Question

a. given: parallelogram abcd and (overline{ab}paralleloverline{cd}) verify that (\triangle abccong\triangle cda).

Explanation:

Step1: Properties of parallelogram

In parallelogram \(ABCD\), \(AB = CD\) (opposite sides of a parallelogram are equal) and \(AD=BC\) (opposite sides of a parallelogram are equal). Also, since \(AB\parallel CD\), \(\angle BAC=\angle DCA\) (alternate - interior angles).

Step2: Use SSS or SAS congruence criterion

We have \(AB = CD\), \(BC = AD\), and \(AC=CA\) (common side). By the SSS (Side - Side - Side) congruence criterion, \(\triangle ABC\cong\triangle CDA\).

Answer:

\(\triangle ABC\cong\triangle CDA\) by the SSS congruence criterion.