Question

what is the missing reason in step 6?
statements

1. $overline{ad} \cong \overline{bc}$; $\overline{ad} \parallel \overline{bc}$
2. $\angle cad$ and $\angle acb$ are alternate interior $\angle$s
3. $\angle cad \cong \angle acb$
4. $\overline{ac} \cong \overline{ac}$
5. $\triangle cad \cong \triangle acb$
6. $overline{ab} \cong \overline{cd}$
7. $abcd$ is a parallelogram

reasons

1. given
2. definition of alternate interior angles
3. alternate interior angles are congruent
4. reflexive property
5. sas congruency theorem

6.?

1. parallelogram side theorem

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

Explanation:

Step 5 proves that $\triangle CAD \cong \triangle ACB$ using SAS congruence. Step 6 states $\overline{AB} \cong \overline{CD}$, which is a corresponding part of these two congruent triangles. CPCTC (Corresponding Parts of Congruent Triangles are Congruent) is the rule that justifies this conclusion.

Answer:

CPCTC