Given:
Line AD is congruent to Line BC
∠1 is congruent to ∠2
From the figure, we also have a common side AC.
Thus, we have:
Line AD = Line BC
ANgle 1 = Angle 2
Line AC = line AC
Since two sides and one angle of one triangle are equal to the corresponding two sides and one angle of the other triangle, the triangles are congruent by Side Angle Side (SAS) theorem.
The Side Angle Side (SAS) theorem states that if two sides and the included angle of a triangle are equal to two sides and the included angle of another triangle, both triangles are congruent.
Therefore, to justify that triangle ABC is congruent to triangle CDA, the theorem to use is Side-Angle-Side (SAS) thorem.
ANSWER:
SAS theorem.