Question

I need help on a problem

Answer 1

Since:

`\begin{gathered} AC\cong BC \\ \end{gathered}`

We can conclude:

`m\angle BAC\cong m\angle ABC`

so:

Using triangle sum theorem:

`\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=(m\angle ACB)/(2) \end{gathered}`

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):

`\Delta ADC\cong\Delta BDC`