Final answer:
Using the given congruences of Line AD to Line CB and Line AB to Line CD, and applying the Side-Side-Side (SSS) Postulate, we can prove that triangles ABC and CDA are congruent.
Step-by-step explanation:
To prove that triangle ABC is congruent to triangle CDA, we can use the information provided:
- Line AD is congruent to Line CB.
- Line AB is congruent to Line CD.
Assuming that the triangles share the side AC (implied by the naming of the triangles), we now have three corresponding parts of the two triangles that are congruent:
- Side AD is congruent to side CB (Given).
- Side AB is congruent to side CD (Given).
- Side AC is congruent to itself by the Reflexive Property of Equality.
By the Side-Side-Side (SSS) Postulate, if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
Therefore, triangles ABC and CDA are congruent.