Given: AB ≅ CD and AD ≅ BC Prove: ABCD is a parallelogram. Quadrilateral A B C D is shown. A diagonal is drawn from point A to point C. Sides A B and D C are congruent. Sides A D and B C are congruent. Statements Reasons 1. AB ≅ CD;AD ≅ BC 1. given 2. AC ≅ AC 2. reflexive property 3. △ADC ≅ △CBA 3. ? 4. ∠DAC ≅ ∠BCA; ∠ACD ≅ ∠CAB 4. CPCTC 5. ∠DAC and ∠BCA are alt. Int. ∠s; ∠ACD and ∠CAB are alt. Int. ∠s 5. definition of alternate interior angles 6. AB ∥ CD; AD ∥ BC 6. converse of the alternate interior angles theorem 7. ABCD is a parallelogram 7. definition of parallelogram What is the missing reason in step 3? triangle angle sum theorem SAS congruency theorem SSS congruency theorem CPCTC