Question

could δabc be congruent to δadc by sss? explain. yes, but only if ab ≅ dc. yes, but only if bc ≅ dc. no, because ab is not congruent to ac. no, because ab ≅ da.

Explanation:

Step1: Recall SSS Congruence Rule

SSS (Side - Side - Side) congruence rule 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 know that \(AC = AC\) (common side). Let's assume the markings: if \(AB\cong AD\) (given by the single tick marks on \(AB\) and \(AD\)). For SSS, we need \(BC\cong DC\).

Step2: Analyze Each Option

• Option 1: \(AB\cong DC\) is not relevant for the SSS congruence of \(\triangle ABC\) and \(\triangle ADC\) as the sides of the triangles are \(AB, BC, AC\) for \(\triangle ABC\) and \(AD, DC, AC\) for \(\triangle ADC\).
• Option 2: If \(BC\cong DC\), along with \(AB\cong AD\) (from the figure's tick - marks) and \(AC = AC\) (common side), then by SSS \(\triangle ABC\cong\triangle ADC\).
• Option 3: \(AB\) and \(AC\) are sides of \(\triangle ABC\), and their congruence (or lack thereof) is not related to the SSS congruence of \(\triangle ABC\) and \(\triangle ADC\).
• Option 4: \(AB\cong DA\) is given (from the figure's tick - marks), but this is not a reason for non - congruence. In fact, we need another pair of sides (\(BC\) and \(DC\)) for SSS.

Answer:

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