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Sagot :

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]

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