Question

what is the missing reason in step 6?
statements\treasons

1. \\(\overline{ad} \cong \overline{bc}\\); \\(\overline{ad} \parallel \overline{bc}\\)\t1. given
2. \\(\angle cad\\) and \\(\angle acb\\) are alternate interior \\(\angle\\)s\t2. definition of alternate interior angles
3. \\(\angle cad \cong \angle acb\\)\t3. alternate interior angles are congruent
4. \\(\overline{ac} \cong \overline{ac}\\)\t4. reflexive property
5. \\(\triangle cad \cong \triangle acb\\)\t5. sas congruency theorem
6. \\(\overline{ab} \cong \overline{cd}\\)\t6.?
7. abcd is a parallelogram\t7. parallelogram side theorem

options: sss congruency theorem, cpctc, definition of a parallelogram, opposite sides in a parallelogram are congruent

Explanation:

Step 5 proves $\triangle CAD \cong \triangle ACB$ using SAS. Step 6 states $\overline{AB} \cong \overline{CD}$, which is a pair of corresponding sides of the congruent triangles. Corresponding parts of congruent triangles are congruent (CPCTC) is the rule that justifies this.

Answer:

CPCTC