Given that ∠ABC = ∠DBC and ∠ACB = ∠DCB, show that ∠BAC = ∠BDC. Are the two triangles congruent?
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Answer
Let ∠ABC = a = ∠DBC and let ∠ACB = b = ∠DCB BC is a common side of the two triangles, then ∆ABC ≅ ∆DBC Angle Side Angle Congruence: When two triangles are congruent, their corresponding parts are equal [CPCT] Since ∆ABC ≅ ∆DBC, their corresponding angles are equal. Hence ∠BAC = ∠BDC
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