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So, the converse statement will say that if the corresponding angles are formed when a transversal "t" cuts two lines "l" and "l'", the lines are parallel.1 answer  ·  Top answer: The theorem is if I and l' are parallel lines cut by a transversal t, the corresponding angles are congruent.The statement can be broken into the following . Yale Hoodie, What is the converse of the corresponding angles theorem?. The only way for corresponding angles to be congruent is for the lines to be parallel. The corresponding angles converse is also a postulate, which means it is . Essential Hoodie Pacsun, Theorem 3.8: Alternate Interior Angles Converse. PPTWho can name another pair for each of the angle types above? Postulates and Theorems of Parallel Lines. Postulate 15 Corresponding Angles Postulate. If two . Champion Cooler, What is the converse of the corresponding angles postulate?. The AIA Converse Theorem says that IF alternate interior angles are congruent, THEN the lines are parallel. 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