Question

given: abcd is a parallelogram and e is the midpoint of \\(\overline{bc}\\). prove: \\(\triangle fbe \cong \triangle dce\\). step statement reason 1 abcd is a parallelogram e is the midpoint of \\(\overline{bc}\\) given 2 \\(\overline{be} \cong \overline{ec}\\) a midpoint divides a segment into two congruent segments 3 \\(\angle dec \cong \angle feb\\) select a reason... note: df, af and bc are segments

Explanation:

Step1: Identify the angle relationship

$\angle DEC$ and $\angle FEB$ are vertical angles.

Step2: Recall the vertical angles theorem

Vertical angles are congruent. So the reason for $\angle DEC \cong \angle FEB$ is that vertical angles are congruent.

Answer:

Vertical angles are congruent