Question

could \\( \triangle a b c \\) be congruent to \\( \triangle a d c \\) by sss? explain.
yes, but only if \\( \overline { a b } \cong \overline { d c } \\).
yes, but only if \\( \overline { b c } \cong \overline { d c } \\).
no, because \\( \overline { a b } \\) is not congruent to \\( \overline { a c } \\).
no, because \\( \overline { a b } \cong \overline { d a } \\).

Explanation:

Step1: Recall SSS congruence criterion

SSS (Side - Side - Side) congruence criterion states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. In \(\triangle ABC\) and \(\triangle ADC\), we already know that \(AC = AC\) (common side) and \(AB=AD\) (given by the tick marks).

Step2: Analyze the third - side requirement

For \(\triangle ABC\cong\triangle ADC\) by SSS, we need \(BC = DC\).

Answer:

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