Question

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Explanation:

Step1: Identify vertical angles

$\angle ACB=\angle ECD$ (Vertical Angles Congruence Theorem)

Step2: Use mid - point definition

Since \(C\) is the mid - point of \(AE\), \(AC = EC\). Since \(C\) is the mid - point of \(BD\), \(BC=DC\) (Definition of midpoint)

Step3: Apply SAS congruence

In \(\triangle ABC\) and \(\triangle EDC\), we have \(AC = EC\), \(\angle ACB=\angle ECD\), \(BC = DC\). By the Side - Angle - Side (SAS) congruence criterion, \(\triangle ABC\cong\triangle EDC\)

Answer:

1. \(\angle ACB=\angle ECD\)
2. \(AC = EC\), \(BC = DC\)
3. Side - Angle - Side (SAS) congruence criterion