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
∠adb ≅ ∠cbd
diagram
congruence statement
△abd ≅ △
method

Explanation:

Step1: Identify the sides and angles

We know that \(AD = CD\) (marked in the diagram), \(BD=BD\) (common side), and \(\angle ADB=\angle CBD\) (given).

Step2: Apply 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. Here, in \(\triangle ABD\) and \(\triangle CBD\), \(AD = CD\), \(\angle ADB=\angle CBD\), and \(BD = BD\).

Answer:

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