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 for the statement \(AB\cong\) is \(CB\) and the reason is "Given".

Step2: Consider the common side

For triangles \(\triangle ABD\) and \(\triangle CBD\), \(BD = BD\) (reflexive property of congruence). So the third - row statement is \(BD\cong BD\) and the reason is "Reflexive Property".

Step3: Determine the congruent triangles

By the SSS (Side - Side - Side) congruence criterion (if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent), since \(AB\cong CB\), \(AD\cong DC\), and \(BD\cong BD\), \(\triangle ABD\cong\triangle CBD\)

Answer:

Statement	Reason
\(AD\cong DC\)	Given
\(BD\cong BD\)	Reflexive Property
\(\triangle ABD\cong\triangle CBD\)	SSS (\(AB\cong CB\), \(AD\cong DC\), \(BD\cong BD\))