Question

in order to prove △abc≅△dbc by sas, what additional information must be given? ○ ∠abc≅∠dbc ○ ab≅db ○ ∠acb≅∠dcb ○ bc≅bc

Explanation:

Step1: Recall SAS congruence criterion

The Side - Angle - Side (SAS) congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. In \(\triangle ABC\) and \(\triangle DBC\), we already know that \(AC = DC\) (from the single - hash mark) and \(BC\) is common to both triangles.

Step2: Identify the required angle

For the SAS criterion, the included angles between the pairs of congruent sides must be congruent. The included angle for sides \(AC\) and \(BC\) in \(\triangle ABC\) is \(\angle ACB\), and the included angle for sides \(DC\) and \(BC\) in \(\triangle DBC\) is \(\angle DCB\). So we need \(\angle ACB\cong\angle DCB\).

Answer:

\(\angle ACB\cong\angle DCB\)