Given: segment AB is parallel to segment CD, Angle ACB is congruent to angle CAD. Prove Triangle ABC is congruent to triangle CDA

Answer 1

I don't believe his is true. You can prove using the fact that parallel line have equal alternate interior angles that angles CAB,,ABC, ACB and CBA are congruent. So we congruent angles for these two triangles.

However, that means these triangles are similar (in shape) and not necessarily congruent.