Question

directions: use the figure and information to set create a formal proof. prove the triangles are congruent, given ( abcong cb ) and ( adcong dc )

Explanation:

Step1: Fill in the first blank

Given \(AB\cong CB\), so the first blank is \(CB\) and the reason is "Given".

Step2: Consider the common side

The side \(BD\) is common to both \(\triangle ABD\) and \(\triangle CBD\). So the third row statement is \(BD\cong BD\) and the reason is "Reflexive Property of Congruence".

Step3: Determine the congruent triangles

Since \(AB\cong CB\), \(AD\cong DC\), and \(BD\cong BD\), by the Side - Side - Side (SSS) congruence criterion, \(\triangle ABD\cong\triangle CBD\).

Answer:

Statement	Reason
\(AD\cong DC\)	Given
\(BD\cong BD\)	Reflexive Property of Congruence
\(\triangle ABD\cong\triangle CBD\)	SSS (Side - Side - Side)