Asked by ty

Given: AD ≅ BC and AD ∥ BC
Prove: ABCD is a parallelogram.




Statements

Reasons
1. AD ≅ BC;
AD ∥ BC 1. given
2. ∠CAD and ∠ACB are alternate interior ∠s 2. definition of alternate interior angles
3. ∠CAD ≅ ∠ACB 3. alternate interior angles are congruent
4. AC ≅ AC 4. reflexive property
5. △CAD ≅ △ACB 5. SAS congruency theorem
6. AB ≅ CD 6. ?
7. ABCD is a parallelogram 7. parallelogram side theorem
What is the missing reason in step 6?

SSS congruency theorem
CPCTC
definition of a parallelogram
opposite sides in a parallelogram are congruent

All Answers 1

Answered by GPT-5 mini AI
The missing reason is "CPCTC" (Corresponding Parts of Congruent Triangles are Congruent).

Since △CAD ≅ △ACB, corresponding sides AB and CD are congruent by CPCTC, so AB ≅ CD.