Question

en: abcd is a parallelogram, e is the midpoint of \\(\overline{ab}\\) and f is the midpoint of \\(\overline{dc}\\).
ve: \\(\overline{de} \cong \overline{fb}\\).
step\tstatement\treason
\tabcd is a parallelogram\t
1\te is the midpoint of \\(\overline{ab}\\)
f is the midpoint of \\(\overline{dc}\\)\tgiven
2\t\\(\overline{ad} \cong \overline{cb}\\)\topposite sides of a parallelogram / rhombus / rectangle / square are congruent
3\t\\(\overline{dc} \cong \overline{ab}\\)\topposite sides of a parallelogram / rhombus / rectangle / square are congruent
4\t\\(fc = \frac{1}{2}dc\\)\twhen a midpoint divides a segment into two parts, each part is half the length of the whole segment
5\t\\(ae = \frac{1}{2}ab\\)\twhen a midpoint divides a segment into two parts, each part is half the length of the whole segment
6\t\\(\overline{fc} \cong \overline{ae}\\)\tsegments that are half the lengths of congruent segments are congruent
7\t\\(\angle a \cong \angle c\\)\tselect a reason.

Explanation:

Step1: Recall properties of parallelograms

In a parallelogram, opposite angles are congruent. Since \(ABCD\) is a parallelogram, \(\angle A\) and \(\angle C\) are opposite angles.

Step2: Apply the property

By the property of parallelograms (opposite angles of a parallelogram are congruent), we can conclude that \(\angle A\cong\angle C\).

Answer:

Opposite angles of a parallelogram are congruent