Question

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

Explanation:

Step1: Recall SSS congruence criterion

For $\triangle ABC$ and $\triangle ADC$ to be congruent by SSS (Side - Side - Side), we need $AB\cong AD$, $BC\cong DC$ and $AC\cong AC$ (common side). We already know from the figure that $AB\cong AD$ (marked with one - dash) and $AC$ is common. We are missing the congruence of $BC$ and $DC$.

Step2: Determine the condition

The triangles $\triangle ABC$ and $\triangle ADC$ will be congruent by SSS if and only if $BC\cong DC$.

Answer:

Yes, but only if $\overline{BC}\cong\overline{DC}$