Question

given: abcd is a parallelogram and \\(\overline{ce} \cong \overline{fa}\\).
prove: fbed is a parallelogram.
step 1: statement: abcd is a parallelogram; \\(\overline{ce} \cong \overline{fa}\\) reason: given
step 2: statement: \\(\overline{bc} \cong \overline{ad}\\) reason: select a reason...

Explanation:

Step1: Recall Parallelogram Property

In a parallelogram, opposite sides are congruent. Since \(ABCD\) is a parallelogram (given), by the definition of a parallelogram (opposite sides of a parallelogram are congruent), we have \(\overline{BC} \cong \overline{AD}\).

Step2: Use Given Congruence

We know \(\overline{CE} \cong \overline{FA}\) (given). Now, we can show that \(FBED\) has opposite sides congruent. First, let's look at \( \overline{BE}\) and \( \overline{FD}\), and \( \overline{FB}\) and \( \overline{ED}\). But for step 2, the reason for \(\overline{BC} \cong \overline{AD}\) is that opposite sides of a parallelogram are congruent.

Answer:

The reason for \(\overline{BC} \cong \overline{AD}\) is "Opposite sides of a parallelogram are congruent".