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Geometry Chapter 5 Section 4 Proofs Using Transitivity Terms: // Lines AIA Theorem If two parallel lines are cut by a transversal, then alternate interior angles are congruent. AIA // Lines Theorem If two lines are cut by a transversal and form congruent alternate interior angles, then the lines are parallel. Questions: 1) List the interior angles. 2) Construct a triangle that is equilateral.