Question

could $\triangle abc$ be congruent to $\triangle adc$ by sss? explain.
\bigcirc\\ yes, but only if $\overline{ab} \cong \overline{dc}$.
\bigcirc\\ yes, but only if $\overline{bc} \cong \overline{dc}$.
\bigcirc\\ no, because $\overline{ab}$ is not congruent to $\overline{ac}$.
\bigcirc\\ no, because $\overline{ab} \cong \overline{da}$.

Explanation:

Step1: Recall SSS Congruence Criterion

SSS (Side - Side - Side) congruence states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Step2: Analyze the Given Triangles \(\triangle ABC\) and \(\triangle ADC\)

We know that \(\overline{AB}\cong\overline{AD}\) (given by the marks on the sides in the figure) and \(\overline{AC}\cong\overline{AC}\) (common side). For \(\triangle ABC\cong\triangle ADC\) by SSS, we need the third pair of sides \(\overline{BC}\) and \(\overline{DC}\) to be congruent.
So, \(\triangle ABC\) could be congruent to \(\triangle ADC\) by SSS only if \(\overline{BC}\cong\overline{DC}\).

Answer:

Yes, but only if \(\overline{BC}\cong\overline{DC}\).