Question

step statement reason 1 ∠dbc ≅ ∠dcb given ab ≅ ac 2 db ≅ dc in a triangle, sides opposite of congruent angles are congruent 3 ad ≅ ad reflexive property 4 △abd ≅ △acd sss 5 ∠bad ≅ ∠cad corresponding parts of congruent triangles are congruent (cpctc) answer attempt 1 out of 3 the proof is incorrect and step number is the first unjustified step due to a missing prior step submit answer

Explanation:

Step1: Analyze the SSS (Side - Side - Side) congruence criterion

For \(\triangle ABD\) and \(\triangle ACD\) to be congruent by SSS, we need \(AB = AC\), \(BD=CD\), and \(AD = AD\). The problem is that the statement \(BD = CD\) (step 2) is justified by "In a triangle, sides opposite of congruent angles are congruent". But for this theorem (isosceles triangle theorem: if \(\angle DBC=\angle DCB\), then \(DB = DC\)), we need to be in \(\triangle DBC\). However, before using this theorem, we have no information about \(\triangle DBC\) in the given proof steps. The first step gives \(\angle DAB=\angle DCA\) (which is not related to \(\triangle DBC\) in a way that can directly apply the isosceles - triangle - side - opposite - angle theorem for \(DB\) and \(DC\)).

Answer:

The first unjustified step is step 2.