Reasons Before we can prove that lines are parallel we need to add to our list of reasons. Corresponding Angles Postulate If two lines in a plane are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
There are several theorems that can be proven using the Corresponding Angles Postulate. If two lines in a plane are cut by a transversal so that a pair of alternate exterior angles is congruent, then the two lines are parallel.
To prove lines are parallel, you must use one of the following postulates or theorems: «If corresponding angles are , then the lines are parallel. «If AEA are , then the lines are parallel. «If AIA are , then the lines are parallel. «If CIA are supplementary, then the lines are parallel. You may also have to use the converse of a postulate or theorem to justify a statement.
Given: Prove: Use the original theorem. If AIA are , the lines are ||. Use the converse. If the lines are ||, AIA are .
More Theorems «If a line is perpendicular to one of two parallel lines, then it is perpendicular to the other. «If two lines are perpendicular to the same line, then the lines are parallel.