We are given line segment AB is parallel to line segment DE Because the lines are parallel and segment CB crosses both lines, we can consider segment CB a transversal of the parallel lines. Angles CED and CBA are corresponding angles of transversal line segment CB and are therefore congruent, so angle CED is congruent to angle CBA We can state angle cap c is congruent to angle cap c using the reflexive property. Therefore, triangle ACB approximates triangle DCE by the
Since AB is parallel to DE and CB is a transversal, ∠CBA and ∠CED are corresponding angles, so they are congruent. The triangles also share the angle at C, so that angle is congruent to itself by the reflexive property. Two pairs of congruent angles establish triangle similarity by the AA similarity theorem, so the answer is AA similarity theorem.
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