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3.3 Prove Lines are Parallel Name __________________________________ Class Period _________ Is it possible to prove that lines p and q are parallel? If so, state the postulate or theorem that you would use. 1. 2. 3. ____________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________ Find the value of x that makes m ∥ n. 4. 5. 6. 7. 8. 9. In Problems 10 – 12, circle the word that best completes the statement. 10. If two lines are cut by a transversal so the alternate interior angles are ( congruent, complementary), then the lines are parallel. 11. If two lines are cut by a transversal so the consecutive interior angles are ( congruent, complementary), then the lines are parallel. 12. If two lines are cut by a transversal so the corresponding angles are ( congruent, complementary), then the lines are parallel. supplementary, supplementary, supplementary, 13. A garden has five rows of vegetables. Each row is parallel to the row immediately next to it. EXPLAIN why the first row is parallel to the last row. ___________________________________________________________________________________________________ ___________________________________________________________________________________________________ ___________________________________________________________________________________________________ ___________________________________________________________________________________________________ In Problems 14 – 18, complete the two column proof. Given: n ∥ m, 1 2 2x-Given, 1x-Alternate Interior Angles Theorem, Prove: p ∥ r 1x-Alternate Interior Angles Converse, Statements n ∥m Reasons 1x-Transitive Property 14. _________________________________________________________ 1 3 15. ___________________________________________________ 1 2 16. ___________________________________________________ 2 3 17. ___________________________________________________ p ∥r 18. ___________________________________________________ 19. Railroad Tracks- Two sets of railroad tracks intersect as shown. How do you know that line n is parallel to line m ? ___________________________________________________________________________________________ ___________________________________________________________________________________________ ___________________________________________________________________________________________ ___________________________________________________________________________________________