MATH-UA 121 Lecture Notes - Lecture 12: Internal And External Angles, Parallel Postulate, Transitive Relation

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Parallel lines are two lines in the same plane that share no points in common (do not intersect. ) Alternate interior angles, on diagonally opposite sides of the inside of a transversal, form a z . Consecutive interior angles, on vertically or horizontally opposite sides of the inside of a transversal, form a c . Corresponding angles, on one side of a transversal (one inside, one outside), form a f . There are four theorems to prove lines parallel: If 2 lines are cut by a transversal, forming congruent alternate interior angles, then the lines are parallel. If 2 lines are cut by a transversal forming congruent corresponding angles, then the lines are parallel. If 2 lines are cut by a transversal, forming supplementary consecutive angles, then the lines are parallel. If two lines are cut by a transversal forming congruent alternate exterior angles, then the lines are parallel.

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