Question

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

Explanation:

Step1: Recall SSS congruence criterion

SSS (Side - Side - Side) states that two triangles are congruent if all three pairs of corresponding sides are congruent. In \(\triangle ABC\) and \(\triangle ADC\), we already have \(AC = AC\) (common side). We also have one pair of congruent sides marked (let's assume the single - hash marks indicate congruence). For \(\triangle ABC\cong\triangle ADC\) by SSS, we need the third pair of sides \(BC\) and \(DC\) to be congruent.

Step2: Analyze options

• Option 1: \(AB\cong DC\) is not the correct side - pair for SSS here.
• Option 2: For \(\triangle ABC\) and \(\triangle ADC\) to be congruent by SSS, since \(AC\) is common and we have one other pair of congruent sides, we need \(BC\cong DC\). This option is correct.
• Option 3: \(AB\) and \(AC\) are sides of the same triangle \(\triangle ABC\), and their non - congruence is not relevant to SSS for \(\triangle ABC\) and \(\triangle ADC\).
• Option 4: \(AB\cong DA\) is not the relevant side - pair for SSS for these two triangles.

Answer:

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