Given lines l and m that are intersected by line t where m∠1 m∠2, the following is an indirect paragraph proof proving lines l and m are not parallel.

Assume lines l and m are parallel. According the Transitive Property of Equality, angle 1 is congruent to angle 2. Angle 1 is congruent to angle 3 by the Corresponding Angles Theorem. Angle 3 is congruent to angle 2 by the Vertical Angles Theorem. And, by the definition of congruence, m∠1 = m∠2. This contradicts the given statement that m∠1 m∠2. Therefore line l is not parallel to line m.

Question

Given lines l and m that are intersected by line t where m∠1 > m∠2, the following is an indirect paragraph proof proving lines l and m are not parallel.

Assume lines l and m are parallel. According the Transitive Property of Equality, angle 1 is congruent to angle 2. Angle 1 is congruent to angle 3 by the Corresponding Angles Theorem. Angle 3 is congruent to angle 2 by the Vertical Angles Theorem. And, by the definition of congruence, m∠1 = m∠2. This contradicts the given statement that m∠1 > m∠2. Therefore line l is not parallel to line m.