Question

complete the triangle congruence statement in order to prove the given statement.
what postulate or theorem would you use (sss, sas, hl, aas or asa)?
given
\\( \angle a \cong \angle d \\)
diagram
congruence statement
\\( \triangle abc \cong \triangle \\)
method

Explanation:

Step1: Identify corresponding parts

From the diagram, we have \( \angle A\cong\angle D\), \( \angle B\cong\angle E\) (implied by the congruent - like markings in the diagram), and \( AC = DC\) (from the equal - length markings).

Step2: Apply the AAS (Angle - Angle - Side) theorem

The AAS (Angle - Angle - Side) theorem states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent. Here, in \( \triangle ABC\) and \( \triangle DEC\), we have two pairs of congruent angles (\( \angle A\cong\angle D\) and \( \angle B\cong\angle E\)) and a pair of congruent non - included sides (\( AC = DC\)).

Answer:

Congruence Statement: \( \triangle ABC\cong\triangle DEC\)
Method: AAS (Angle - Angle - Side)