Question

given ( abcong cd ) and ( bccong ad ). prove that ( \triangle abccong\triangle cda ).

Explanation:

Step1: Identify the sides

Given \(AB\cong CD\) and \(BC\cong AD\).

Step2: Identify the common side

\(AC\) is a common side to both \(\triangle ABC\) and \(\triangle CDA\), so \(AC\cong AC\) (Reflexive Property of Congruence).

Step3: Apply SSS (Side - Side - Side) Congruence Criterion

In \(\triangle ABC\) and \(\triangle CDA\), we have \(AB = CD\), \(BC = AD\), and \(AC=AC\). By the SSS congruence criterion, \(\triangle ABC\cong\triangle CDA\).

Answer:

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