Question

given
\\( \angle a d b \cong \angle c b d \\)
diagram
congruence statement
\\( \triangle a b d \cong \triangle \\)
method
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)?

Explanation:

Step1: Analyze the given information

We are given that \( \angle ADB\cong\angle CBD\), \(AD = BC\) (from the marks on the sides in the diagram), and \(BD=DB\) (common side).

Step2: Recall the SAS (Side - Angle - Side) postulate

The SAS postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
In \(\triangle ABD\) and \(\triangle CDB\), we have \(AD = BC\), \( \angle ADB\cong\angle CBD\), and \(BD = DB\).

Answer:

Congruence Statement: \(\triangle ABD\cong\triangle CDB\)
Method: \(SAS\) (Side - Angle - Side)