Quadrilateral ABCD has diagonal AC , as shown below. Joanne knows that AB and CD are congruent and parallel. She claims that quadrilateral ABCD is a parallelogram. She writes the proof below to justify her claim. Statement Reason 1 AB⎯⎯⎯⎯⎯≅CD⎯⎯⎯⎯⎯⎯; AB⎯⎯⎯⎯⎯∥CD⎯⎯⎯⎯⎯⎯ Given 2 ∠BAC≅∠DCA Alternate interior angles are congruent 3 AC⎯⎯⎯⎯⎯≅AC⎯⎯⎯⎯⎯ Reflexive property 4 △BAC≅△DCA Side-angle-side (SAS) triangle congruence criterion 5 ∠BCA≅∠DAC Alternate interior angles are congruent 6 BC⎯⎯⎯⎯⎯∥DA⎯⎯⎯⎯⎯ If two lines are cut by a transversal and a pair of alternate interior angles is congruent, the lines are parallel. 7 ABCD is a parallelogram Definition of a parallelogram Joanne made a mistake in her proof. What was her mistake?
