2. Lesson 3-1 & 3-2 n Parallel Lines & Related Angles n Objective: To identify pairs of angles formed by two // lines & to prove lines are //

3. Parallel Lines n Are coplanar lines that DO NOT intersect. n Notation: // m Line m // Line n Remember: Slopes are the same! n

4. Transversal- defined A line that intersects two coplanar lines at two distinct points. Line t is the transversal of line m & n. m n t

5. Angles formed by a Transversal: Alternate Interior Angles: Same Side Interior Angles: Corresonding Angles: angles that lie on the same side of the transversal and in the same position in relation to the lines that the transversal intersects. Alternate Exterior Angles: Same Side Exterior Angles: Interior Angles- angles formed in between the lines & the transversal. Exterior Angles- angles formed outside the lines & the transversal. 12 34 56 78 t

6. Try This… Name a pair of alternate interior angles ab w yz x cd Name a pair of same side interior angles Name a pair of same side exterior angles Name a pair of corresponding angles

7. Visualize e f h g l m o n Name a pair of alternate interior angles Name a pair of same side interior angles Name a pair of same side exterior angles Name a pair of corresponding angles

8. Draw 2 parallel lines & a Transversal. Measure each angle. 12 34 56 78 Conjecture about Corresponding Angles? Conjecture about Alternate Interior Angles? Conjecture about Same Side Interior Angles? <1 = 100<5 <2<6 <3<7 <4<8

9. Corresponding Angle Postulate (fact): If 2 // lines are cut by a transversal then the corresponding angles are =. 12 34 56 78 l m t If l // m then:

10. Try This 2x - 6 30

11. Alternate Interior Angle Theorem. If 2 // lines are cut by a transversal then the alternate interior angles are =. Proof: Given l // m, prove that <3 = <6 Statements: 1. l // m 2. <2 = <6 3. < 2 = <3 4. <3 = < 6 Reasons: 1. Given 2. Corresponding <s = 3. Vertical <s = 4. Substitution (AIA Theorem) 12 34 56 78 l m

12. Try This 2x - 20 50

13. Same Side Interior Angles Theorem If 2 // lines are cut by a transversal then the same side interior angles are supplementary. Proof: Given l // m, prove that <4 & <6 are supplementary 12 34 56 78 Statements: 1. l // m 2. <2 + <4 = 180 3. < 2 = <6 4. <6 + <4 = 180 5. <4 & <6 are supplementary Reasons: 1. Given 2. Angle Addition 3. Corresponding <s = 4. Substitution 5. Definition of supplementary angles l m

14. Try This 130 a b c d e f g So…Alternate Exterior Angles are = too! Same Side Exterior Anges are supplementary!

15. To Prove that lines are //. 1.Corresponding Angles 2.Alternate Interior Angles 3.Alternate Exterior Angle 4.Same Side Interior Angles 5.Same Side Exterior Angles

16. Using Our Algebra Skills! Determine X so that the lines are parallel. 5x + 5 11x + 15

17. 3x + 20 5x - 32 Determine X so that the lines are parallel.

18. 11x + 5 4x + 10 Determine X so that the lines are parallel.

19. Check yourself on set up! Determine X so that the lines are parallel. 3x - 15 2x + 7