Question

given: abcd is a parallelogram, e is the midpoint of \\(\overline{ab}\\) and f is the midpoint of \\(\overline{dc}\\).
prove: \\(\overline{de} \cong \overline{fb}\\).

step\tstatement\treason
1\tabcd is a parallelogram
e 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}\\)\tselect a reason...

Explanation:

Step1: Recall parallelogram property

In a parallelogram, opposite sides are congruent. So for parallelogram \(ABCD\), \( \overline{DC} \) and \( \overline{AB} \) are opposite sides.

Step2: Determine the reason

The reason for \( \overline{DC} \cong \overline{AB} \) is the same as the reason for \( \overline{AD} \cong \overline{CB} \), which is "Opposite sides of a parallelogram / rhombus / rectangle / square are congruent".

Answer:

Opposite sides of a parallelogram / rhombus / rectangle / square are congruent