Answer/Explanation:
Our main goal is to prove triangles DCA and triangle BCA are congruent, then by corresponding parts of congruent triangles are congruent say that those sides in the prove part are congruent.
Put any given down first,
Statement one: Segment BC is parallel to segment DA
Reason one: Given
Statement two: Angle BCA and angle DAC are congruent
Reason two: Alternate interior angles theorem
Now list the other given,
Statement three: Segment CD is parallel to segment AB
Reason three: Given
Statement four: Angle BAC and angle DCA are congruent
Reason four: Alternate interior angles theorem
List another thing you observe in the diagram to prove by the ASA postulate the triangles are congruent,
Statement five: Segment CA is congruent to segment CA
Reason five: Reflexive property of congruence
Statement six: Triangles DCA and BCA are congruent
Reason six: Angle - side - angle postulate
Statement seven: Segment AB is congruent to segment CD
Reason seven: CPCTC (look at underlined words with bold initials)