Question

Please all the statements and reasons

Answer 1

Statement 1.
`\angle BCA\cong\angle DAC.`

Reason 1. Alternate interior angles formed when two parallel lines are cut by a transversal are congruent.

Statement 2.
`\overline{AC}\cong\overline{AC}.`

Reason 2. Reflexive congruence of segments (a segment is congruent to itself).

Statement 3.
`\triangle ACD \cong\triangle CAB.`

Reason 3. SAS congruence (using our two congruences above and the given congruence).

Statement 4.
`\angle ACD=\angle CAB.`

Reason 4. Corresponding parts of congruent triangles are congruent.

Statement 5.
`\overline{AB}\parallel\overline{CD}.`

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.
`ABCD` is a parallelogram.

Reason 6. The quadrilateral satisfies the definition of a parallelogram: a quadrilateral where both pairs of opposite sides are parallel.