Triangle ABC is congruent to Triangle CDA by the ASA congruence criterion due to two pairs of parallel sides creating corresponding congruent angles and sides.
To prove that Triangle ABC ≅ Triangle CDA, given that AB || CD and BC || AD, we need to establish a congruence criteria for the triangles. Since AB is parallel to CD and BC is parallel to AD, by the converse of the Alternate Interior Angles Theorem, angle ABC is congruent to angle CDA, and angle BCA is congruent to angle DAC.
Additionally, BC being parallel to AD implies that side BC in triangle ABC is equal in length to side AD in triangle CDA because they are the same line segment between parallel lines (if extended). Consequently, we have two angles and the included side of Triangle ABC congruent to two angles and the included side of Triangle CDA, satisfying the ASA (Angle-Side-Angle) congruence criterion, thus proving the triangles congruent.
Final answer in 2 lines: Triangle ABC is congruent to Triangle CDA by the ASA congruence criterion as they have two congruent angles and a congruent side.