If I am interpreting your question correctly, what you have is 2 triangles with a common side, namely AC.
If points B and D are on opposite sides of AC, you have ΔBAD and ΔBCD with one side common (BD) and the 2 angles enclosing that side equal, which makes those 2 triangles congruent by ASA.
If points B and D are on the same side of AC, the 2 triangles are still congruent although you have the additional step of using the supplementary angles to prove ASA.
BTW: your English grammar needs improvement too: sentences begin with a capital letter and end with a period.
