3.4; 16-42 Even 16. 110 18. 50 20. 127 22. 131 24. 60 26.m<1=135: Corr. Angles Theorem m<2=135: Vertical Angles Theorem 28. m<1=118: Alternate Interior Angles Theorem m<2=62: Same-side Interior Angles Theorem 30. 103 32. 35 34. 10 36. 7 38. See board 40. See board 42. J

3.5 Showing Lines are Parallel Goal: Show that two lines are parallel.

Key words Converse Statement: Reversing the hypothesis and conclusion in an If-Then statement. Statement: If you live in Mt. Laurel, then you live in New Jersey. Converse: If you live in New Jersey, then you live in Mt. Laurel.

Write the Converse of an If-Then Statement If two segments are congruent, then the two segments have the same length. What is the converse? If two segments have the same length, then they are congruent. Is this true? YES!

Postulate 9 Corresponding Angles Converse If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. t 1 2 r 3 4 5 6 s 7 8 If , then

Apply Corresponding Angles Converse Is enough information given to conclude that lines are parallel? Explain.

Theorem 3.8 Alternate Interior Angles Converse If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel. t 1 If , then 2 r 3 4 5 6 s 7 8

Theorem 3.9 Alternate Exterior Angles Converse If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel. t 1 If , then 2 r 3 4 5 6 s 7 8

Identify Parallel Lines Does the diagram give enough information to conclude that lines are parallel? Explain.

Theorem 3.10 Same-side Interior Angles Converse If two lines are cut by a transversal so that same-side interior angles are supplementary, then the lines are parallel. t 1 If , then 2 r 3 4 5 6 s 7 8

Use same-side interior angles converse Find the value of x so that lines are parallel.

Homework 3.5 pg. 140 6-28 Even