Statement 1. [tex]\angle BCA\cong\angle DAC.[/tex]
Reason 1. Alternate interior angles formed when two parallel lines are cut by a transversal are congruent.
Statement 2. [tex]\overline{AC}\cong\overline{AC}.[/tex]
Reason 2. Reflexive congruence of segments (a segment is congruent to itself).
Statement 3. [tex]\triangle ACD \cong\triangle CAB.[/tex]
Reason 3. SAS congruence (using our two congruences above and the given congruence).
Statement 4. [tex]\angle ACD=\angle CAB.[/tex]
Reason 4. Corresponding parts of congruent triangles are congruent.
Statement 5. [tex]\overline{AB}\parallel\overline{CD}.[/tex]
Reason 5. If the alternate interior angles formed when two lines are cut by a transversal are congruent, then the lines are parallel.
Statement 6. [tex]ABCD[/tex] is a parallelogram.
Reason 6. The quadrilateral satisfies the definition of a parallelogram: a quadrilateral where both pairs of opposite sides are parallel.
