Question

given: \\( \overline{ab} \cong \overline{dc}, \overline{ab} \parallel \overline{dc} \\) prove: \\( \triangle abc \cong \triangle dcb \\) proof: statements reasons

Explanation:

Step1: Identify the included angle

Since \(AB\parallel DC\), then \(\angle ABC=\angle DCB\) (alternate - interior angles).

Step2: Use the SAS (Side - Angle - Side) congruence criterion

We are given \(AB = DC\) (from \(AB\cong DC\)), \(\angle ABC=\angle DCB\) (proven above), and \(BC = CB\) (common side).
By the SAS congruence criterion, \(\triangle ABC\cong\triangle DCB\).

Answer:

\(\triangle ABC\cong\triangle DCB\) by the SAS (Side - Angle - Side) congruence criterion.