Question

given: \\(\overline{ar}\\) bisects \\(\angle bac\\); \\(ab = ac\\)\
which congruence theorem can be used to prove \\(\triangle abr \cong \triangle acr\\)?\
\\(\circ\\) aas\
\\(\circ\\) sss\
\\(\circ\\) asa\
\\(\circ\\) sas

Explanation:

Step1: Identify given congruent sides

Given $AB = AC$

Step2: Identify angle bisector property

Since $\overline{AR}$ bisects $\angle BAC$, $\angle BAR = \angle CAR$

Step3: Identify common side

$\overline{AR} = \overline{AR}$ (reflexive property)

Step4: Match to congruence rule

We have two sides and the included angle congruent, which fits SAS.

Answer:

SAS