Question

prove \\( \triangle ace \\) is an isosceles triangle.

statements
\\( a b=e d, b c=d c, \angle a b c=\angle e d c \\)
\\( \triangle a b c=\triangle e d c \\)
reasons
given

Explanation:

Step1: Recall the SAS (Side - Angle - Side) congruence criterion

Two triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
In \(\triangle ABC\) and \(\triangle EDC\), we have \(AB = ED\) (given), \(BC = DC\) (given), and \(\angle ABC=\angle EDC\) (given). The angle \(\angle ABC\) is the included angle between \(AB\) and \(BC\) in \(\triangle ABC\), and \(\angle EDC\) is the included angle between \(ED\) and \(DC\) in \(\triangle EDC\).

Step2: Apply the SAS congruence criterion

Since \(AB = ED\), \(BC = DC\), and \(\angle ABC=\angle EDC\), by the SAS (Side - Angle - Side) congruence criterion, we can conclude that \(\triangle ABC\cong\triangle EDC\).

Answer:

SAS