Proving lines parallel Chapter 3 Section 5

converse corresponding angles postulate If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel If <1 = <5, <3 = <7, <2 = <6, and <4 = <8, then l II m

converse alternate ext. angles theorem If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel. If <1 = <8 and <2 = <7, then l II m

converse alternate interior angles theorem If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel If <4 = <5 and <3 = <6, then l II m

converse same-side interior angles theorem If two lines are cut by a transversal so that same-side interior angles are supplementary, then the lines are parallel. If <3 + <5 = 180 and <4 + <6 = 180, then l II m

Perpendicular transversal converse If two lines are perpendicular to the same line, then they are parallel l m p If p l and p m then l II m

Example 1 Given the following information, determine which lines, if any, are parallel. State the postulate or theorem that justifies your answer. <3 = <7 <12 = <10 <3 = <9 <6 + <13 = 180 <9 + <10 = 180 <12 = <14 <4 = <10 l 11 m; converse corresponding angles None (just vertical angles) r 11 s; converse alt. int. angles r 11 s; converse S.S. int. angles None; (just a linear pair) l 11 m; converse alt. int. angles r 11 s; converse alt. ext. angles

example 2 Just solve these for x, like we did in 3-2

example proof Given vertical angles Transitive converse corr. angles <1 = <5 l 11 m

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