Question

Triangles ABC and DBC have side BC common, AB = BD and AC = CD. Are the two triangles congruent? State in symbolic form. Which congruence condition do you use? Does ∠ABD equal ∠ACD? Why or why not?

Answer 1

Yes.

$$\begin{gathered} \text{In ∆ABC and ∆DBC} \\ \text{AB=DB (Given)} \\ \text{AC=DC (Given)} \\ \text{BC=BC (Common)} \\ \text{By SSS criterion of congruency, ∆ABC≅∆DBC} \end{gathered}$$

No, $\text{∠ABD and∠ACD are not equal}$
because AB $\ne$ AC.