Section 3.2: Proving Lines Parallel

1. Section 3.2: Proving Lines Parallel Objectives: Use a transversal to prove lines are parallel Relate parallel and perpendicular lines

2. What is the converse of this statement? If a transversal intersects 2 parallel lines, then corresponding angles are congruent.

3. Postulate 3-2 Converse of the Corresponding Angles Postulate • If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel.

4. Write the converse: If a transversal intersects 2 parallel lines, then alternate interior angles are congruent.

5. Theorem 3-3 Converse of the Alternate Interior Angle Theorem • If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel. If , then line1llline2

6. Write the converse: If a transversal intersects 2 parallel lines, then same side interior angles are supplementary.

7. Theorem 3-4 Converse of the Same-Side Interior Angles Theorem • If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel. If are supplementary, then mlln

8. Which lines or segments are parallel? How do you know?? 1. 2. C H e 45° 45° M A R g c b

9. Which segments are parallel? J K L O N M

10. Theorem 3-5 • If two lines are parallel to the same line, then they are parallel to each other. allb * Lines can be coplanar or noncoplanar

11. Theorem 3-6 • In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. klll

12. In City Hall, Corridor 1 and Corridor 2 are both perpendicular to Corridor 3. What can you say about corridor 1 and corridor 2?

13. Solve for x and then solve for each angle such that n ll m n 14 + 3x 5x- 66 m

14. Find the value of x so that m||n. 62 m 7x - 8 n 1

15. Proof: Given Prove: n ll m 3 n 5 m 7 StatementsReasons 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. 6. n ll m 6.