To solve the problem (assuming it's about proving △ABC ≅ △DCB given AB=DC and AC=DB), here's the step-by-step proof:
Given:
AB = DC, AC = DB
To Prove:
△ABC ≅ △DCB
Proof:
- AB = DC (Given)
- AC = DB (Given)
- BC = CB (Reflexive property of equality: a side is equal to itself)
By the SSS (Side-Side-Side) Congruence Criterion, if three corresponding sides of two triangles are equal, the triangles are congruent.
Thus, △ABC ≅ △DCB.
Answer: △ABC ≅ △DCB by SSS congruence. (Or if the question asks for the reason, it's SSS.)
If the problem had a different goal (e.g., proving ∠A=∠D), after congruence, we use CPCTC (Corresponding Parts of Congruent Triangles are Congruent) to conclude ∠A=∠D.
Final Answer:
The triangles are congruent by SSS. (Or as per the exact question, e.g., if it's a fill-in-the-blank, the reason is "SSS".)
\boxed{SSS} (if the answer expects the congruence criterion) or \boxed{△ABC ≅ △DCB} (if it expects the congruent triangles).
Assuming the question asks for the congruence reason, the answer is \boxed{SSS}.
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