Proving lines parallelChapter 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

lm

p

If p l and p m then l II m

Example 1Given 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 anglesNone (just vertical angles)

r 11 s; converse alt. int. anglesr 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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