when two lines are cut by a transversal so that the corresponding angles are congruent, the the lines are parallel
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converse of the corresponding angles postulate
any two or more angles that equeal 90 degrees supplementary angles are when two or more angles equal 180 degrees
angles are congruent. That is sufficient to force the corresponding sides to be proportional - which is the other definition of similarity.
Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.
Always. If not, they are not called corresponding angles.