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.
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 .
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
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 m b n a
Find x so that the lines are parallel x+64x-6 10x-5 9x+1 8x+8 2x+12 5x-15
Write a 2-column proof Given: 1 and 3 are supplementary Prove: a b 1. 1 and 3 are supplementary 2. 1 + 3 = 2 and 3 form a linear pair 4. 2 and 3 are supp. 5. 2+ 3= 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 a b
Homework p even, even,