3.1 Parallel Lines & Transversals

1. 3.1 Parallel Lines & Transversals

2. Objectives: Objectives: • Prove and use results about parallel lines and transversals. • Use properties of parallel lines.

3. Corresponding s Post. • If 2  lines are cut by a transversal, then the pairs of corresponding s are . • i.e. If l m, then 12. 1 2 l m

4. Alternate Int. s Thm. • If 2  lines are cut by a transversal, then the pairs of alternate interior s are . • i.e. If l m, then 12. 1 2 l m

5. Statements l m 3  2 1  3 1  2 Reasons Given Corresponding s post. Vert. s Thm   is transitive Proof of Alt. Int. s Thm. 3 1 2 l m

6. Consecutive Int. s Thm(same-side interior) • If 2  lines are cut by a transversal, then the pairs of consecutive int. s are supplementary. • i.e. If l m, then 1 & 2 are supp. l m 1 2

7. Alternate Ext. s Thm. • If 2  lines are cut by a transversal, then the pairs of alternate exterior s are . • i.e. If l m, then 12. l m 1 2

8. Ex: Find: m1= m2= m3= m4= m5= m6= x= 1 125o 2 3 5 4 6 x+15o

9. Ex: Find: m1=55° m2=125° m3=55° m4=125° m5=55° m6=125° x=40° 1 125o 2 3 5 4 6 x+15o