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Since:
[tex]\begin{gathered} AC\cong BC \\ \end{gathered}[/tex]We can conclude:
[tex]m\angle BAC\cong m\angle ABC[/tex]so:
Using triangle sum theorem:
[tex]\begin{gathered} m\angle BAC+m\angle ABC+m\angle ACB=180 \\ m\angle ACB=2m\angle ABC \\ m\angle ADC\cong m\angle BDC=\frac{m\angle ACB}{2} \end{gathered}[/tex]Therefore, if 2 angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent by Angle-Side-Angle (ASA):
[tex]\Delta ADC\cong\Delta BDC[/tex]