Question

move reasons to the table to prove that abcd is a parallelogram.

statement	reason
$angle1congangle4$
$overline{db}congoverline{db}$
$\triangle dabcong\triangle bcd$
$angle3congangle2$	corresponding parts of congruent triangles are congruent
$overline{ad}paralleloverline{bc}$	if alternate interior angles are congruent for two lines cut by a transversal, the lines are parallel.
abcd is a parallelogram	a parallelogram is a quadrilateral with opposite sides parallel.

asa sas sss
parallel postulate reflexive property
alternate interior angles theorem corresponding angles theorem

Explanation:

Step1: For $\angle1\cong\angle4$

By Alternate Interior Angles Theorem (since $AB\parallel CD$ and $DB$ is a transversal).

Step2: For $\overline{DB}\cong\overline{DB}$

By Reflexive Property (a segment is congruent to itself).

Step3: For $\triangle DAB\cong\triangle BCD$

Since $\overline{AB}\cong\overline{CD}$, $\angle1\cong\angle4$, $\overline{DB}\cong\overline{DB}$, by SAS (Side - Angle - Side) congruence criterion.

Answer:

Statement	Reason
$\angle1\cong\angle4$	Alternate Interior Angles Theorem
$\overline{DB}\cong\overline{DB}$	Reflexive Property
$\triangle DAB\cong\triangle BCD$	SAS
$\angle3\cong\angle2$	Corresponding Parts of Congruent Triangles are Congruent
$\overline{AD}\parallel\overline{BC}$	If alternate interior angles are congruent for two lines cut by a transversal, the lines are parallel.
$ABCD$ is a parallelogram	A parallelogram is a quadrilateral with opposite sides parallel.