Introduction to Parallel Line Proofs

2-3 Proving Lines Parallel

Corresponding Angles Converse

If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
Example: 

If $<1\cong<5$ , then  $line\ l\ \parallel\ line\ m$   

Alternate Interior Angles Converse

If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.
Example: 

If $<4\cong<6$ , then  $line\ l\ \parallel\ line\ m$   

Alternate Exterior Angles Converse

If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
Example: 

If $<2\cong<8$ , then  $line\ l\ \parallel\ line\ m$   

Consecutive Interior Angles Converse

If two lines are cut by a transversal so that corresponding angles are supplementary, then the lines are parallel.
Example: 

If $<4+<5=180\degree$ , then  $line\ l\ \parallel\ line\ m$