1. 3.5 Proving Lines Parallel What you’ll learn: 1.To recognize angle conditions that occur with parallel lines. 2.To prove two lines are parallel based on given angle relationships.

2. Ways to prove that 2 lines are parallel 1.Postulate 3.4 If 2 lines in a plane are cut by a transversal so that corresponding  are,  then the lines are parallel. 2.Thm 3.5 If alt. ext.  s are , then the lines are parallel. 3.Thm 3.6 If cons. int.  s are supplementary, then the lines are . 4.Thm. 3.7 If alt. int.  s are , then the lines are parallel. 5.If 2 lines are  to the same line, the lines are .

3. Which lines, if any are parallel? Find x and m  ZYN so that the lines are parallel 103  77  100  Z YN 11x-25 7x+35

4. From the given information, determine which lines are parallel. State the postulate or theorem that justifies your answer. 1.  13  2 a  b,  alt. ext.  s 2.  11  8 a  b,  alt. int.  s 3.  2  4 m  n,  corres.  s 4.  10+  11=180 m  n, supp. cons. int.  s 1 2 34 5 6 7 8 910 11 12 13 14 1516 m b n a

5. Find x so that the lines are parallel. 1. 2. 3. 4. 3x+64x-6 10x-5 9x+1 8x+8 2x+12 5x-15

6. Write a 2-column proof Given:  1 and  3 are supplementary Prove: a  b 1.  1 and  3 are supplementary 2.  1 +  3 =180 3.  2 and  3 form a linear pair 4.  2 and  3 are supp. 5.  2+  3=180 6.  1+  3=  2+  3 7.  1=  3 8.a  b 1.Given 2. defn. supp. Angles 3.Given 4.Supp. Thm 5.Defn supp. Angles 6.Subs. 7.Subt. 8.If corres. Angles are congruent, then the lines are parallel 1 2 3 a b

7. Homework p. 155 14-30 even, 34-36 even,