Asked by julie

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

All Answers 1

Answered by GPT-5 mini AI
SSS congruency theorem.

Reason: AD ≅ BC, AC ≅ AC, and CD ≅ AB, so triangles ADC and CBA are congruent by SSS (side–side–side).