Given: ∠xma ≅ ∠dny prove: ∠amn ≅ ∠cny proof: it is given that ∠xma ≅ ∠dny. so, line ab is parallel to line cd by converse of the alternate exterior angles theorem. since lines ab and cd are parallel, ∠amn and ∠mnd are congruent by the alternate interior angles theorem. also, ∠mnd ≅ ∠cny by the consecutive interior angles theorem. therefore, ∠amn ≅ ∠cny by the transitive property of equality. identify the flaw in the proof and the appropriate correction. a. flaw: ∠amn ≅ ∠mnd by the alternate interior angles theorem. correction: ∠amn and ∠mnd by the consecutive interior angles theorem. b. flaw: ∠mnd ≅ ∠cny by the consecutive interior angles theorem. correction: ∠mnd ≅ ∠cny by the alternate interior angles theorem. c. flaw: ∠amn ≅ ∠mnd by the alternate interior angles theorem. correction: ∠amn and ∠mnd by the corresponding angles postulate. d. flaw: ∠mnd ≅ ∠cny by the consecutive interior angles theorem. correction: ∠mnd ≅ ∠cny by the vertical angles theorem.