x for which a || b. 5. Find the value of x for which m || n. Suppose that m 1 = 3x + 10, m 2 = 3x + 14, and m 6 = x + 58 in the diagram above. Use the diagram and the given information to determine which lines, if any, are parallel. Justify your answer with a theorem or postulate.