"given that segment bd is congruent to segment ca and segment ab is congruent to segment dc, which theorem or postulate proves acd is congruent to dba? "

 SSS postulate and CPCTC will be used to prove ∠ ACD ≅ ∠ DBA.

Step-by-step explanation:

By joining the points A, C with points D and B respectively,

We get a quadrilateral ABCD in which AB ≅ CA ( given)

And, diagonal AC ≅ diagonal BD

In triangles ABD and ADC,

AB ≅ CA

AC ≅  BD

AD ≅ AD ( reflexive )

Thus, by SSS postulate,

Δ ABD ≅ Δ ADC

Thus, By CPCTC,

∠ ACD ≅ ∠ DBA

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step-by-step explanation:

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