Error Analysis What is the student's error?

The student's error is in the application of the Converse of the Corresponding Angles Theorem. The angles given (∠1 ≅ ∠2 and ∠1 ≅ ∠3) do not imply that lines a and b are parallel. The Corresponding Angles Theorem applies to angles formed by a transversal intersecting two parallel lines, but in this case, the angles are not corresponding angles that would prove the lines are parallel.