
Concept explainers
Summarize the five methods used to prove that the two lines are parallel.

Explanation of Solution
Calculation : s t
Let l, m be lines , t is transversal such that :
- Alternate Exterior Angle Converse :
If two lines in a plane are cut by a transversal such that a pair of alternate exterior angles is congruent , then the lines are parallel.
t
Since ,
- Consecutive Interior Angles Converse :
If two lines in a plane are cut by a transversal such that a pair of consecutive interior angles is supplementary , then the lines are parallel.
t
Since ,
- Alternate Interior Angle Converse :
If two lines in a plane are cut by a transversal such that a pair of alternate interior angles is congruent , then the lines are parallel.
t
Since ,
- Converse of Corresponding angles Postulate :
If two lines in a plane are cut by a transversal such that corresponding angles are congruent , then they are parallel.
t
Since ,
- Perpendicular Transversal Converse :
In a plane , if two lines are perpendicular to the same line, then the two lines are parallel.
Since ,
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