Final answer:
To prove △BAD ≅ △CDA, we identify the two triangles, use the given congruent sides and the common side AD to apply the Side-Side-Side (SSS) congruence postulate, concluding that the triangles are congruent.
Step-by-step explanation:
To prove that △BAD ≅ △CDA with the given information BD ≅ AC and BA ≅ DC, one can follow these steps:
Identify the two triangles in question: △BAD and △CDA.
Notice that the given information provides two pairs of congruent sides: BD ≅ AC (Given) and BA ≅ DC (Given).
Recognize that the side AD is common to both triangles, thus AD ≅ AD (Reflexive Property).
By Side-Side-Side (SSS) congruence postulate, if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
Combine the given congruences and the common side to apply the SSS postulate.
△BAD ≅ △CDA by SSS congruence postulate (Step 4).
Conclude that the two triangles are congruent based on the given information and the SSS postulate.