Question

given: abcd is a parallelogram. prove: \\(\overline{ab} \cong \overline{cd}\\) and \\(\overline{bc} \cong \overline{da}\\)
diagram of parallelogram abcd with vertices a, b, c, d
statements

1. abcd is a parallelogram

reasons

1. given

options to assemble next statement/reason: draw \\(\overline{ac}\\), \\(\angle dca\\) and \\(\angle bac\\) are alt. interior angles, abcd is a parallelogram, \\(\angle bca\\) and \\(\angle dac\\) are alt. interior angles, etc.
correct! assemble the next statement.

Explanation:

Step1: Recall parallelogram properties

In a parallelogram, opposite sides are parallel. To prove \( \overline{AB} \cong \overline{CD} \) and \( \overline{BC} \cong \overline{DA} \), we can use triangle congruence. The first step after stating the parallelogram is to draw the diagonal \( \overline{AC} \) to form two triangles (\( \triangle ABC \) and \( \triangle CDA \)).

Step2: Identify the next statement

From the options, the next statement after "ABCD is a parallelogram" (given) should be "draw \( \overline{AC} \)" as it is the necessary step to create triangles for congruence proof.

Answer:

draw \( \overline{AC} \)